#  @beardmeetscalculus Beard Meets Calculus Beard Meets Calculus posts on YouTube about vimeo, link, intro, spring the most. They currently have [------] followers and [---] posts still getting attention that total [-----] engagements in the last [--] hours. ### Engagements: [-----] [#](/creator/youtube::UC2VuCzJx_9luS0y-WDfL3Tg/interactions)  - [--] Week [-----] +32% - [--] Month [-----] +2,995% - [--] Months [------] +121% - [--] Year [------] +152% ### Mentions: [--] [#](/creator/youtube::UC2VuCzJx_9luS0y-WDfL3Tg/posts_active)  - [--] Month [--] +125% - [--] Months [---] +176% - [--] Year [---] +220% ### Followers: [------] [#](/creator/youtube::UC2VuCzJx_9luS0y-WDfL3Tg/followers)  - [--] Week [------] no change - [--] Month [------] +1.40% - [--] Months [------] +12% - [--] Year [------] +20% ### CreatorRank: [---------] [#](/creator/youtube::UC2VuCzJx_9luS0y-WDfL3Tg/influencer_rank)  ### Social Influence **Social category influence** [social networks](/list/social-networks) [countries](/list/countries) [finance](/list/finance) **Social topic influence** [vimeo](/topic/vimeo) #44, [link](/topic/link), [intro](/topic/intro), [spring](/topic/spring), [eq](/topic/eq), [walk](/topic/walk), [math](/topic/math), [to the](/topic/to-the), [for the](/topic/for-the), [integration](/topic/integration) **Top assets mentioned** [Integral (ITGR)](/topic/integral) ### Top Social Posts Top posts by engagements in the last [--] hours "Practice for Exam [--] = Cumulative final (Finite math; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1145133680 A walkthrough of a practice exam for the fourth exam dealing with the topics of the semester with emphasis on the last part (sets probabilities data). These problems are slight variations of the posted practice exam. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.businessmath.org/ Presenter: Steve Butler" [YouTube Link](https://youtube.com/watch?v=TSWFKJNfP-g) 2025-12-10T05:36Z 15.1K followers, [----] engagements "Spring-Mass-Damper systems (Diff. Eq.; Lecture 1-12; Spring 2026) Vimeo (ad-free) link to same video: https://vimeo.com/1165430203 * Spring-mass-damper systems --- example of application of differential equations tied to oscillation / vibration For more information: https://www.calc4.org/spring-2026 Presenter: Steve Butler (https://www.stevebutler.org/) differential equations differential equations" [YouTube Link](https://youtube.com/watch?v=lxL81dmwKLQ) 2026-02-16T18:01Z 15.1K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Fall 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1164897402 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:50 1-Distance from point to plane 4:27 2-Volume of shape given by inequalities 9:16 3-Area of triangle given three points 14:03 4-Spherical to rectangular coordinates 16:48 5-Using information about acceleration velocity and curvature 21:52 6-Identify quadric surface from formula 25:46 7-Find line" [YouTube Link](https://youtube.com/watch?v=y4szcOjrw2E) 2026-02-14T03:50Z 15.1K followers, [---] engagements "Partial fractions (Calc 2; Lecture 17; Spring 25) * Discuss partial fractions (or how I learned to stop worrying and embrace rational functions) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=-1X9hjF9MzY) 2025-03-05T01:40Z 12.7K followers, [---] engagements "Continuity (Calc 1; Lecture 4; Fall 24) An introduction to continuity (what should happen is what actually happens). Lecture given in-class on Wednesday September [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=-B5LCun1iZM) 2024-09-04T22:10Z 11.4K followers, [---] engagements "Applications for Taylor series (Part 1) (Calc 2; Lecture 36; Spring 25) * Applications for Taylor series ** Finding particular derivative ** Finding Taylor polynomial ** Finding Taylor series for rational function For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=-Et2-3NmMs0) 2025-05-05T16:45Z 13.2K followers, [---] engagements "L'Hospital's Rule (Calc 1; Lecture 23; Fall 24) We discuss one of the most popular ways for students to do limits namely by the use of L'Hospital's rule. (The funner way of dealing with indeterminates.) Lecture recorded in class on Monday October [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=-GWNdefL2Ms) 2024-10-29T00:06Z 14.1K followers, [---] engagements "Diff Eq Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1123060879 A walk-through of the solutions for Exam [--] of Differential Equations administered in Spring [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:34 1-Solve ODE using substitution (homogeneous) 10:10 2-Exact ODE 19:02 3-Autonomous ODE 29:03 4-Compute Wronskian; find ODE given solution 42:49 5-Find general solution to nonhomogeneous ODE 52:00 6-Spring-mass-dashpot solution" [YouTube Link](https://youtube.com/watch?v=-SlyC0Hz3is) 2025-09-30T01:49Z 14.1K followers, [---] engagements "Volume by shell method (Calc 2; Lecture 2; Spring 25) * Use of the shell method * Comparing/contrasting with washer method For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=09e6pIUTe_A) 2025-01-24T17:15Z 12.2K followers, [---] engagements "Lines and planes (Calc 3; Lecture 6; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1116906033 We discuss our flat objects namely lines and planes. How to represent them with formulas and how to find the distance to them. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=0fmAMg3i4Kw) 2025-09-08T20:49Z 13.8K followers, [---] engagements "Differentiability; tangent plane; chain rule (Calc 3; Lecture 2-3; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1123700853 * Differentiability = locally flat (a bit more than just having partial derivatives) * Tangent planes = local approximation * Implicit differentiation For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=1S4wTckS1js) 2025-10-01T20:49Z 14.1K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1127919023 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:52 1-Implicit differentiation 4:35 2-Critical points 6:44 3-Derivative with chain rule 10:16 4-Use linearization to approximate 14:34 5-Derivative with natural log 18:21 6-Find/classify extrema 23:29 7-Logarithmic differentiation 29:17 8-Related rates (holey problem) 37:35" [YouTube Link](https://youtube.com/watch?v=1b7Y2TVYV-U) 2025-10-16T15:43Z 14.2K followers, [---] engagements "Mean Value Theorem (Calc 1; Lecture 25; Fall 24) We discuss the Mean Value Theorem which states that if we have a "nice" function then at some point in time the instantaneous rate of change has to match the average rate of change. Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=1narRWHF6Ns) 2024-11-01T22:46Z 11.4K followers, [--] engagements "Practice for Exam [--] = Algebra and lines (Finite math; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1118374731 A walkthrough of a practice exam for the first exam dealing with the topics of algebra and lines. These problems are slight variations of the posted practice exam. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.businessmath.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-This is only a practice test" [YouTube Link](https://youtube.com/watch?v=2xqRfX13rkw) 2025-09-13T16:31Z 13.8K followers, [---] engagements "Exponential functions (Finite math; Lecture 13; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1121571518 * Exponential functions * Cumulative interest (both discrete and continuous) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=3WRHIjwg-bE) 2025-09-24T15:39Z 14K followers, [--] engagements "Practice 1-B problems for Calculus [--] (Fall 2025) --- Dot and cross product Vimeo (ad-free) link to same video: https://vimeo.com/1115845155 A set of problems that cover material from the second week of the first block for Calculus [--] (e.g. dot and cross products). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:40 1-Find value so that projection works 7:18 2-Find values to make vectors perpendicular 12:55 3-Find the area of a triangle 24:30 4-Find unit vector perpendicular to two vectors" [YouTube Link](https://youtube.com/watch?v=3j1thUq1ZCw) 2025-09-05T21:00Z 13.7K followers, [---] engagements "Rational exponents (Finite math; Lecture 05; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1116184704 * Working with rational exponents Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=43frfwoBBo0) 2025-09-05T20:58Z 13.7K followers, [--] engagements "Taylor polynomials + Taylor polynomial lower bound (Calc 2; Lecture 33; Spring 25) * Taylor polynomial (="best" polynomial to locally approximate the function) * Taylor polynomial error bound (How good is our estimate Pretty good) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=4FQV5kjZA5w) 2025-04-23T16:22Z 13K followers, [---] engagements "Parametric curves; tangents (Calc 3; Lecture 8; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1118229960 We introduce parametric curves and talk calculus (work term-by-term). We also do tangent lines to parametric curves. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=6IXu5Yzl-xU) 2025-09-12T20:42Z 13.8K followers, [---] engagements "(DiffEQ Fall 23) Exam [--] review - ODE systems Course site: http://calc4.org Instructor: Steve Butler (http://stevebutler.org) 0:00:00 Intro 0:01:26 [--] -- Mixing problem with tanks 0:15:20 [--] -- Elimination method 0:25:11 [--] -- x'=A(t)x; verify solution; Wronskian 0:40:22 [--] -- General form for system (distinct eigenvalues) 0:51:38 [--] -- Initial value problem (repeated eigenvalues) 1:05:28 [--] -- Initial value problem (complex eigenvalues) 1:16:38 [--] -- eAt for distinct eigenvalues 1:24:20 [--] -- Undetermined coefficients 1:41:00 [--] -- Variation of parameters" [YouTube Link](https://youtube.com/watch?v=6YKpn6ckJOs) 2023-10-23T02:52Z [----] followers, [---] engagements "Changing order of integration (Calc 3; Lecture 22; Fall 24) Vimeo (ad-free) link to same video: https://vimeo.com/1021901132 We discuss the strategy involved for changing the order of integration over non-rectangular regions. Lecture recorded in class on Monday October [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=71dH8F8OGSE) 2024-10-21T22:13Z 14.1K followers, [---] engagements "Integration in cylindrical and spherical coordinates (Calc 3; Lecture 26; Fall 24) We discuss integration in cylindrical and spherical coordinates. Lecture recorded in class on Monday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=76WxGDOhXNk) 2024-11-04T23:16Z 11.5K followers, [--] engagements "Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:53 1-Integration by parts 8:48 2-Trigonometric integrals 19:45 3-Partial fractions 32:30 4-Numerical integration (Trapezoid and Simpson's) 40:28 5-Improper integral 49:38 6-Application (volume + trig substitution)" [YouTube Link](https://youtube.com/watch?v=80pAzu-xp5Y) 2025-03-23T16:06Z 12.7K followers, [---] engagements "Tangent lines and length for parameterized curves (Calc 2; Lecture 8; Spring 25) * More practice working with parameterized curves. * First and second derivatives for parameterized curves. * Length (=distance traveled) for parameterized curves. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=8EdMXe1CgjY) 2025-02-07T16:16Z 12.4K followers, [---] engagements "Week [--] review problems for Calculus [--] (Spring 2025) --- Mass moments parameterized curves A set of problems that cover material from the third week of Calculus [--] (e.g. using integration to find mass center of mass and parameterized curves (tangent lines second derivatives applications)). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:52 1-Find where parametric curve hits a given line 6:09 2-Plot a parameterized curve 13:06 3-Length of parametric curve 19:26 4-Find density given center of" [YouTube Link](https://youtube.com/watch?v=8FQf8-7XY40) 2025-02-08T18:42Z 12.4K followers, [----] engagements "Mass and Center of Mass (Calc 2; Lecture 6; Spring 25) * Finding Mass and Center of Mass for both 1D and 2D regions. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=8lGzwOzCvFo) 2025-02-03T16:56Z 12.4K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:36 1-Find absolute minimum 7:09 2-Derivative of inverse 10:14 3-Logarithmic differentiation 14:04 4-Derivative of arctan 16:20 5-Linearization of a cube root 22:12 6-Critical points of a function 26:26 7-Implicit differentiation 33:33 8-Related rates (extend the boom) 45:06 9-Find constants given function properties 51:05 10-Optimization (maximize volume of can)" [YouTube Link](https://youtube.com/watch?v=8q2-nycOzD8) 2025-03-23T02:30Z 12.7K followers, [---] engagements "Example in Calc [--] class on March [--] [----] (day before Exam 2) For more information visit: https://www.calc2.org Presented by Steve Butler: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=99ecSMo1TVE) 2025-03-26T18:44Z 12.8K followers, [---] engagements "Comparison tests for series (Calc 2; Lecture 27; Spring 25) * Comparison test * Limit comparison test For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=9YGeWmQAZ-0) 2025-04-09T15:25Z 12.9K followers, [---] engagements "Building a LEGO dodecahedron This goes through the steps of making a dodecahedron out of LEGO. This uses the following pieces: [--] of the 3-Branch Cross Axle (57585) [--] of the Angle Element [---] Degree (42156)" [YouTube Link](https://youtube.com/watch?v=9rVK8f1nuZA) 2024-12-24T20:40Z 13.4K followers, [----] engagements "(Spectral; Fall 23) [--] - Matrix Tree Theorem Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ We continue the discussion of the Laplacian matrix by talking about the Matrix Tree Theorem (one of the most well-known results related to eigenvalues of the Laplacian)" [YouTube Link](https://youtube.com/watch?v=AcVPX2JOM1U) 2023-10-16T23:09Z 11.5K followers, [---] engagements "(DiffEQ Fall 23) [--] - Population models We do a short-ish review of the major techniques of solving first-order differential equations. We then move to talking about population models with particular discussion about the exponential and logistic models. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/ 0:00 Review of ways to solve first-order ODEs 9:22 Introduction to population models 13:08 Solution to the exponential model 19:39 Example (exponential model) 27:15 Introduction to logistic model 29:19 Solution to the logistic model 44:27 Example" [YouTube Link](https://youtube.com/watch?v=BiNNxKiWulM) 2023-09-06T02:33Z 11.5K followers, [----] engagements "Cross product of vectors (Calc 3; Lecture 5; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1116281043 We discuss the cross product which can be used to form perpendicular vectors as well as compute area of parallelograms and triangles as well as volumes of parallelepipeds. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=Bzi8WkSTIto) 2025-09-05T20:59Z 13.7K followers, [---] engagements "Numbers (Finite math; Lecture 01; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1112935912 * Overview of the course and advice * Different types of numbers (natural integers rational irrational real) * Rules for addition and multiplication of numbers Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=CkDoAdXPNzA) 2025-08-25T15:47Z 13.5K followers, [---] engagements "Practice 1-C problems for Calculus [--] (Fall 2025) --- Lines planes quadric surfaces parametric Vimeo (ad-free) link to same video: https://vimeo.com/1118422531 A set of problems that cover material from the third week of the first block for Calculus [--] (e.g. Lines planes quadric surfaces parametric). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:36 1-Finding location of a coasting spaceship 9:58 2-cos(theta) for intersecting parametric curves 21:43 3-Find the plane equidistant between two" [YouTube Link](https://youtube.com/watch?v=DBzFUttkN1Q) 2025-09-13T23:36Z 14.1K followers, [----] engagements "Implicit differentiation; gradient; directional derivative (Calc 3; Lecture 2-4; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1124333128 * Implicit differentiation * Gradient (analog of the derivative) * Directional derivatives For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=DCUify5FijM) 2025-10-03T20:50Z 14.1K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Logarithmic differentiation 4:04 2-Tangent line to implicit curve 9:50 3-Linear approximation 15:51 4-Related rates (ohms) 24:07 5-Increasing/decreasing and classifying 33:43 6-Maximizing area of garden" [YouTube Link](https://youtube.com/watch?v=Dh3GEXTDOnQ) 2024-10-16T12:35Z 11.2K followers, [---] engagements "Line integrals (the easy way) (Calc 3; Lecture 31; Fall 24) We look at conservative functions and show that doing line integrals with conservative functions is easy(-ish). Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=ECZ8vQ_JHPY) 2024-11-15T22:56Z 11.6K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2025) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:45 1-Vertical tangent line 3:25 2-Set up volume of revolution 9:04 3-Setting up surface area in polar curve 14:52 4-Given an integral for length find f(x) 19:13 5-Find polar graph from among choices 24:05 6-Find moment of triangle region 29:25 7-Set up volume by shell method 38:04 8-Surface area for parametric curve 50:33 9-Find work to pump out of a tank" [YouTube Link](https://youtube.com/watch?v=Eq5l8UMxnU8) 2025-03-02T19:53Z 12.6K followers, [---] engagements "Line integrals (the hard way) (Calc 3; Lecture 30; Fall 24) We introduce line integrals and how to compute them. We also go over a discussion of how to compute work along a curve with varying force. Lecture recorded in class on Wednesday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=Ery7XN_GjgU) 2024-11-13T22:48Z 11.6K followers, [---] engagements "Walkthrough of solutions to practice exam [--] (Calc 1; Fall 2024) The one where we walk through the solutions of practice Exam [--] from Fall [----] Calc [--] (aka single variable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc1.org 0:00 1-Implicit function; increasing/decreasing; concavity 4:48 2-Derivative of inverse function 9:06 3-Second derivative test 13:23 4-Logarithmic differentiation 18:46 5-Linearization 22:45 6-Absolute max/min procedure 29:07 7-Increasing/decreasing; concavity 35:55 8-Linearization 38:40 9-Related rates 44:24 10-Frosting" [YouTube Link](https://youtube.com/watch?v=EsQU8KqG-a0) 2024-10-23T21:51Z 14.1K followers, [---] engagements "Quadratic functions (Finite math; Lecture 11; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1120174029 * Quadratic functions Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=FM5TTpcJbQo) 2025-09-19T15:20Z 13.9K followers, [--] engagements "Decomposing acceleration and curvature (Calc 3; Lecture 11; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1120282075 We look at the problem of decomposing acceleration into a part that lies in the direction of motion (the part of acceleration speeding you up or slowing you down) and a part that lies perpendicular to motion (the part of acceleration pulling you to the side). We also connect this to curvature which tries to answer the age-old question of how "bendy" a curve is. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler" [YouTube Link](https://youtube.com/watch?v=FNBYcRs9t6g) 2025-09-19T20:47Z 13.9K followers, [---] engagements "Work and force problems (Calc 2; Lecture 5; Spring 25) * Finding work and force by splitting things into parts; finding the contribution of each part; adding up to get the total For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=FQsbIjR9GC0) 2025-01-31T15:45Z 12.3K followers, [---] engagements "2025 Ice bucket challenge w/ Steve Butler #SpeakYourMIND [----] Ice bucket challenge w/ Steve Butler #SpeakYourMIND" [YouTube Link](https://youtube.com/watch?v=Fpsa-VMLvI8) 2025-04-23T23:47Z 13K followers, [----] engagements "Week [--] review problems for Calculus [--] (Spring 2025) --- Applications of integration: volume A set of problems that cover material from the first week of Calculus [--] (e.g. using integration to find volumes). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:26 1-Volume by cross section; isosceles right triangle 15:34 2-Volume by cross section (Cavalieri's Principle) 22:01 3-Volume by washer method 28:49 4-Volume by washer method (handling tan4(x)) 42:54 5-Volume by shell method 50:05 6-Volume" [YouTube Link](https://youtube.com/watch?v=GpGjpPICMcs) 2025-01-25T19:06Z 12.2K followers, [---] engagements "Interval of convergence for power series (Calc 2; Lecture 31; Spring 25) * Finding interval of convergence for power series (root/ratio tests followed by checking endpoints) * Rewriting geometric sum as rational function For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=HDe6aS1hUgw) 2025-04-18T15:41Z 13.2K followers, [---] engagements "Solutions to practice exam 3-A (Calc 1; Fall 2024) The one where we walk through the solutions of practice Exam 3-A from Fall [----] Calc [--] (aka basic class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc1.org Problems and scanned solutions can be found in the website https://www.calc1.org by going to the Fall [--] page and scrolling down to Week fourteen. 0:00 Intro 0:29 1-Recursion for Newton's Method 5:01 2-Riemann sum 11:07 3-Fundamental Theorem of Calculus 15:13 4-Average value of function 22:12 5-Using linearity of integrals 30:27 6-Find" [YouTube Link](https://youtube.com/watch?v=HhlmfXzTTFE) 2024-11-28T18:54Z 11.8K followers, [---] engagements "Rational functions (Finite math; Lecture 12; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1120873519 * Rational functions Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=IvKOAD5uKb4) 2025-09-22T15:25Z 13.9K followers, [--] engagements "Week [--] review problems for Calculus [--] (Spring 2025) --- Alternating series/Interval of convergence A set of problems that cover material from the twelfth week of Calculus [--] (e.g. alternating series and interval of convergence). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:26 1-Apply alternating series test 4:18 2-Absolute vs Conditional vs Diverge 8:14 3-Error bound for alternating series test 14:52 4-Rewrite geometric series as rational function 22:29 5-Radius of convergence (ratio" [YouTube Link](https://youtube.com/watch?v=JMiO8j4nnIg) 2025-04-19T16:53Z 13K followers, [----] engagements "Integration in polar coordinates (Calc 3; Lecture 23; Fall 24) Vimeo (ad-free) link to same video: https://vimeo.com/1022501447 We discuss integration in polar coordinates and how to approach integrations in general. Lecture (pre-)recorded for class on Monday October [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=KXQa8bypHk0) 2024-10-29T00:04Z 14.1K followers, [---] engagements "Triple integrals changing order of integration (Calc 3; Lecture 24; Fall 24) Vimeo (ad-free) link to same video: https://vimeo.com/1024917451 We discuss triple integrals and also how to go about changing the order of integration.Lecture recorded in class on Wednesday October [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=Kawny4wMsGs) 2024-10-30T22:48Z 14.1K followers, [---] engagements "Alternating series test (Calc 2; Lecture 29; Spring 25) * Alternating series test (terms alternate + decrease to [--] implies converge) * Bound for alternating series (=next term) * Absolute and conditional convergence For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=LDg0aToxSpQ) 2025-04-14T15:17Z 12.9K followers, [---] engagements "Vector fields; curl; div (Calc 3; Lecture 29; Fall 24) Introduction to vector fields and a discussion of the del operator including gradient (grad) divergence (div) and curl (curl). Lecture recorded in class on Monday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=LQ1ACn6fiA0) 2024-11-11T23:23Z 11.6K followers, [---] engagements "Week [--] review problems for Calculus [--] (Fall 2024) A set of problems that cover material from the twelfth week of Calculus [--] (e.g. curl divergence gradient line integrals and conservative line integrals). For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Find divergence of a vector field 3:58 2-Find curl of a vector field 13:26 3-Find mass of a wire 20:44 4-Set parameters to make a gradient field 27:39 5-Line integral (non-conservative) 33:28 6-Work along a curve (non-conservative) 42:02 7-Line integral (conservative) 51:47 8-Line" [YouTube Link](https://youtube.com/watch?v=M9HO0SJef60) 2024-11-17T15:55Z 11.7K followers, [---] engagements "Introduction to the Jacobian (Calc 3; Lecture 27; Fall 24) We discuss the Jacobian and more generally how to change coordinate systems. Lecture recorded in class on Wednesday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=MSPoR8P_eSE) 2024-11-06T23:11Z 11.5K followers, [---] engagements "Arc length (=distance) (Calc 3; Lecture 10; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1119580003 We look at the problem of finding the distance a particle travels. This can be found by integrating speed (r'(t)). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=NqQM6BAtXd8) 2025-09-17T20:42Z 13.9K followers, [---] engagements "Practice 2-B problems for Calculus [--] (Fall 2025) -- Taylor polynomials and friends Vimeo (ad-free) link to same video: https://vimeo.com/1126504892 A set of problems that cover material from the second week of the second block for Calculus [--] (e.g. properties of the gradient Taylor polynomials finding and classifying critical points). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:34 1-Getting partial derivatives from Taylor polynomial 6:52 2-Third order Taylor polynomial 31:29 3-Find" [YouTube Link](https://youtube.com/watch?v=NwCRxRWQGus) 2025-10-11T22:25Z 14.2K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1128072611 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:50 1-Identify correct substitution for trigonometric integral 3:18 2-Carry out a trig substitution 7:40 3-Partial fraction decomposition 11:50 4-Convergence for improper integral 16:10 5-Integration by parts 22:50 6-Simpson's rule (numerical integration) 27:10 7-Integration by parts (done twice" [YouTube Link](https://youtube.com/watch?v=OoDqqA0a6YQ) 2025-10-17T02:33Z 14.2K followers, [---] engagements "Functions (Finite math; Lecture 9; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1118778964 * Functions * Domain and range of functions * Graphing; vertical line test * Combining functions together Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=Ov_T5C33Q5s) 2025-09-15T15:19Z 13.8K followers, [--] engagements "Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1127734834 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:49 1-Find mixed partial derivative 3:04 2-Chain rule 10:17 3-Find directional derivative 15:24 4-Graph domain of function 19:48 5-Implicit differentiation 25:50 6-Properties of the gradient 34:03 7-Second order Taylor polynomial 49:21 8-Lagrange multiplier problem 1:01:20 9-Find and classify" [YouTube Link](https://youtube.com/watch?v=PCxI0JprTow) 2025-10-16T03:04Z 14.2K followers, [---] engagements "Motion; osculating planes; antiderivatives (Calc 3; Lecture 9; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1118895271 We continue parametric curves by framing them in terms of position velocity and acceleration. We also look at the osculating plane (which uses all of the information). And finally talk anti-derivatives which work entry-by-entry. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=PND8GZ9C7sQ) 2025-09-15T21:56Z 13.8K followers, [---] engagements "Riemann sums and area (Calc 1; Lecture 29; Fall 24) We use Riemann sum along with geometry to calculate some areas. Something suspicious seems to be emerging. Lecture recorded in class on Monday November [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=PqKdP7meCQs) 2024-11-11T23:24Z 11.6K followers, [---] engagements "Arc length for the case y=f(x) (Calc 2; Lecture 3; Spring 25) * More practice with volume * Arc length for the case y=f(x) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=Q9_fQI2345c) 2025-01-27T16:19Z 12.4K followers, [---] engagements "Surface area of revolution (Calc 2; Lecture 4; Spring 25) * Surface area from revolving around an axis For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=QfLYbNQw3fg) 2025-01-29T16:44Z 12.5K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Change 2D order of integration and integrate 4:41 2-Find potential function; conservative line integral 14:20 3-Green's Theorem 20:41 4-Convert integral to spherical coordinates 31:42 5-Surface integral; Mass 41:30 6-Change of variables/coordinates" [YouTube Link](https://youtube.com/watch?v=QmCZdNRbS5E) 2024-11-25T18:20Z 11.8K followers, [---] engagements "Taylor polynomials (Calc 3; Lecture 2-6; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1125701426 * Linear approximation = Tangent plane * Taylor polynomials * Quadratic form (for the theory) For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=QoUiKDprbGs) 2025-10-08T23:14Z 14.2K followers, [---] engagements "Quadratic equtions (Finite math; Lecture 06; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1116809782 * Solving quadratic equations by factoring and/or using the quadratic formula Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=RaNOgUIjecg) 2025-09-08T15:22Z 13.8K followers, [--] engagements "Critical points; Second partials test (Calc 3; Lecture 2-7; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1126316931 * Critical points * Second partials test for classifying critical points For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=S6ZCm_4uO1U) 2025-10-10T21:35Z 14.2K followers, [---] engagements "Cartesian coordinates; distance (Calc 3; Lecture 1; Fall 24) An introduction to 3D geometry using Cartesian coordinates and distance. Lecture recorded in studio on Tuesday August [--] [----]. (Unfortunately markers were forgotten so not recorded in-class.) For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=SYSZ7UIRmvY) 2024-08-27T12:59Z 11.4K followers, [---] engagements "Transformation of functions (Finite math; Lecture 10; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1119474321 * Basic functions * Transformations * Piecewise functions Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=Sg-PgC-tbWk) 2025-09-17T15:16Z 13.9K followers, [--] engagements "Surface integrals (Calc 3; Lecture 34; Fall 24) We look at surface integrals finishing up with computing flux through a surface. Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=Si5mh6PkC6s) 2024-11-22T23:07Z 11.8K followers, [---] engagements "Practice 1-A problems for Calculus [--] (Fall 2025) --- Coordinate systems and vectors Vimeo (ad-free) link to same video: https://vimeo.com/1114085772 A set of problems that cover material from the first week of the first block for Calculus [--] (e.g. coordinate systems and vectors). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:40 1-Make three points collinear 9:24 2-Rewrite plane using spherical coordinates 15:43 3-Minimum distance between spheres 27:10 4-Identify sphere in spherical" [YouTube Link](https://youtube.com/watch?v=SqWYHGeRRCE) 2025-08-29T21:00Z 13.6K followers, [---] engagements "Quadric surfaces (Calc 3; Lecture 7; Fall 24) A review of doing things with lines and planes; then a speed run through quadric surfaces). Lecture recorded in class on Wednesday September [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=TUrzL-qMwvM) 2024-09-11T21:55Z 10.6K followers, [---] engagements "Absolute max and min (Calc 3; Lecture 2-8; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1126965781 * Absolute max and min for continuous function on a closed and bounded domain For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=V-eXm6ShcMM) 2025-10-13T20:37Z 14.2K followers, [---] engagements "Everything looks like a polynomial; sequences (Calc 2; Lecture 23; Spring 25) * Introduction to the third part of the course where we think that everything looks like a polynomial (=nice). Woohoo * Start down the road to making (almost) everything into polynomial by talking about sequences. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=VkXnW39bq58) 2025-03-31T15:39Z 12.8K followers, [---] engagements "Numerical integration including Trapezoid Rule and Simpson's Rule (Calc 2; Lecture 19; Spring 25) * Numerical integration including Trapezoid Rule and Simpson's Rule For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=W-hDC3JAZLY) 2025-03-10T16:02Z 12.7K followers, [---] engagements "Simple interest (Finite math; Lecture 15; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1122902088 * Simple interest Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=WIq0S23VZjw) 2025-09-29T15:37Z 14.1K followers, [--] engagements "Area between curves (Calc 1; Lecture 34; Fall 24) We look at how to use definite integrals to find the area between curves. Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=WbAlgyc2Ivc) 2024-11-22T23:08Z 11.8K followers, [---] engagements "Solutions to practice exam 3-B (Calc 3; Fall 2024) The one where we walk through the solutions of practice Exam 3-B from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org Problems and scanned solutions can be found in the website https://www.calc3.org by going to the Fall [--] page and scrolling down to Week fourteen. 0:00 Intro 0:29 1-2D change order of integration 4:49 2-Integral for surface area 8:38 3-Change cylindrical to spherical 23:48 4-Compute Jacobian 31:35 5-Compute divergence 34:51 6-Set up" [YouTube Link](https://youtube.com/watch?v=X51txq5SQrM) 2024-11-29T18:23Z 11.9K followers, [---] engagements "Integral test; p-series (Calc 2; Lecture 26; Spring 25) * Integral test * p-series For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=Y2Jrrl59z9Y) 2025-04-07T16:01Z 12.9K followers, [---] engagements "Diff Eq Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Differential Equations administered in Fall [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:31 1-Setting up system of equations 10:24 2-Take second order equation to first-order system 16:46 3-Take first-order system to second order equation 23:06 4-Use matrix exponential (repeated roots) 30:12 5-Verify solutions; Wronskian 38:01 6-Compute matrix exponential (distinct roots)" [YouTube Link](https://youtube.com/watch?v=YJIDJ7yE-vU) 2025-04-01T14:12Z 12.8K followers, [---] engagements "Cartesian coordinates; distance; spheres (Calc 3; Lecture 1; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1113028021 An introduction to 3D geometry using Cartesian coordinates distance and spheres. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=YjxSJYnLJLU) 2025-08-25T20:52Z 13.5K followers, [---] engagements "Week [--] review problems for Calculus [--] (Fall 2024) A set of problems that cover material from the eleventh week of Calculus [--] (e.g. integration in spherical/cylindrical coordinates and changing variables). For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Find mass (cylindrical coordinates) 5:59 2-Set up volume integral (spherical coordinates) 16:30 3-Find new bounding curves (substitution) 24:06 4-Find center of mass (cylindrical coordinates) 39:51 5-Find volume (spherical coordinates) 48:34 6-Inertia (cylindrical coordinates) 58:54" [YouTube Link](https://youtube.com/watch?v=ZLNtcdL2_i4) 2024-11-10T15:03Z 11.6K followers, [----] engagements "Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:51 1-Volume over region 3:46 2-Change order of integration 7:57 3-Convert integral from Cartesian to polar 10:47 4-Identify bounds for triple integral 16:15 5-Compute divergence 19:20 6-Compute flux through surface 24:57 7-Find center of mass of cone 39:52 8-Do a change of variable (Jacobian) 55:29 9-Find potential / Fundamental Theorem of Line Integrals 1:06:12" [YouTube Link](https://youtube.com/watch?v=ZlymT_C6HtY) 2025-04-29T03:47Z 13.1K followers, [---] engagements "DiffEQ Exam [--] walkthrough (Fall 2023) A walk-through of the solutions for Exam [--] of Differential Equations administered in Fall [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:31 [--] -- First order ODE 7:50 [--] -- Exact ODE 14:38 [--] -- Autonomous ODE 20:07 [--] -- Properties of ODEs (Wronskian superposition .) 28:38 [--] -- Spring-mass-damper system 38:17 [--] -- Nonhomogeneous ODE (undetermined coefficients)" [YouTube Link](https://youtube.com/watch?v=Zx3zNO7S7bw) 2023-10-03T16:38Z 11.5K followers, [---] engagements "(Spectral; Fall 23) [--] - How graph labeling naturally connects with distance matrices Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ We continue the discussion on distance matrices and the graph labeling problem and show how these are naturally connected to one another" [YouTube Link](https://youtube.com/watch?v=aG5Dxyc9Xrg) 2023-12-05T06:00Z 11.5K followers, [--] engagements "Week [--] review problems for Calculus [--] (Fall 2024) A set of problems that cover material from the thirteenth week of Calculus [--] (e.g. substitution rule; area between curves). For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Find area between two curves 11:45 2-Find area under curve + substitution 20:34 3-Find antiderivative + substitution 25:53 4-Find area between two curves (w.r.t y) 40:45 5-Set up integrals to find area (w.r.t x and y) 51:41 6-Find antiderivative + trig substitution 1:00:14 7-Definite integral + substitution (arctan)" [YouTube Link](https://youtube.com/watch?v=aOoHJNuOKhM) 2024-11-25T04:58Z 11.8K followers, [---] engagements "Linear equations (Finite math; Lecture 7; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1117485972 * Solving linear equations Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=agqS7hCEiv8) 2025-09-10T15:31Z 13.8K followers, [--] engagements "Week [--] review problems for Calculus [--] (Fall 2024) A set of problems that cover material from the eighth week of Calculus [--] (e.g. properties of the first/second derivative and optimization). For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Introduction 0:37 1-Using f' to find/classify critical points; concavity 18:14 2-Find and classify critical points 26:31 3-Find where function is increasing/decreasing 36:33 4-Finding c; finding inflection points 44:50 5-Optimizing fencing next to a barn 51:54 6-Find where function is" [YouTube Link](https://youtube.com/watch?v=anIBY-XFkgI) 2024-10-17T22:00Z 11.2K followers, [---] engagements "Annuities part [--] (Finite math; Lecture 18; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1125570887 * Annuities (finding the value of many payments over time) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=ar_IpbqBHFg) 2025-10-08T15:28Z 14.2K followers, [--] engagements "Graphing linear equations (Finite math; Lecture 8; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1118144225 Audio did not record properly so using backup audio track. Sorry * Word problems * Graphing lines * Different forms for lines Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=bFqAZSpnT6A) 2025-09-12T15:09Z 13.8K followers, [--] engagements "Math [---] Fall [----] Practice Exam 1-1 Presenter: Steve Butler (http://stevebutler.org) Course website: http://calc4.org 0:00 Introduction 1:22 Problem [--] -- radioactive decay 8:06 Problem [--] -- linear first-order 15:11 Problem [--] -- homogeneous ODE 31:15 Problem [--] --- find/classify critical points for autonomous ODE 36:36 Problem [--] -- constant coefficient linear homogeneous ODE 40:08 Problem [--] -- spring-mass system" [YouTube Link](https://youtube.com/watch?v=baam1B-vJV8) 2021-09-28T05:21Z 13.3K followers, [----] engagements "Series (both geometric and telescoping); nth term test; harmonic sum (Calc 2; Lecture 25; Spring 25) * More practice with geometric series * Telescoping series (where the terms cancel leading to collapse) * N-th term test (if terms don't go to [--] then sum diverges) * Harmonic series For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=bzX3SfmFouQ) 2025-04-04T14:45Z 12.9K followers, [---] engagements "Walkthrough of solutions to practice exam [--] (Calc 3; Fall 2024) Vimeo (ad-free) link to same video: https://vimeo.com/1022678528 The one where we walk through the solutions of practice Exam [--] from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org 0:00 1-Give domain of function 2:48 2-Direction of greatest decrease 5:59 3-Implicit differentiation (mixed partial) 14:56 4-Linear approximation 18:15 5-Tangent plane to implicit surface 23:39 6-Directional derivative 26:16 7-Second order Taylor polynomial" [YouTube Link](https://youtube.com/watch?v=cAI02fnGQv8) 2024-10-23T21:45Z 14.1K followers, [----] engagements "Multivariable functions (Calc 3; Lecture 2-1; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1120970874 We talk about multivariable functions including finding/sketching domain and level curves/surfaces For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=cIvJEhNrVaw) 2025-09-22T20:45Z 13.9K followers, [---] engagements "Practice for Exam [--] = Sequences and series (Calc 2; Spring 25) A walkthrough of a practice exam for the sequences and series exam. These problems highlight a variety of ideas. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:45 1-Find term in sequence using recurrence 7:02 2-Find sum of telescoping series 15:04 3-Error bound for integral test 19:50 4-Interval of" [YouTube Link](https://youtube.com/watch?v=cP8u0qQJRqw) 2025-04-27T20:44Z 13.1K followers, [---] engagements "Compound interest (Finite math; Lecture 16; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1123597974 * Compound interest (both discrete and continuous) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=cfiYuHfzm78) 2025-10-01T15:22Z 14.1K followers, [--] engagements "Dot product of vectors (Calc 3; Lecture 4; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1115629306 We discuss the dot product which can be used to compute the angle between vectors test orthogonality and carry out projection. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=cipZC-kk_ZE) 2025-09-03T21:14Z 13.7K followers, [---] engagements "(Spectral; Fall 23) [--] - Properties of Laplacian including joins Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ We continue the discussion of the Laplacian matrix including complements join and the introduction of the signed incidence matrix" [YouTube Link](https://youtube.com/watch?v=cwp10WyEcqc) 2023-10-12T22:46Z 13.4K followers, [---] engagements "Logarithmic functions (Finite math; Lecture 14; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1122269921 * Inverse functions * Logarithmic functions Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=d2NA3_9Ngdo) 2025-09-26T16:44Z 14K followers, [--] engagements "(DiffEQ Fall 23) [--] - Matrix exponentials In this lecture we introduce the fundamental matrix see how it connects to matrix exponentials and how to use this to find solutions. We also look at what happens in the 2x2 case for repeated eigenvectors giving an alternative to what was done in the previous lecture. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/ 0:00 Introduction to idea of matrix exponentials 4:49 Fundamental matrices; exponential matrix 14:39 Example (fundamental matrix) 27:08 Computing matrix exponential as series 29:44 Example" [YouTube Link](https://youtube.com/watch?v=dLNLOHVIb20) 2023-10-15T15:09Z [----] followers, [---] engagements "Polar Cylindrical and Spherical coordinates (Calc 3; Lecture 2; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1113707001 We discuss other coordinate systems which use combinations of distances and directions (=angles). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=fN9kP6Eb7uw) 2025-08-27T20:52Z 13.6K followers, [---] engagements "Diff Eq Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Differential Equations administered in Fall [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:23 1-Linear first-order + separable 7:46 2-General solution to nonhomogeneous 15:45 3-Exact ODE 19:57 4-First order substitution 24:39 5-Autonomous ODE 30:54 6-Wronskian" [YouTube Link](https://youtube.com/watch?v=g-Oa2O0HTYk) 2025-02-27T14:57Z 12.6K followers, [---] engagements "Vectors (Calc 3; Lecture 3; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1114370452 We discuss vectors including geometric and component approaches; adding and scaling; magnitude and direction (=unit vector); and midpoints. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=gCI241UVGG4) 2025-08-29T20:59Z 13.6K followers, [---] engagements "Sequences; (geometric) series (Calc 2; Lecture 24; Spring 25) * Finish talking about sequences and finding the limit of a_n * Start talking about series and finding infinite sums by looking at the limit of partial sums. We then turn to finding the value of geometric series (=(first term)/(1-(multiplying factor))). For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=gNAZRLPDk-I) 2025-04-02T15:32Z 12.9K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:07 1-Find term in sequence from recurrence 3:13 2-Find limit of sequence 5:00 3-Find limit of sequence from recurrence 7:10 4-Determine which series converge 10:44 5-Determine convergence type for series 13:26 6-Taylor polynomial question 18:03 7-Sum of telescoping series 26:43 8-Apply integral test 33:44 9-Interval of convergence 43:23 10-Error bound for Taylor" [YouTube Link](https://youtube.com/watch?v=h7R3s1wveq0) 2025-04-27T17:53Z 13.1K followers, [---] engagements "Applications of parameterized curves and introduction to polar (Calc 2; Lecture 9; Spring 25) * We go through some applications of parameterized curves (e.g. surface area mass area). * Introduction to polar coordinates. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=hQYUOlDnonI) 2025-02-10T16:21Z 12.4K followers, [---] engagements "More practice with center of mass; start of parameterized curves (Calc 2; Lecture 7; Spring 25) * More practice related to mass and center of mass. * Introduction of parameterized curves. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=j5l7rbYK9_I) 2025-02-05T16:29Z 12.4K followers, [---] engagements "Practice for Exam [--] = Techniques of integration (Calc 2; Spring 25) A walkthrough of a practice exam for the techniques of integration exam. These problems highlight a variety of ideas. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 3:41 1-Integration by parts (loop back) 18:21 1-Integration by parts -- alternate solution 24:43 2-Power reduction for trig 32:23 3-Identify" [YouTube Link](https://youtube.com/watch?v=jSGUpFi1Q24) 2025-03-16T20:48Z 12.7K followers, [---] engagements "Polynomials (Finite math; Lecture 02; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1113608508 * What are polynomials * How to add and multiply polynomials Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=jcBsfnC0t9o) 2025-08-27T15:19Z 13.6K followers, [--] engagements "Stokes' Theorem (Calc 3; Lecture 35; Fall 24) We start looking at Stokes' Theorem; a generalization of Green's Theorem to exciting 3D. Lecture recorded in class on Monday December [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=k0FkUQsacHg) 2024-12-02T23:04Z 11.9K followers, [---] engagements "Working in polar and graphing (Calc 2; Lecture 10; Spring 25) * We work through examples of how to change equations between cartesian and polar. * Introduction to graphing in polar (hint: connect the dots of interesting points). For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=kF2Sf6mdbsg) 2025-02-12T17:36Z 12.4K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Newton's Method to find intersections 5:02 2-Area between two curves 10:08 3-L'Hospital to find limits 19:29 4-Use initial conditions to find antiderivative 24:27 5-Fundamental Theorem of Calculus 29:20 6-Riemann sums" [YouTube Link](https://youtube.com/watch?v=kkDmxeLQ0vI) 2024-11-25T18:25Z 11.8K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:31 1-Ratio and root tests 8:19 2-Direct and limit comparison tests 18:36 3-Integral test 25:34 4-Interval of convergence 34:41 5-Telescoping sums 41:13 6-Taylor polynomial + error bound" [YouTube Link](https://youtube.com/watch?v=lXxjT9Nq8tg) 2025-04-27T16:13Z 13.1K followers, [---] engagements "Week [--] review problems for Calculus [--] (Spring 2025) --- Convergence test for series A set of problems that cover material from the eleventh week of Calculus [--] (e.g. convergence tests including integral test direct comparison test limit comparison test root test and ratio test). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:45 1-Apply Direct Comparison Test 8:54 2-Apply Limit Comparison Test (get rid of noise) 18:50 3-Set C for Ratio Test convergence 25:07 4-Apply Ratio Test 38:37" [YouTube Link](https://youtube.com/watch?v=laJtLxjZ7DI) 2025-04-12T23:05Z 13.2K followers, [----] engagements "Calculus [--] Session [--] -- Absolute (global) max/min Course site: http://math265.org Instructor: Steve Butler (http://mathbutler.org)" [YouTube Link](https://youtube.com/watch?v=lv-AJBRS8uU) 2019-10-18T16:45Z 11.4K followers, [----] engagements "Separable differential equations (Calc 1; Lecture 35; Fall 24) We look at separable differential equations; these can be solved by "separate; integrate; uncomplicate". Lecture recorded in class on Monday December [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=m8061IoYoz4) 2024-12-02T23:06Z 11.9K followers, [---] engagements "Optimization; round [--] (Calc 1; Lecture 22; Fall 24) Second day of doing optimization (blending of word problems with max and min). Lecture recorded in class on Monday October [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=mJh8NbRyG2k) 2024-10-21T22:14Z 14.1K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:47 1-Take a second-order partial derivative 3:36 2-Chain rule 10:25 3-Identify contour map 12:44 4-Find a second-order Taylor polynomial 17:16 5-Find a critical point 20:04 6-Implicit differentiation 26:45 7-Gradient directional derivative gradient properties 34:33 8-Tangent plane (=linear approximation) to level surface 42:35 9-Find and classify all critical" [YouTube Link](https://youtube.com/watch?v=maxxOIK4u4Q) 2025-03-23T02:26Z 12.7K followers, [---] engagements "Applications for Taylor series (Part 2) (Calc 2; Lecture 37; Spring 25) * Applications for Taylor series ** Finding some sums ** Integration For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=nAbiMAilGCg) 2025-05-07T16:06Z 13.2K followers, [---] engagements "Derivative as a function (Calc 1; Lecture 7; Fall 24) An introduction to derivatives as a function and the ever important using the limit definition to take derivatives. Lecture recorded in class on Wednesday September [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=nD3YA_LBLgA) 2024-09-11T22:02Z 11.4K followers, [---] engagements "Ratio and root tests for series (Calc 2; Lecture 28; Spring 25) * Ratio test = limit of a_(n+1)/a_n * Root test = limit of a_n(1/n) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=nNGAELfrRxY) 2025-04-11T16:36Z 12.9K followers, [--] engagements "Calculus with power series (Calc 2; Lecture 32; Spring 25) * More practice with interval of convergence * Calculus of power series (work term-by-term) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=ny_7cQSzeRg) 2025-04-21T15:41Z 13K followers, [---] engagements "Practice and review of trig substitution and partial fractions (Calc 2; Lecture 18; Spring 25) * Practice and review of trig substitution and partial fractions For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=oTjtca4Ry98) 2025-03-07T16:11Z 12.7K followers, [---] engagements "Quadric surfaces (Calc 3; Lecture 7; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1117592701 We go through some strategies of how to work with lines and/or planes. We (briefly) also go through the quadric surfaces. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=onbBjDAfsEA) 2025-09-10T21:22Z 13.8K followers, [---] engagements "(DiffEQ Fall 23) Review of ODE Systems We sprint through the material covering ODE systems. This is meant to be a brief discussion of the main ideas and so does not go into much detail. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/" [YouTube Link](https://youtube.com/watch?v=pHXTHAKy05o) 2023-10-23T15:14Z 11.4K followers, [---] engagements "Rational expressions (Finite math; Lecture 04; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1115526418 * Working with rational expressions; a wonderful blending of fractions and polynomials. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=peILRKLkFFk) 2025-09-03T15:22Z 13.7K followers, [--] engagements "Integration involving trigonometry and applications (Calc 2; Lecture 15; Spring 25) * Finish with integration involving trigonometry * Brief discussion with applications For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=qQ8fv01_GyQ) 2025-02-28T17:10Z 12.6K followers, [---] engagements "Week [--] review problems for Calculus [--] (Spring 2025) --- Length surface area work force A set of problems that cover material from the second week of Calculus [--] (e.g. using integration to find length surface area work and force). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:56 1-Set up integral for surface area (two directions) 11:44 2-Work problem for a spring 18:55 3-Work lifting person up to a chopper 30:38 4-Force on window in an aquarium 39:12 5-Find perimeter around region 48:16" [YouTube Link](https://youtube.com/watch?v=qb0zlQJUhrQ) 2025-02-01T01:02Z 12.4K followers, [----] engagements "Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1120453169 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:52 1-Describe region given by inequalities 3:54 2-Find direction vector of intersection of planes 8:22 3-Orthogonality of two vectors 10:22 4-Using decomposition of acceleration 12:26 5-Scaling vector to right length 15:05 6-Find formula for volume of sphere 19:40 7-Find volume given in" [YouTube Link](https://youtube.com/watch?v=qrwioOr2ons) 2025-09-20T17:47Z 13.9K followers, [---] engagements "(Physics) applications of integration (Calc 3; Lecture 25; Fall 24) We discuss applications of integration with a particular eye on physics. Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=qwP2y_Rse6k) 2024-11-01T22:44Z 11.4K followers, [---] engagements "Factoring (Finite math; Lecture 03; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1114369142 * Facoring (or at least one possible approach to factoring) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=s-4Kj5NyPms) 2025-08-29T20:58Z 13.6K followers, [--] engagements "(Spectral; Fall 23) [--] - Adjacency matrix as walk counting matrix; Perron-Frobenius Theorem Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ In this video we work through how to use the adjacency matrix to count walks how the adjacency matrix can detect properties including bipartiteness number of edges number of triangles and odd girth. We also have a brief discussion about Perron-Frobenius. 0:00 Similarity argument for bipartite graphs 6:58 Counting walks 19:28 Applications of counting walks 29:51 Bipartite and symmetry of eigenvalues 34:35 Odd" [YouTube Link](https://youtube.com/watch?v=trQRxsGIbF0) 2023-09-06T20:50Z 11.4K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:03 1-Newton's Method 3:45 2-Riemann sum (midpoint) 7:27 3-Using sum notation 12:33 4-Mean Value Theorem for derivatives 17:00 5-u-substitution (indefinite) 21:11 6-u-substitution (definite) 26:02 7-Indeterminate limits 34:13 8-Indefinite integrals 39:27 9-Area between curves 50:48 10-Integrals as area; Fundamental Theorem of Calculus" [YouTube Link](https://youtube.com/watch?v=u69KR8zmutc) 2025-04-29T00:41Z 13.1K followers, [---] engagements "Diff Eq Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Differential Equations administered in Fall [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:58 1-Laplace and inverse Laplace transforms 7:22 2-Use Laplace transform to solve diff. eq. 16:10 3-Laplace of piecewise function 23:34 4-Diff. eq. with delta function 30:05 5-Recurrence relationship for series solution 41:53 6-Find first few coefficients for series solution" [YouTube Link](https://youtube.com/watch?v=uTbnh-fQ6ME) 2025-04-29T14:26Z 13.1K followers, [---] engagements "Taylor series (Calc 2; Lecture 34; Spring 25) * Taylor series For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=uYWq3ImUvMA) 2025-04-25T15:47Z 13K followers, [---] engagements "(DiffEQ Fall 23) [--] - Spring-Mass-Damper systems We discuss spring-mass-damper systems which have the generic form of mx'''+cx'+kx=0 where m is mass c is damping constant and k is spring constant. We also talk about the different types of behavior that can occur e.g. undamped under damped critically damped and over damped. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/ 0:00 Setup of spring-mass-damper systems 5:38 Example (spring-mass-damper system) 17:49 Types of behavior for damping 26:29 Example (critical damping)" [YouTube Link](https://youtube.com/watch?v=ursDOrJCHnE) 2023-09-16T22:24Z 11.4K followers, [----] engagements "Week [--] review problems for Calculus [--] (Spring 2025) --- Integration by parts and trig integrals A set of problems that cover material from the sixth week of Calculus [--] (e.g. using integration by parts trig integrals and applications involving these techniques). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:11 1-By parts with log (and surprise arctan) 10:56 2-By parts w/ unknown function 18:26 3-Integral of sin3 25:18 4-Integral with secants and tangents 33:24 5-Reduction formula 39:23" [YouTube Link](https://youtube.com/watch?v=vn9dMnCEvF4) 2025-03-02T07:34Z 12.6K followers, [----] engagements "Solutions to practice exam [--] (Calc 3; Fall 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1121185836 The one where we walk through the solutions of practice Exam [--] from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org 0:00 Intro 0:33 1-Identify solid from inequalities 7:13 2-Find angle between rays in spherical coordinates 17:44 3-Distance between a point and a line 26:25 4-Identify quadric surface 30:13 5-Find tangent line not intersecting a plane 39:11 6-Find distance a particle" [YouTube Link](https://youtube.com/watch?v=vqe_bOEKJPc) 2025-09-24T20:00Z 14K followers, [---] engagements "Annuities part [--] (Finite math; Lecture 18; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1124877369 * Annuities (finding the value of many payments over time) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=vqwOLO8oSXg) 2025-10-06T15:23Z 14.1K followers, [--] engagements "Solutions to practice exam 3-A (Calc 3; Fall 2024) The one where we walk through the solutions of practice Exam 3-A from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org Problems and scanned solutions can be found in the website https://www.calc3.org by going to the Fall [--] page and scrolling down to Week fourteen. 0:00 Intro 0:29 1-2D change order of integration 10:40 2-Identify 3D region of integration 17:27 3-Find curl 22:22 4-Identify conservative vector function 32:01 5-Line integral" [YouTube Link](https://youtube.com/watch?v=wdQ1fqCIQVI) 2024-11-28T01:18Z 11.8K followers, [---] engagements "Practice with convergence tests (Calc 2; Lecture 30; Spring 25) * Review and practice with tests for convergence For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=xZSlfzsfC6o) 2025-04-16T15:27Z 12.9K followers, [---] engagements "Examples in Calc [--] class on April [--] [----] (day before Exam 3) For more information visit: https://www.calc2.org Presented by Steve Butler: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=xu_KNQu8ThM) 2025-04-30T15:41Z 13.1K followers, [---] engagements "Augmented matrices (Finite math; Lecture 21; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1127556008 * Introduced matrices particularly augmented matrices and how they can relate to systems of equations. * Translate manipulation of systems of equations to row operations. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=yfBRJg74c9c) 2025-10-15T15:15Z 14.2K followers, [--] engagements "Partial derivatives (Calc 3; Lecture 2-2; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1123002745 We talk about importance of simplifying for a few minutes. We then get into the main topic of the day which is partial derivatives including notation and higher order derivatives. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=yzNDFkYRjPg) 2025-09-29T21:01Z 14.1K followers, [---] engagements "Applications for Taylor series (Part 3) (Calc 2; Lecture 38; Spring 25) * Applications for Taylor series ** Finding indeterminates For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=zjp0RAwy3CE) 2025-05-09T15:15Z 13.2K followers, [---] engagements "Linear inequalities (Finite math; Lecture 28; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1133177159 * Introduction to linear inequalities. * Bit of practice with word problems. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=-rYKxXgxIYM) 2025-11-03T16:15Z 14.4K followers, [--] engagements "Comments made in Calc [--] class on February [--] [----] (day before Exam 1) For more information visit: https://www.calc2.org Presented by Steve Butler: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=10Qy1qlQ7G8) 2025-02-19T16:26Z 12.5K followers, [---] engagements "Matrix inverse; Identity matrix (Finite math; Lecture 25; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1130945068 * Identity matrix acting like "1" in multiplication of matrices. * Matrix inverses. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=1m6EWKHcodI) 2025-10-27T15:16Z 14.4K followers, [--] engagements "Integration in polar coordinates (Calc 3; Lecture 3-3; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1131070677 * Integrating in polar coordinates; including (re)writing integrals in polar coordinates. * The three parts to every integral problem. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=1zscYUuerDI) 2025-10-27T20:40Z 14.4K followers, [---] engagements "Conditional probability and independence (Finite math; Lecture 37; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1143134866 * Conditional probability * Probability trees * Independence Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=2fYV_jWiG38) 2025-12-03T16:23Z 15.1K followers, [---] engagements "(Spectral; Fall 23) [--] - A few more comments about Laplacian; introduction to signless Laplacian Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ We give a few additional comments about the Laplacian matrix including why is the product of the nonzero eigenvalues an integer why do we call it the Laplacian what is spectral partitioning and spectral graph drawing. We then introduce the signless Laplacian matrix which is the optimistic version of the Laplacian Q=D+A and discuss a few basic properties" [YouTube Link](https://youtube.com/watch?v=3Pwy3OWwfAk) 2023-10-18T20:36Z 14.6K followers, [---] engagements "Integration in cylindrical and spherical coordinates (Calc 3; Lecture 3-6; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1133277054 * Finish discussing applications particularly inertia. * Discuss integration in cylindrical and spherical coordinates. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=4AYtsj3RRuU) 2025-11-03T21:46Z 14.4K followers, [---] engagements "Properties of the gradient; tangent planes to implicit surfaces (Calc 3; Lecture 2-5; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1124996830 * Some practice with directional derivative * Properties of the gradient (greatest increase / decrease) * Tangent plane to implicit surface For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=6lnUjMaEz5c) 2025-10-06T22:06Z 14.3K followers, [---] engagements "Lagrange multipliers -- bonus problem (Calc 3; Lecture 2-9; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1128345396 * One more problem done using Lagrange multiplier method for solving constrained optimization. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=7KZ5N3e33jk) 2025-10-17T20:42Z 14.2K followers, [--] engagements "Introduction to probability (Finite math; Lecture 34; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1137749915 * Sample spaces; events * Probability Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=7ZE5G7Tdu4w) 2025-11-17T16:48Z 15.1K followers, [---] engagements "Stokes' Theorem (Calc 3; Lecture 3-15; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1145019471 * Stokes' Theorem For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=87oT-4ohY10) 2025-12-09T20:41Z 15.1K followers, [---] engagements "Standard deviation (Finite math; Lecture 40; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1145324028 * Standard deviation Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=9xgqXEAEGt0) 2025-12-10T16:44Z 15.1K followers, [---] engagements "Integration by parts (Calc 2; Lecture 13; Spring 25) * Introduction to the techniques of integration portion of the course. * Integration by parts For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=BO1EFsJ44z4) 2025-02-24T17:30Z 12.6K followers, [---] engagements "Triple integrals (Calc 3; Lecture 3-4; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1131862739 * Setting up integrals over solids (=triple integrals). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=E-lXB92bjwg) 2025-10-29T21:39Z 14.4K followers, [---] engagements "Bayes' formula and Expected value (Finite math; Lecture 38; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1143881421 * Bayes formula * Expected value Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=FTKLO0Bri_Y) 2025-12-05T16:07Z 15.1K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1120453466 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:56 1-Average rate of change of a function 4:17 2-Finding tangent lines perpendicular to given line 7:34 3-Vertical and horizontal asymptotes 12:02 4-Making a function continuous 18:25 5-Testing types of discontinuity 22:01 6-Applying product and chain rules 26:59 7-Using the limit definition of" [YouTube Link](https://youtube.com/watch?v=FkkY8c3ISOY) 2025-09-20T17:49Z 14.5K followers, [----] engagements "Solving systems (Finite math; Lecture 27; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1132549190 * Solving systems using matrices. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=GA8tBJQvIPs) 2025-10-31T15:26Z 14.4K followers, [--] engagements "Changing order of integration (Calc 3; Lecture 3-2; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1128990217 * Using bounds to find the region and vice-versa. * Changing order of integration (from dx dy to dy dx and vice versa). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=Hwl2qoLt8JE) 2025-10-20T20:51Z 14.3K followers, [---] engagements "Sets (Finite math; Lecture 31; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1135449088 * Sets Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=IaEUhM765qw) 2025-11-10T18:24Z 15.1K followers, [---] engagements "Linear programming (Finite math; Lecture 30; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1134690892 * Linear programming (test the corners) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=Ig7Nu9Q9RUU) 2025-11-07T18:08Z 14.4K followers, [--] engagements "Vector-valued functions; grad div and curl (Calc 3; Lecture 3-9; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1135514550 * Vector-valued functions. * Gradient (grad) Divergence (div) and Curl (curl). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=Jy1ASFZaUj0) 2025-11-10T21:40Z 15.1K followers, [---] engagements "More practice with Stokes' Theorem and Gauss's Divergence Theorem (Calc 3; Lecture 3-17; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1146075363 * More practice with Stokes' Theorem and Gauss's Divergence Theorem * Four variations of the Fundamental Theorem of Calculus For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=K8dMUas1Bno) 2025-12-12T21:50Z 15.1K followers, [---] engagements "Two equations and two unknowns (Finite math; Lecture 20; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1126868599 * Start working on systems of equations with the classic of two equations with two unknowns. * Solving by graphing substitution elimination Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=KAMTN4_JeB4) 2025-10-13T15:11Z 14.5K followers, [---] engagements "Surface area (Calc 3; Lecture 3-13; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1138718900 * More about Green's Theorem * Area of surfaces For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=KID1v_2LXT8) 2025-11-19T23:37Z 15.1K followers, [---] engagements "Gauss-Jordan elimination (Finite math; Lecture 22; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1128903266 * Reduced form of matrices. * Gauss-Jordan elimination. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=L0wkWzeszSs) 2025-10-20T15:48Z 14.4K followers, [---] engagements "Practice 2-A problems for Calculus [--] (Fall 2025) -- partial derivatives and friends Vimeo (ad-free) link to same video: https://vimeo.com/1123936930 A set of problems that cover material from the first week of the second block for Calculus [--] (e.g. multivariable functions partial derivatives implicit differentiation chain rule gradient). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:35 1-Find domain; give level surface 9:42 2-Sketch and label level curves 18:52 3-Steepest descent 29:52" [YouTube Link](https://youtube.com/watch?v=L2Wc9_n_lIU) 2025-10-02T15:49Z 14.3K followers, [----] engagements "Tangent lines and area for polar (Calc 2; Lecture 11; Spring 25) * We go through how to find tangent lines for polar curves by reducing to parametric. * We work through how to find area in polar curves which boils down to finding wedges and adding many wedges together. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=LLkN7kNa3EA) 2025-02-14T16:43Z 12.5K followers, [---] engagements "Odds (Finite math; Lecture 36; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1139363471 * Odds Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=LXN_dOBqS9k) 2025-11-21T16:06Z 15.1K followers, [--] engagements "Matrix inverse practice; solving systems (Finite math; Lecture 26; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1131728260 * More practice with inverses of matrices. * Solving systems using matrices. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=MIgx3ChOrjo) 2025-10-29T15:18Z 14.4K followers, [--] engagements "Line integrals -- an introduction (Calc 3; Lecture 3-10; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1136268979 * Line integrals For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=N-ag0LdtM6E) 2025-11-12T21:56Z 15.1K followers, [---] engagements "More practice with probability (Finite math; Lecture 35; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1138583906 * Empirical probability * Union intersection and complement Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=NdO3TzKhZ1s) 2025-11-19T16:57Z 15.1K followers, [--] engagements "Applications (Calc 3; Lecture 3-5; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1132638458 * Applications in physics mass moment and a touch of inertia. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=OYx6QMAHQQs) 2025-10-31T20:44Z 14.4K followers, [---] engagements "Practice for Exam [--] = Matrices and Linear Equations (Finite math; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1134095791 A walkthrough of a practice exam for the third exam dealing with the topics of matrices and linear equations. These problems are slight variations of the posted practice exam. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.businessmath.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-This is" [YouTube Link](https://youtube.com/watch?v=Oe9owYV7mwc) 2025-11-06T05:01Z 14.4K followers, [---] engagements "Algebra review (Diff. Eq.; Lecture 1-2; Spring 2026) Vimeo (ad-free) link to same video: https://vimeo.com/1157413275 * Review of algebra tools that will show up in the course For more information: https://www.calc4.org/spring-2026 Presenter: Steve Butler (https://www.stevebutler.org/) differential equations differential equations" [YouTube Link](https://youtube.com/watch?v=PuVNVq-vYY8) 2026-01-23T01:46Z 15.1K followers, [---] engagements "Systems of linear inequalities (Finite math; Lecture 29; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1133917745 * Systems of linear inequalities. * Bounded vs unbounded. * Corner points Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=RrUQMV8TBUA) 2025-11-05T17:46Z 14.4K followers, [--] engagements "Calc [--] Final walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1146397506 A walk-through of the solutions for the Final of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:44 1-Find point where tangent line passes through 3:48 2-Motion of a particle 6:21 3-Find equation y satisfies 11:49 4-Dealing with sum notation 14:26 5-Finding properties of function from graph 19:24 6-Integration using substitution 25:42 7-Second derivative of an inverse 32:09 8-Using" [YouTube Link](https://youtube.com/watch?v=UNwM8OH96ko) 2025-12-14T21:08Z 15.1K followers, [----] engagements "(DiffEQ Fall 23) [--] - Higher order ODEs; Wronskian We start into higher order ODEs. We discuss linear ODEs superposition Wronskian and some basic solutions to constant coefficient linear homogeneous ODEs. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/ 0:00 Introduction to higher order ODEs 3:49 Superposition for linear ODEs 14:41 Example (using superposition) 22:18 Wronskian 27:48 Example (computing Wronskian) 31:44 Constant coefficient linear homogeneous ODEs 36:10 Example (finding solution to second-order ODE)" [YouTube Link](https://youtube.com/watch?v=Uxq8C2f2hgI) 2023-09-10T18:05Z 14.6K followers, [----] engagements "Solutions to practice exam [--] (Calc 3; Fall 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1142768957 The one where we walk through the solutions of practice Exam [--] from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org 0:00 Intro 0:52 1-Find a divergence 5:02 2-Orient curve for Green's Theorem 14:37 3-Integrate by changing order of integration 24:17 4-Switching between spherical and cylindrical integration 36:34 5-Identify a conservative function 43:48 6-Set up integral to find flux" [YouTube Link](https://youtube.com/watch?v=WvuICW9Z9CM) 2025-12-03T21:00Z 15.1K followers, [----] engagements "Practice for Exam [--] = Functions and financial math (Finite math; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1126053363 A walkthrough of a practice exam for the first exam dealing with the topics of algebra and lines. These problems are slight variations of the posted practice exam. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.businessmath.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro & [--] 1:59" [YouTube Link](https://youtube.com/watch?v=Wy3YI4kPvu8) 2025-10-10T01:25Z 14.2K followers, [----] engagements "Counting (Finite math; Lecture 32; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1136169749 * Counting; addition and multiplication Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=_XWBWFAaYeg) 2025-11-12T16:54Z 15.1K followers, [---] engagements "Verifying solutions (Diff. Eq.; Lecture 1-3; Spring 2026) Vimeo (ad-free) link to same video: https://vimeo.com/1158509697 * Verifying solutions * Plugging in and setting parameters to make a solution * Initial condition problems * Word problems and differential equations * Existence and uniqueness For more information: https://www.calc4.org/spring-2026 Presenter: Steve Butler (https://www.stevebutler.org/) differential equations differential equations" [YouTube Link](https://youtube.com/watch?v=aexoBj4jlbQ) 2026-01-26T18:30Z 15.1K followers, [---] engagements "Diff Eq Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1139636229 A walk-through of the solutions for Exam [--] of Differential Equations administered in Spring [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:06 1-Inverse Laplace (partial fractions) 9:54 2-Laplace transform of piecewise function 19:03 3-Finding some inverse Laplace expressions 32:33 4-Set up and solve diff. eq. with delta 47:29 5-Find first few terms in series solution 56:00 6-Find recurrence relation of series solution" [YouTube Link](https://youtube.com/watch?v=cDw2Z6EHOrc) 2025-11-22T16:15Z 15.1K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1138200604 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:43 1-Grad div curl 3:32 2-Set up volume in cylindrical 12:08 3-Find potential function 14:40 4-Make sure function is conservative 17:36 5-Green's Theorem problem 21:10 6-Surface area of paraboloid 29:42 7-Line integral (put in terms of t) 35:03 8-Substitution / change of variables 46:33" [YouTube Link](https://youtube.com/watch?v=cMmeYtM7_ME) 2025-11-18T19:09Z 15.1K followers, [----] engagements "Calculus [--] -- Limits with infinity -- Overview Presenter: Steve Butler (http://mathbutler.org) Course website: http://calc1.org 0:00 Introduction 1:15 Limits with infinity 6:19 Horizontal asymptotes 13:36 Vertical asymptotes" [YouTube Link](https://youtube.com/watch?v=dxk6oO0IB-c) 2020-06-10T23:45Z 14.3K followers, [----] engagements "Calc [--] Final walkthrough (Fall 2024) Vimeo (ad-free) link to same video: https://vimeo.com/1146397327 A walk-through of the solutions for the Final of Calculus [--] administered in Fall [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:51 1-Limit of indeterminant (L'Hospital) 2:32 2-Limit definition of derivative 5:30 3-Product rule 6:59 4-Motion of a particle 9:53 5-Derivative rules (be careful with constants) 13:41 6-Absolute maximum 17:36 7-Using algebra to do an integral 21:05 8-Integration using substitution 25:14" [YouTube Link](https://youtube.com/watch?v=eZdERl3SEo4) 2025-12-14T21:08Z 15.1K followers, [---] engagements "Calc [--] Final walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1146637590 A walk-through of the solutions for the Final of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:47 1-Angle between planes 5:01 2-Use linearization (tangent planes) to estimate 10:13 3-Identify quadric surfaces 15:56 4-Find max rate of change (magnitude of gradient) 20:15 5-Find average of a function 26:26 6-Distance between centers 29:14 7-Find projection of vectors 32:03 8-Find speed" [YouTube Link](https://youtube.com/watch?v=elJxQdtW7j4) 2025-12-15T16:58Z 15.1K followers, [----] engagements "Applications of Gauss-Jordan and matrices (Finite math; Lecture 23; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1129567314 * Applications with Gauss-Jordan elimination. * Adding/scaling/comparing matrices (work entry-by-entry). Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=gXDH3M6J-nY) 2025-10-22T15:27Z 14.3K followers, [--] engagements "Green's Theorem (Calc 3; Lecture 3-12; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1137857757 * More practice with conservative line integrals and finding potential functions * Green's Theorem * Practice with Green's Theorem For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=hbt2Bgwz3Dk) 2025-11-17T21:47Z 15.1K followers, [---] engagements "Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1138190176 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:40 1-L'Hospital 2:47 2-Evaluate indefinite integral 5:33 3-Mean Value Theorem 7:57 4-Riemann sum (left endpoints) 10:18 5-Substitution 13:29 6-Fundamental Theorem of Calculus 18:13 7-Newton's Method (finding roots) 25:27 8-Area of a region (slice horizontally) 32:32 9-Integrals using" [YouTube Link](https://youtube.com/watch?v=i8S36rQW3hw) 2025-11-18T19:09Z 15.1K followers, [---] engagements "Arc length for polar curves (Calc 2; Lecture 12; Spring 25) * We go through how to find arc length for polar curves (spoiler we do it by linking back to parametric curves). For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)" [YouTube Link](https://youtube.com/watch?v=iaeJsG7mC90) 2025-02-17T16:50Z 12.5K followers, [---] engagements "Matrix multiplication (Finite math; Lecture 24; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1130258433 * Different view of what a matrix represents. * Matrix multiplication. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=ifApciKvhnI) 2025-10-24T15:26Z 14.3K followers, [--] engagements "Calc [--] Final walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1146815456 A walk-through of the solutions for the Final of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:58 1-Trapezoid rule 5:08 2-Center of mass of wire (1D) 12:12 3-Improper integral 15:17 4-Sum of geometric series 19:58 5-Direct comparison test 23:10 6-Center of power series 25:38 7-Find sum of geometric series 29:01 8-Find coefficient in Taylor series 34:16 9-Find length of parametric curve" [YouTube Link](https://youtube.com/watch?v=ii4F_tbcxFw) 2025-12-16T04:15Z 15.1K followers, [---] engagements "Annual Percentage Yield = APY (Finite math; Lecture 17; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1124244003 * Annual Percentage Yield (APY) -- The answer to the question what would be the equivalent if we just donated once a year Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org" [YouTube Link](https://youtube.com/watch?v=kI9hBqnTQo0) 2025-10-03T15:12Z 14.3K followers, [--] engagements Limited data mode. Full metrics available with subscription: lunarcrush.com/pricing
@beardmeetscalculus Beard Meets Calculus
Beard Meets Calculus posts on YouTube about vimeo, link, intro, spring the most. They currently have [------] followers and [---] posts still getting attention that total [-----] engagements in the last [--] hours.
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Social Influence
Social category influence social networks countries finance
Social topic influence vimeo #44, link, intro, spring, eq, walk, math, to the, for the, integration
Top assets mentioned Integral (ITGR)
Top Social Posts
Top posts by engagements in the last [--] hours
"Practice for Exam [--] = Cumulative final (Finite math; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1145133680 A walkthrough of a practice exam for the fourth exam dealing with the topics of the semester with emphasis on the last part (sets probabilities data). These problems are slight variations of the posted practice exam. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.businessmath.org/ Presenter: Steve Butler"
YouTube Link 2025-12-10T05:36Z 15.1K followers, [----] engagements
"Spring-Mass-Damper systems (Diff. Eq.; Lecture 1-12; Spring 2026) Vimeo (ad-free) link to same video: https://vimeo.com/1165430203 * Spring-mass-damper systems --- example of application of differential equations tied to oscillation / vibration For more information: https://www.calc4.org/spring-2026 Presenter: Steve Butler (https://www.stevebutler.org/) differential equations differential equations"
YouTube Link 2026-02-16T18:01Z 15.1K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Fall 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1164897402 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:50 1-Distance from point to plane 4:27 2-Volume of shape given by inequalities 9:16 3-Area of triangle given three points 14:03 4-Spherical to rectangular coordinates 16:48 5-Using information about acceleration velocity and curvature 21:52 6-Identify quadric surface from formula 25:46 7-Find line"
YouTube Link 2026-02-14T03:50Z 15.1K followers, [---] engagements
"Partial fractions (Calc 2; Lecture 17; Spring 25) * Discuss partial fractions (or how I learned to stop worrying and embrace rational functions) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-03-05T01:40Z 12.7K followers, [---] engagements
"Continuity (Calc 1; Lecture 4; Fall 24) An introduction to continuity (what should happen is what actually happens). Lecture given in-class on Wednesday September [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-09-04T22:10Z 11.4K followers, [---] engagements
"Applications for Taylor series (Part 1) (Calc 2; Lecture 36; Spring 25) * Applications for Taylor series ** Finding particular derivative ** Finding Taylor polynomial ** Finding Taylor series for rational function For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-05-05T16:45Z 13.2K followers, [---] engagements
"L'Hospital's Rule (Calc 1; Lecture 23; Fall 24) We discuss one of the most popular ways for students to do limits namely by the use of L'Hospital's rule. (The funner way of dealing with indeterminates.) Lecture recorded in class on Monday October [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-10-29T00:06Z 14.1K followers, [---] engagements
"Diff Eq Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1123060879 A walk-through of the solutions for Exam [--] of Differential Equations administered in Spring [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:34 1-Solve ODE using substitution (homogeneous) 10:10 2-Exact ODE 19:02 3-Autonomous ODE 29:03 4-Compute Wronskian; find ODE given solution 42:49 5-Find general solution to nonhomogeneous ODE 52:00 6-Spring-mass-dashpot solution"
YouTube Link 2025-09-30T01:49Z 14.1K followers, [---] engagements
"Volume by shell method (Calc 2; Lecture 2; Spring 25) * Use of the shell method * Comparing/contrasting with washer method For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-01-24T17:15Z 12.2K followers, [---] engagements
"Lines and planes (Calc 3; Lecture 6; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1116906033 We discuss our flat objects namely lines and planes. How to represent them with formulas and how to find the distance to them. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-08T20:49Z 13.8K followers, [---] engagements
"Differentiability; tangent plane; chain rule (Calc 3; Lecture 2-3; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1123700853 * Differentiability = locally flat (a bit more than just having partial derivatives) * Tangent planes = local approximation * Implicit differentiation For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-01T20:49Z 14.1K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1127919023 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:52 1-Implicit differentiation 4:35 2-Critical points 6:44 3-Derivative with chain rule 10:16 4-Use linearization to approximate 14:34 5-Derivative with natural log 18:21 6-Find/classify extrema 23:29 7-Logarithmic differentiation 29:17 8-Related rates (holey problem) 37:35"
YouTube Link 2025-10-16T15:43Z 14.2K followers, [---] engagements
"Mean Value Theorem (Calc 1; Lecture 25; Fall 24) We discuss the Mean Value Theorem which states that if we have a "nice" function then at some point in time the instantaneous rate of change has to match the average rate of change. Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-01T22:46Z 11.4K followers, [--] engagements
"Practice for Exam [--] = Algebra and lines (Finite math; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1118374731 A walkthrough of a practice exam for the first exam dealing with the topics of algebra and lines. These problems are slight variations of the posted practice exam. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.businessmath.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-This is only a practice test"
YouTube Link 2025-09-13T16:31Z 13.8K followers, [---] engagements
"Exponential functions (Finite math; Lecture 13; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1121571518 * Exponential functions * Cumulative interest (both discrete and continuous) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-24T15:39Z 14K followers, [--] engagements
"Practice 1-B problems for Calculus [--] (Fall 2025) --- Dot and cross product Vimeo (ad-free) link to same video: https://vimeo.com/1115845155 A set of problems that cover material from the second week of the first block for Calculus [--] (e.g. dot and cross products). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:40 1-Find value so that projection works 7:18 2-Find values to make vectors perpendicular 12:55 3-Find the area of a triangle 24:30 4-Find unit vector perpendicular to two vectors"
YouTube Link 2025-09-05T21:00Z 13.7K followers, [---] engagements
"Rational exponents (Finite math; Lecture 05; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1116184704 * Working with rational exponents Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-05T20:58Z 13.7K followers, [--] engagements
"Taylor polynomials + Taylor polynomial lower bound (Calc 2; Lecture 33; Spring 25) * Taylor polynomial (="best" polynomial to locally approximate the function) * Taylor polynomial error bound (How good is our estimate Pretty good) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-23T16:22Z 13K followers, [---] engagements
"Parametric curves; tangents (Calc 3; Lecture 8; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1118229960 We introduce parametric curves and talk calculus (work term-by-term). We also do tangent lines to parametric curves. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-12T20:42Z 13.8K followers, [---] engagements
"(DiffEQ Fall 23) Exam [--] review - ODE systems Course site: http://calc4.org Instructor: Steve Butler (http://stevebutler.org) 0:00:00 Intro 0:01:26 [--] -- Mixing problem with tanks 0:15:20 [--] -- Elimination method 0:25:11 [--] -- x'=A(t)x; verify solution; Wronskian 0:40:22 [--] -- General form for system (distinct eigenvalues) 0:51:38 [--] -- Initial value problem (repeated eigenvalues) 1:05:28 [--] -- Initial value problem (complex eigenvalues) 1:16:38 [--] -- eAt for distinct eigenvalues 1:24:20 [--] -- Undetermined coefficients 1:41:00 [--] -- Variation of parameters"
YouTube Link 2023-10-23T02:52Z [----] followers, [---] engagements
"Changing order of integration (Calc 3; Lecture 22; Fall 24) Vimeo (ad-free) link to same video: https://vimeo.com/1021901132 We discuss the strategy involved for changing the order of integration over non-rectangular regions. Lecture recorded in class on Monday October [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-10-21T22:13Z 14.1K followers, [---] engagements
"Integration in cylindrical and spherical coordinates (Calc 3; Lecture 26; Fall 24) We discuss integration in cylindrical and spherical coordinates. Lecture recorded in class on Monday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-04T23:16Z 11.5K followers, [--] engagements
"Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:53 1-Integration by parts 8:48 2-Trigonometric integrals 19:45 3-Partial fractions 32:30 4-Numerical integration (Trapezoid and Simpson's) 40:28 5-Improper integral 49:38 6-Application (volume + trig substitution)"
YouTube Link 2025-03-23T16:06Z 12.7K followers, [---] engagements
"Tangent lines and length for parameterized curves (Calc 2; Lecture 8; Spring 25) * More practice working with parameterized curves. * First and second derivatives for parameterized curves. * Length (=distance traveled) for parameterized curves. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-07T16:16Z 12.4K followers, [---] engagements
"Week [--] review problems for Calculus [--] (Spring 2025) --- Mass moments parameterized curves A set of problems that cover material from the third week of Calculus [--] (e.g. using integration to find mass center of mass and parameterized curves (tangent lines second derivatives applications)). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:52 1-Find where parametric curve hits a given line 6:09 2-Plot a parameterized curve 13:06 3-Length of parametric curve 19:26 4-Find density given center of"
YouTube Link 2025-02-08T18:42Z 12.4K followers, [----] engagements
"Mass and Center of Mass (Calc 2; Lecture 6; Spring 25) * Finding Mass and Center of Mass for both 1D and 2D regions. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-03T16:56Z 12.4K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:36 1-Find absolute minimum 7:09 2-Derivative of inverse 10:14 3-Logarithmic differentiation 14:04 4-Derivative of arctan 16:20 5-Linearization of a cube root 22:12 6-Critical points of a function 26:26 7-Implicit differentiation 33:33 8-Related rates (extend the boom) 45:06 9-Find constants given function properties 51:05 10-Optimization (maximize volume of can)"
YouTube Link 2025-03-23T02:30Z 12.7K followers, [---] engagements
"Example in Calc [--] class on March [--] [----] (day before Exam 2) For more information visit: https://www.calc2.org Presented by Steve Butler: https://www.stevebutler.org"
YouTube Link 2025-03-26T18:44Z 12.8K followers, [---] engagements
"Comparison tests for series (Calc 2; Lecture 27; Spring 25) * Comparison test * Limit comparison test For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-09T15:25Z 12.9K followers, [---] engagements
"Building a LEGO dodecahedron This goes through the steps of making a dodecahedron out of LEGO. This uses the following pieces: [--] of the 3-Branch Cross Axle (57585) [--] of the Angle Element [---] Degree (42156)"
YouTube Link 2024-12-24T20:40Z 13.4K followers, [----] engagements
"(Spectral; Fall 23) [--] - Matrix Tree Theorem Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ We continue the discussion of the Laplacian matrix by talking about the Matrix Tree Theorem (one of the most well-known results related to eigenvalues of the Laplacian)"
YouTube Link 2023-10-16T23:09Z 11.5K followers, [---] engagements
"(DiffEQ Fall 23) [--] - Population models We do a short-ish review of the major techniques of solving first-order differential equations. We then move to talking about population models with particular discussion about the exponential and logistic models. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/ 0:00 Review of ways to solve first-order ODEs 9:22 Introduction to population models 13:08 Solution to the exponential model 19:39 Example (exponential model) 27:15 Introduction to logistic model 29:19 Solution to the logistic model 44:27 Example"
YouTube Link 2023-09-06T02:33Z 11.5K followers, [----] engagements
"Cross product of vectors (Calc 3; Lecture 5; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1116281043 We discuss the cross product which can be used to form perpendicular vectors as well as compute area of parallelograms and triangles as well as volumes of parallelepipeds. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-05T20:59Z 13.7K followers, [---] engagements
"Numbers (Finite math; Lecture 01; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1112935912 * Overview of the course and advice * Different types of numbers (natural integers rational irrational real) * Rules for addition and multiplication of numbers Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-08-25T15:47Z 13.5K followers, [---] engagements
"Practice 1-C problems for Calculus [--] (Fall 2025) --- Lines planes quadric surfaces parametric Vimeo (ad-free) link to same video: https://vimeo.com/1118422531 A set of problems that cover material from the third week of the first block for Calculus [--] (e.g. Lines planes quadric surfaces parametric). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:36 1-Finding location of a coasting spaceship 9:58 2-cos(theta) for intersecting parametric curves 21:43 3-Find the plane equidistant between two"
YouTube Link 2025-09-13T23:36Z 14.1K followers, [----] engagements
"Implicit differentiation; gradient; directional derivative (Calc 3; Lecture 2-4; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1124333128 * Implicit differentiation * Gradient (analog of the derivative) * Directional derivatives For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-03T20:50Z 14.1K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Logarithmic differentiation 4:04 2-Tangent line to implicit curve 9:50 3-Linear approximation 15:51 4-Related rates (ohms) 24:07 5-Increasing/decreasing and classifying 33:43 6-Maximizing area of garden"
YouTube Link 2024-10-16T12:35Z 11.2K followers, [---] engagements
"Line integrals (the easy way) (Calc 3; Lecture 31; Fall 24) We look at conservative functions and show that doing line integrals with conservative functions is easy(-ish). Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-15T22:56Z 11.6K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2025) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:45 1-Vertical tangent line 3:25 2-Set up volume of revolution 9:04 3-Setting up surface area in polar curve 14:52 4-Given an integral for length find f(x) 19:13 5-Find polar graph from among choices 24:05 6-Find moment of triangle region 29:25 7-Set up volume by shell method 38:04 8-Surface area for parametric curve 50:33 9-Find work to pump out of a tank"
YouTube Link 2025-03-02T19:53Z 12.6K followers, [---] engagements
"Line integrals (the hard way) (Calc 3; Lecture 30; Fall 24) We introduce line integrals and how to compute them. We also go over a discussion of how to compute work along a curve with varying force. Lecture recorded in class on Wednesday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-13T22:48Z 11.6K followers, [---] engagements
"Walkthrough of solutions to practice exam [--] (Calc 1; Fall 2024) The one where we walk through the solutions of practice Exam [--] from Fall [----] Calc [--] (aka single variable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc1.org 0:00 1-Implicit function; increasing/decreasing; concavity 4:48 2-Derivative of inverse function 9:06 3-Second derivative test 13:23 4-Logarithmic differentiation 18:46 5-Linearization 22:45 6-Absolute max/min procedure 29:07 7-Increasing/decreasing; concavity 35:55 8-Linearization 38:40 9-Related rates 44:24 10-Frosting"
YouTube Link 2024-10-23T21:51Z 14.1K followers, [---] engagements
"Quadratic functions (Finite math; Lecture 11; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1120174029 * Quadratic functions Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-19T15:20Z 13.9K followers, [--] engagements
"Decomposing acceleration and curvature (Calc 3; Lecture 11; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1120282075 We look at the problem of decomposing acceleration into a part that lies in the direction of motion (the part of acceleration speeding you up or slowing you down) and a part that lies perpendicular to motion (the part of acceleration pulling you to the side). We also connect this to curvature which tries to answer the age-old question of how "bendy" a curve is. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler"
YouTube Link 2025-09-19T20:47Z 13.9K followers, [---] engagements
"Work and force problems (Calc 2; Lecture 5; Spring 25) * Finding work and force by splitting things into parts; finding the contribution of each part; adding up to get the total For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-01-31T15:45Z 12.3K followers, [---] engagements
"2025 Ice bucket challenge w/ Steve Butler #SpeakYourMIND [----] Ice bucket challenge w/ Steve Butler #SpeakYourMIND"
YouTube Link 2025-04-23T23:47Z 13K followers, [----] engagements
"Week [--] review problems for Calculus [--] (Spring 2025) --- Applications of integration: volume A set of problems that cover material from the first week of Calculus [--] (e.g. using integration to find volumes). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:26 1-Volume by cross section; isosceles right triangle 15:34 2-Volume by cross section (Cavalieri's Principle) 22:01 3-Volume by washer method 28:49 4-Volume by washer method (handling tan4(x)) 42:54 5-Volume by shell method 50:05 6-Volume"
YouTube Link 2025-01-25T19:06Z 12.2K followers, [---] engagements
"Interval of convergence for power series (Calc 2; Lecture 31; Spring 25) * Finding interval of convergence for power series (root/ratio tests followed by checking endpoints) * Rewriting geometric sum as rational function For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-18T15:41Z 13.2K followers, [---] engagements
"Solutions to practice exam 3-A (Calc 1; Fall 2024) The one where we walk through the solutions of practice Exam 3-A from Fall [----] Calc [--] (aka basic class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc1.org Problems and scanned solutions can be found in the website https://www.calc1.org by going to the Fall [--] page and scrolling down to Week fourteen. 0:00 Intro 0:29 1-Recursion for Newton's Method 5:01 2-Riemann sum 11:07 3-Fundamental Theorem of Calculus 15:13 4-Average value of function 22:12 5-Using linearity of integrals 30:27 6-Find"
YouTube Link 2024-11-28T18:54Z 11.8K followers, [---] engagements
"Rational functions (Finite math; Lecture 12; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1120873519 * Rational functions Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-22T15:25Z 13.9K followers, [--] engagements
"Week [--] review problems for Calculus [--] (Spring 2025) --- Alternating series/Interval of convergence A set of problems that cover material from the twelfth week of Calculus [--] (e.g. alternating series and interval of convergence). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:26 1-Apply alternating series test 4:18 2-Absolute vs Conditional vs Diverge 8:14 3-Error bound for alternating series test 14:52 4-Rewrite geometric series as rational function 22:29 5-Radius of convergence (ratio"
YouTube Link 2025-04-19T16:53Z 13K followers, [----] engagements
"Integration in polar coordinates (Calc 3; Lecture 23; Fall 24) Vimeo (ad-free) link to same video: https://vimeo.com/1022501447 We discuss integration in polar coordinates and how to approach integrations in general. Lecture (pre-)recorded for class on Monday October [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-10-29T00:04Z 14.1K followers, [---] engagements
"Triple integrals changing order of integration (Calc 3; Lecture 24; Fall 24) Vimeo (ad-free) link to same video: https://vimeo.com/1024917451 We discuss triple integrals and also how to go about changing the order of integration.Lecture recorded in class on Wednesday October [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-10-30T22:48Z 14.1K followers, [---] engagements
"Alternating series test (Calc 2; Lecture 29; Spring 25) * Alternating series test (terms alternate + decrease to [--] implies converge) * Bound for alternating series (=next term) * Absolute and conditional convergence For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-14T15:17Z 12.9K followers, [---] engagements
"Vector fields; curl; div (Calc 3; Lecture 29; Fall 24) Introduction to vector fields and a discussion of the del operator including gradient (grad) divergence (div) and curl (curl). Lecture recorded in class on Monday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-11T23:23Z 11.6K followers, [---] engagements
"Week [--] review problems for Calculus [--] (Fall 2024) A set of problems that cover material from the twelfth week of Calculus [--] (e.g. curl divergence gradient line integrals and conservative line integrals). For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Find divergence of a vector field 3:58 2-Find curl of a vector field 13:26 3-Find mass of a wire 20:44 4-Set parameters to make a gradient field 27:39 5-Line integral (non-conservative) 33:28 6-Work along a curve (non-conservative) 42:02 7-Line integral (conservative) 51:47 8-Line"
YouTube Link 2024-11-17T15:55Z 11.7K followers, [---] engagements
"Introduction to the Jacobian (Calc 3; Lecture 27; Fall 24) We discuss the Jacobian and more generally how to change coordinate systems. Lecture recorded in class on Wednesday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-06T23:11Z 11.5K followers, [---] engagements
"Arc length (=distance) (Calc 3; Lecture 10; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1119580003 We look at the problem of finding the distance a particle travels. This can be found by integrating speed (r'(t)). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-17T20:42Z 13.9K followers, [---] engagements
"Practice 2-B problems for Calculus [--] (Fall 2025) -- Taylor polynomials and friends Vimeo (ad-free) link to same video: https://vimeo.com/1126504892 A set of problems that cover material from the second week of the second block for Calculus [--] (e.g. properties of the gradient Taylor polynomials finding and classifying critical points). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:34 1-Getting partial derivatives from Taylor polynomial 6:52 2-Third order Taylor polynomial 31:29 3-Find"
YouTube Link 2025-10-11T22:25Z 14.2K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1128072611 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:50 1-Identify correct substitution for trigonometric integral 3:18 2-Carry out a trig substitution 7:40 3-Partial fraction decomposition 11:50 4-Convergence for improper integral 16:10 5-Integration by parts 22:50 6-Simpson's rule (numerical integration) 27:10 7-Integration by parts (done twice"
YouTube Link 2025-10-17T02:33Z 14.2K followers, [---] engagements
"Functions (Finite math; Lecture 9; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1118778964 * Functions * Domain and range of functions * Graphing; vertical line test * Combining functions together Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-15T15:19Z 13.8K followers, [--] engagements
"Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1127734834 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:49 1-Find mixed partial derivative 3:04 2-Chain rule 10:17 3-Find directional derivative 15:24 4-Graph domain of function 19:48 5-Implicit differentiation 25:50 6-Properties of the gradient 34:03 7-Second order Taylor polynomial 49:21 8-Lagrange multiplier problem 1:01:20 9-Find and classify"
YouTube Link 2025-10-16T03:04Z 14.2K followers, [---] engagements
"Motion; osculating planes; antiderivatives (Calc 3; Lecture 9; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1118895271 We continue parametric curves by framing them in terms of position velocity and acceleration. We also look at the osculating plane (which uses all of the information). And finally talk anti-derivatives which work entry-by-entry. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-15T21:56Z 13.8K followers, [---] engagements
"Riemann sums and area (Calc 1; Lecture 29; Fall 24) We use Riemann sum along with geometry to calculate some areas. Something suspicious seems to be emerging. Lecture recorded in class on Monday November [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-11T23:24Z 11.6K followers, [---] engagements
"Arc length for the case y=f(x) (Calc 2; Lecture 3; Spring 25) * More practice with volume * Arc length for the case y=f(x) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-01-27T16:19Z 12.4K followers, [---] engagements
"Surface area of revolution (Calc 2; Lecture 4; Spring 25) * Surface area from revolving around an axis For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-01-29T16:44Z 12.5K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Change 2D order of integration and integrate 4:41 2-Find potential function; conservative line integral 14:20 3-Green's Theorem 20:41 4-Convert integral to spherical coordinates 31:42 5-Surface integral; Mass 41:30 6-Change of variables/coordinates"
YouTube Link 2024-11-25T18:20Z 11.8K followers, [---] engagements
"Taylor polynomials (Calc 3; Lecture 2-6; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1125701426 * Linear approximation = Tangent plane * Taylor polynomials * Quadratic form (for the theory) For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-08T23:14Z 14.2K followers, [---] engagements
"Quadratic equtions (Finite math; Lecture 06; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1116809782 * Solving quadratic equations by factoring and/or using the quadratic formula Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-08T15:22Z 13.8K followers, [--] engagements
"Critical points; Second partials test (Calc 3; Lecture 2-7; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1126316931 * Critical points * Second partials test for classifying critical points For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-10T21:35Z 14.2K followers, [---] engagements
"Cartesian coordinates; distance (Calc 3; Lecture 1; Fall 24) An introduction to 3D geometry using Cartesian coordinates and distance. Lecture recorded in studio on Tuesday August [--] [----]. (Unfortunately markers were forgotten so not recorded in-class.) For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-08-27T12:59Z 11.4K followers, [---] engagements
"Transformation of functions (Finite math; Lecture 10; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1119474321 * Basic functions * Transformations * Piecewise functions Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-17T15:16Z 13.9K followers, [--] engagements
"Surface integrals (Calc 3; Lecture 34; Fall 24) We look at surface integrals finishing up with computing flux through a surface. Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-22T23:07Z 11.8K followers, [---] engagements
"Practice 1-A problems for Calculus [--] (Fall 2025) --- Coordinate systems and vectors Vimeo (ad-free) link to same video: https://vimeo.com/1114085772 A set of problems that cover material from the first week of the first block for Calculus [--] (e.g. coordinate systems and vectors). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:40 1-Make three points collinear 9:24 2-Rewrite plane using spherical coordinates 15:43 3-Minimum distance between spheres 27:10 4-Identify sphere in spherical"
YouTube Link 2025-08-29T21:00Z 13.6K followers, [---] engagements
"Quadric surfaces (Calc 3; Lecture 7; Fall 24) A review of doing things with lines and planes; then a speed run through quadric surfaces). Lecture recorded in class on Wednesday September [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-09-11T21:55Z 10.6K followers, [---] engagements
"Absolute max and min (Calc 3; Lecture 2-8; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1126965781 * Absolute max and min for continuous function on a closed and bounded domain For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-13T20:37Z 14.2K followers, [---] engagements
"Everything looks like a polynomial; sequences (Calc 2; Lecture 23; Spring 25) * Introduction to the third part of the course where we think that everything looks like a polynomial (=nice). Woohoo * Start down the road to making (almost) everything into polynomial by talking about sequences. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-03-31T15:39Z 12.8K followers, [---] engagements
"Numerical integration including Trapezoid Rule and Simpson's Rule (Calc 2; Lecture 19; Spring 25) * Numerical integration including Trapezoid Rule and Simpson's Rule For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-03-10T16:02Z 12.7K followers, [---] engagements
"Simple interest (Finite math; Lecture 15; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1122902088 * Simple interest Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-29T15:37Z 14.1K followers, [--] engagements
"Area between curves (Calc 1; Lecture 34; Fall 24) We look at how to use definite integrals to find the area between curves. Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-22T23:08Z 11.8K followers, [---] engagements
"Solutions to practice exam 3-B (Calc 3; Fall 2024) The one where we walk through the solutions of practice Exam 3-B from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org Problems and scanned solutions can be found in the website https://www.calc3.org by going to the Fall [--] page and scrolling down to Week fourteen. 0:00 Intro 0:29 1-2D change order of integration 4:49 2-Integral for surface area 8:38 3-Change cylindrical to spherical 23:48 4-Compute Jacobian 31:35 5-Compute divergence 34:51 6-Set up"
YouTube Link 2024-11-29T18:23Z 11.9K followers, [---] engagements
"Integral test; p-series (Calc 2; Lecture 26; Spring 25) * Integral test * p-series For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-07T16:01Z 12.9K followers, [---] engagements
"Diff Eq Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Differential Equations administered in Fall [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:31 1-Setting up system of equations 10:24 2-Take second order equation to first-order system 16:46 3-Take first-order system to second order equation 23:06 4-Use matrix exponential (repeated roots) 30:12 5-Verify solutions; Wronskian 38:01 6-Compute matrix exponential (distinct roots)"
YouTube Link 2025-04-01T14:12Z 12.8K followers, [---] engagements
"Cartesian coordinates; distance; spheres (Calc 3; Lecture 1; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1113028021 An introduction to 3D geometry using Cartesian coordinates distance and spheres. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-08-25T20:52Z 13.5K followers, [---] engagements
"Week [--] review problems for Calculus [--] (Fall 2024) A set of problems that cover material from the eleventh week of Calculus [--] (e.g. integration in spherical/cylindrical coordinates and changing variables). For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Find mass (cylindrical coordinates) 5:59 2-Set up volume integral (spherical coordinates) 16:30 3-Find new bounding curves (substitution) 24:06 4-Find center of mass (cylindrical coordinates) 39:51 5-Find volume (spherical coordinates) 48:34 6-Inertia (cylindrical coordinates) 58:54"
YouTube Link 2024-11-10T15:03Z 11.6K followers, [----] engagements
"Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:51 1-Volume over region 3:46 2-Change order of integration 7:57 3-Convert integral from Cartesian to polar 10:47 4-Identify bounds for triple integral 16:15 5-Compute divergence 19:20 6-Compute flux through surface 24:57 7-Find center of mass of cone 39:52 8-Do a change of variable (Jacobian) 55:29 9-Find potential / Fundamental Theorem of Line Integrals 1:06:12"
YouTube Link 2025-04-29T03:47Z 13.1K followers, [---] engagements
"DiffEQ Exam [--] walkthrough (Fall 2023) A walk-through of the solutions for Exam [--] of Differential Equations administered in Fall [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:31 [--] -- First order ODE 7:50 [--] -- Exact ODE 14:38 [--] -- Autonomous ODE 20:07 [--] -- Properties of ODEs (Wronskian superposition .) 28:38 [--] -- Spring-mass-damper system 38:17 [--] -- Nonhomogeneous ODE (undetermined coefficients)"
YouTube Link 2023-10-03T16:38Z 11.5K followers, [---] engagements
"(Spectral; Fall 23) [--] - How graph labeling naturally connects with distance matrices Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ We continue the discussion on distance matrices and the graph labeling problem and show how these are naturally connected to one another"
YouTube Link 2023-12-05T06:00Z 11.5K followers, [--] engagements
"Week [--] review problems for Calculus [--] (Fall 2024) A set of problems that cover material from the thirteenth week of Calculus [--] (e.g. substitution rule; area between curves). For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Find area between two curves 11:45 2-Find area under curve + substitution 20:34 3-Find antiderivative + substitution 25:53 4-Find area between two curves (w.r.t y) 40:45 5-Set up integrals to find area (w.r.t x and y) 51:41 6-Find antiderivative + trig substitution 1:00:14 7-Definite integral + substitution (arctan)"
YouTube Link 2024-11-25T04:58Z 11.8K followers, [---] engagements
"Linear equations (Finite math; Lecture 7; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1117485972 * Solving linear equations Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-10T15:31Z 13.8K followers, [--] engagements
"Week [--] review problems for Calculus [--] (Fall 2024) A set of problems that cover material from the eighth week of Calculus [--] (e.g. properties of the first/second derivative and optimization). For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Introduction 0:37 1-Using f' to find/classify critical points; concavity 18:14 2-Find and classify critical points 26:31 3-Find where function is increasing/decreasing 36:33 4-Finding c; finding inflection points 44:50 5-Optimizing fencing next to a barn 51:54 6-Find where function is"
YouTube Link 2024-10-17T22:00Z 11.2K followers, [---] engagements
"Annuities part [--] (Finite math; Lecture 18; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1125570887 * Annuities (finding the value of many payments over time) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-08T15:28Z 14.2K followers, [--] engagements
"Graphing linear equations (Finite math; Lecture 8; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1118144225 Audio did not record properly so using backup audio track. Sorry * Word problems * Graphing lines * Different forms for lines Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-12T15:09Z 13.8K followers, [--] engagements
"Math [---] Fall [----] Practice Exam 1-1 Presenter: Steve Butler (http://stevebutler.org) Course website: http://calc4.org 0:00 Introduction 1:22 Problem [--] -- radioactive decay 8:06 Problem [--] -- linear first-order 15:11 Problem [--] -- homogeneous ODE 31:15 Problem [--] --- find/classify critical points for autonomous ODE 36:36 Problem [--] -- constant coefficient linear homogeneous ODE 40:08 Problem [--] -- spring-mass system"
YouTube Link 2021-09-28T05:21Z 13.3K followers, [----] engagements
"Series (both geometric and telescoping); nth term test; harmonic sum (Calc 2; Lecture 25; Spring 25) * More practice with geometric series * Telescoping series (where the terms cancel leading to collapse) * N-th term test (if terms don't go to [--] then sum diverges) * Harmonic series For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-04T14:45Z 12.9K followers, [---] engagements
"Walkthrough of solutions to practice exam [--] (Calc 3; Fall 2024) Vimeo (ad-free) link to same video: https://vimeo.com/1022678528 The one where we walk through the solutions of practice Exam [--] from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org 0:00 1-Give domain of function 2:48 2-Direction of greatest decrease 5:59 3-Implicit differentiation (mixed partial) 14:56 4-Linear approximation 18:15 5-Tangent plane to implicit surface 23:39 6-Directional derivative 26:16 7-Second order Taylor polynomial"
YouTube Link 2024-10-23T21:45Z 14.1K followers, [----] engagements
"Multivariable functions (Calc 3; Lecture 2-1; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1120970874 We talk about multivariable functions including finding/sketching domain and level curves/surfaces For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-22T20:45Z 13.9K followers, [---] engagements
"Practice for Exam [--] = Sequences and series (Calc 2; Spring 25) A walkthrough of a practice exam for the sequences and series exam. These problems highlight a variety of ideas. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:45 1-Find term in sequence using recurrence 7:02 2-Find sum of telescoping series 15:04 3-Error bound for integral test 19:50 4-Interval of"
YouTube Link 2025-04-27T20:44Z 13.1K followers, [---] engagements
"Compound interest (Finite math; Lecture 16; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1123597974 * Compound interest (both discrete and continuous) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-01T15:22Z 14.1K followers, [--] engagements
"Dot product of vectors (Calc 3; Lecture 4; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1115629306 We discuss the dot product which can be used to compute the angle between vectors test orthogonality and carry out projection. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-03T21:14Z 13.7K followers, [---] engagements
"(Spectral; Fall 23) [--] - Properties of Laplacian including joins Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ We continue the discussion of the Laplacian matrix including complements join and the introduction of the signed incidence matrix"
YouTube Link 2023-10-12T22:46Z 13.4K followers, [---] engagements
"Logarithmic functions (Finite math; Lecture 14; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1122269921 * Inverse functions * Logarithmic functions Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-26T16:44Z 14K followers, [--] engagements
"(DiffEQ Fall 23) [--] - Matrix exponentials In this lecture we introduce the fundamental matrix see how it connects to matrix exponentials and how to use this to find solutions. We also look at what happens in the 2x2 case for repeated eigenvectors giving an alternative to what was done in the previous lecture. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/ 0:00 Introduction to idea of matrix exponentials 4:49 Fundamental matrices; exponential matrix 14:39 Example (fundamental matrix) 27:08 Computing matrix exponential as series 29:44 Example"
YouTube Link 2023-10-15T15:09Z [----] followers, [---] engagements
"Polar Cylindrical and Spherical coordinates (Calc 3; Lecture 2; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1113707001 We discuss other coordinate systems which use combinations of distances and directions (=angles). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-08-27T20:52Z 13.6K followers, [---] engagements
"Diff Eq Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Differential Equations administered in Fall [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:23 1-Linear first-order + separable 7:46 2-General solution to nonhomogeneous 15:45 3-Exact ODE 19:57 4-First order substitution 24:39 5-Autonomous ODE 30:54 6-Wronskian"
YouTube Link 2025-02-27T14:57Z 12.6K followers, [---] engagements
"Vectors (Calc 3; Lecture 3; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1114370452 We discuss vectors including geometric and component approaches; adding and scaling; magnitude and direction (=unit vector); and midpoints. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-08-29T20:59Z 13.6K followers, [---] engagements
"Sequences; (geometric) series (Calc 2; Lecture 24; Spring 25) * Finish talking about sequences and finding the limit of a_n * Start talking about series and finding infinite sums by looking at the limit of partial sums. We then turn to finding the value of geometric series (=(first term)/(1-(multiplying factor))). For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-02T15:32Z 12.9K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:07 1-Find term in sequence from recurrence 3:13 2-Find limit of sequence 5:00 3-Find limit of sequence from recurrence 7:10 4-Determine which series converge 10:44 5-Determine convergence type for series 13:26 6-Taylor polynomial question 18:03 7-Sum of telescoping series 26:43 8-Apply integral test 33:44 9-Interval of convergence 43:23 10-Error bound for Taylor"
YouTube Link 2025-04-27T17:53Z 13.1K followers, [---] engagements
"Applications of parameterized curves and introduction to polar (Calc 2; Lecture 9; Spring 25) * We go through some applications of parameterized curves (e.g. surface area mass area). * Introduction to polar coordinates. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-10T16:21Z 12.4K followers, [---] engagements
"More practice with center of mass; start of parameterized curves (Calc 2; Lecture 7; Spring 25) * More practice related to mass and center of mass. * Introduction of parameterized curves. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-05T16:29Z 12.4K followers, [---] engagements
"Practice for Exam [--] = Techniques of integration (Calc 2; Spring 25) A walkthrough of a practice exam for the techniques of integration exam. These problems highlight a variety of ideas. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 3:41 1-Integration by parts (loop back) 18:21 1-Integration by parts -- alternate solution 24:43 2-Power reduction for trig 32:23 3-Identify"
YouTube Link 2025-03-16T20:48Z 12.7K followers, [---] engagements
"Polynomials (Finite math; Lecture 02; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1113608508 * What are polynomials * How to add and multiply polynomials Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-08-27T15:19Z 13.6K followers, [--] engagements
"Stokes' Theorem (Calc 3; Lecture 35; Fall 24) We start looking at Stokes' Theorem; a generalization of Green's Theorem to exciting 3D. Lecture recorded in class on Monday December [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-12-02T23:04Z 11.9K followers, [---] engagements
"Working in polar and graphing (Calc 2; Lecture 10; Spring 25) * We work through examples of how to change equations between cartesian and polar. * Introduction to graphing in polar (hint: connect the dots of interesting points). For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-12T17:36Z 12.4K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-Newton's Method to find intersections 5:02 2-Area between two curves 10:08 3-L'Hospital to find limits 19:29 4-Use initial conditions to find antiderivative 24:27 5-Fundamental Theorem of Calculus 29:20 6-Riemann sums"
YouTube Link 2024-11-25T18:25Z 11.8K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:31 1-Ratio and root tests 8:19 2-Direct and limit comparison tests 18:36 3-Integral test 25:34 4-Interval of convergence 34:41 5-Telescoping sums 41:13 6-Taylor polynomial + error bound"
YouTube Link 2025-04-27T16:13Z 13.1K followers, [---] engagements
"Week [--] review problems for Calculus [--] (Spring 2025) --- Convergence test for series A set of problems that cover material from the eleventh week of Calculus [--] (e.g. convergence tests including integral test direct comparison test limit comparison test root test and ratio test). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:45 1-Apply Direct Comparison Test 8:54 2-Apply Limit Comparison Test (get rid of noise) 18:50 3-Set C for Ratio Test convergence 25:07 4-Apply Ratio Test 38:37"
YouTube Link 2025-04-12T23:05Z 13.2K followers, [----] engagements
"Calculus [--] Session [--] -- Absolute (global) max/min Course site: http://math265.org Instructor: Steve Butler (http://mathbutler.org)"
YouTube Link 2019-10-18T16:45Z 11.4K followers, [----] engagements
"Separable differential equations (Calc 1; Lecture 35; Fall 24) We look at separable differential equations; these can be solved by "separate; integrate; uncomplicate". Lecture recorded in class on Monday December [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-12-02T23:06Z 11.9K followers, [---] engagements
"Optimization; round [--] (Calc 1; Lecture 22; Fall 24) Second day of doing optimization (blending of word problems with max and min). Lecture recorded in class on Monday October [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-10-21T22:14Z 14.1K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:47 1-Take a second-order partial derivative 3:36 2-Chain rule 10:25 3-Identify contour map 12:44 4-Find a second-order Taylor polynomial 17:16 5-Find a critical point 20:04 6-Implicit differentiation 26:45 7-Gradient directional derivative gradient properties 34:33 8-Tangent plane (=linear approximation) to level surface 42:35 9-Find and classify all critical"
YouTube Link 2025-03-23T02:26Z 12.7K followers, [---] engagements
"Applications for Taylor series (Part 2) (Calc 2; Lecture 37; Spring 25) * Applications for Taylor series ** Finding some sums ** Integration For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-05-07T16:06Z 13.2K followers, [---] engagements
"Derivative as a function (Calc 1; Lecture 7; Fall 24) An introduction to derivatives as a function and the ever important using the limit definition to take derivatives. Lecture recorded in class on Wednesday September [--] [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-09-11T22:02Z 11.4K followers, [---] engagements
"Ratio and root tests for series (Calc 2; Lecture 28; Spring 25) * Ratio test = limit of a_(n+1)/a_n * Root test = limit of a_n(1/n) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-11T16:36Z 12.9K followers, [--] engagements
"Calculus with power series (Calc 2; Lecture 32; Spring 25) * More practice with interval of convergence * Calculus of power series (work term-by-term) For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-21T15:41Z 13K followers, [---] engagements
"Practice and review of trig substitution and partial fractions (Calc 2; Lecture 18; Spring 25) * Practice and review of trig substitution and partial fractions For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-03-07T16:11Z 12.7K followers, [---] engagements
"Quadric surfaces (Calc 3; Lecture 7; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1117592701 We go through some strategies of how to work with lines and/or planes. We (briefly) also go through the quadric surfaces. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-10T21:22Z 13.8K followers, [---] engagements
"(DiffEQ Fall 23) Review of ODE Systems We sprint through the material covering ODE systems. This is meant to be a brief discussion of the main ideas and so does not go into much detail. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/"
YouTube Link 2023-10-23T15:14Z 11.4K followers, [---] engagements
"Rational expressions (Finite math; Lecture 04; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1115526418 * Working with rational expressions; a wonderful blending of fractions and polynomials. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-09-03T15:22Z 13.7K followers, [--] engagements
"Integration involving trigonometry and applications (Calc 2; Lecture 15; Spring 25) * Finish with integration involving trigonometry * Brief discussion with applications For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-28T17:10Z 12.6K followers, [---] engagements
"Week [--] review problems for Calculus [--] (Spring 2025) --- Length surface area work force A set of problems that cover material from the second week of Calculus [--] (e.g. using integration to find length surface area work and force). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:56 1-Set up integral for surface area (two directions) 11:44 2-Work problem for a spring 18:55 3-Work lifting person up to a chopper 30:38 4-Force on window in an aquarium 39:12 5-Find perimeter around region 48:16"
YouTube Link 2025-02-01T01:02Z 12.4K followers, [----] engagements
"Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1120453169 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:52 1-Describe region given by inequalities 3:54 2-Find direction vector of intersection of planes 8:22 3-Orthogonality of two vectors 10:22 4-Using decomposition of acceleration 12:26 5-Scaling vector to right length 15:05 6-Find formula for volume of sphere 19:40 7-Find volume given in"
YouTube Link 2025-09-20T17:47Z 13.9K followers, [---] engagements
"(Physics) applications of integration (Calc 3; Lecture 25; Fall 24) We discuss applications of integration with a particular eye on physics. Lecture recorded in class on Friday November [--] [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2024-11-01T22:44Z 11.4K followers, [---] engagements
"Factoring (Finite math; Lecture 03; Spring 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1114369142 * Facoring (or at least one possible approach to factoring) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-08-29T20:58Z 13.6K followers, [--] engagements
"(Spectral; Fall 23) [--] - Adjacency matrix as walk counting matrix; Perron-Frobenius Theorem Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ In this video we work through how to use the adjacency matrix to count walks how the adjacency matrix can detect properties including bipartiteness number of edges number of triangles and odd girth. We also have a brief discussion about Perron-Frobenius. 0:00 Similarity argument for bipartite graphs 6:58 Counting walks 19:28 Applications of counting walks 29:51 Bipartite and symmetry of eigenvalues 34:35 Odd"
YouTube Link 2023-09-06T20:50Z 11.4K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Calculus [--] administered in Fall [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:03 1-Newton's Method 3:45 2-Riemann sum (midpoint) 7:27 3-Using sum notation 12:33 4-Mean Value Theorem for derivatives 17:00 5-u-substitution (indefinite) 21:11 6-u-substitution (definite) 26:02 7-Indeterminate limits 34:13 8-Indefinite integrals 39:27 9-Area between curves 50:48 10-Integrals as area; Fundamental Theorem of Calculus"
YouTube Link 2025-04-29T00:41Z 13.1K followers, [---] engagements
"Diff Eq Exam [--] walkthrough (Fall 2024) A walk-through of the solutions for Exam [--] of Differential Equations administered in Fall [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:58 1-Laplace and inverse Laplace transforms 7:22 2-Use Laplace transform to solve diff. eq. 16:10 3-Laplace of piecewise function 23:34 4-Diff. eq. with delta function 30:05 5-Recurrence relationship for series solution 41:53 6-Find first few coefficients for series solution"
YouTube Link 2025-04-29T14:26Z 13.1K followers, [---] engagements
"Taylor series (Calc 2; Lecture 34; Spring 25) * Taylor series For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-25T15:47Z 13K followers, [---] engagements
"(DiffEQ Fall 23) [--] - Spring-Mass-Damper systems We discuss spring-mass-damper systems which have the generic form of mx'''+cx'+kx=0 where m is mass c is damping constant and k is spring constant. We also talk about the different types of behavior that can occur e.g. undamped under damped critically damped and over damped. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/ 0:00 Setup of spring-mass-damper systems 5:38 Example (spring-mass-damper system) 17:49 Types of behavior for damping 26:29 Example (critical damping)"
YouTube Link 2023-09-16T22:24Z 11.4K followers, [----] engagements
"Week [--] review problems for Calculus [--] (Spring 2025) --- Integration by parts and trig integrals A set of problems that cover material from the sixth week of Calculus [--] (e.g. using integration by parts trig integrals and applications involving these techniques). For more information including scanned copies of the material: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:11 1-By parts with log (and surprise arctan) 10:56 2-By parts w/ unknown function 18:26 3-Integral of sin3 25:18 4-Integral with secants and tangents 33:24 5-Reduction formula 39:23"
YouTube Link 2025-03-02T07:34Z 12.6K followers, [----] engagements
"Solutions to practice exam [--] (Calc 3; Fall 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1121185836 The one where we walk through the solutions of practice Exam [--] from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org 0:00 Intro 0:33 1-Identify solid from inequalities 7:13 2-Find angle between rays in spherical coordinates 17:44 3-Distance between a point and a line 26:25 4-Identify quadric surface 30:13 5-Find tangent line not intersecting a plane 39:11 6-Find distance a particle"
YouTube Link 2025-09-24T20:00Z 14K followers, [---] engagements
"Annuities part [--] (Finite math; Lecture 18; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1124877369 * Annuities (finding the value of many payments over time) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-06T15:23Z 14.1K followers, [--] engagements
"Solutions to practice exam 3-A (Calc 3; Fall 2024) The one where we walk through the solutions of practice Exam 3-A from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org Problems and scanned solutions can be found in the website https://www.calc3.org by going to the Fall [--] page and scrolling down to Week fourteen. 0:00 Intro 0:29 1-2D change order of integration 10:40 2-Identify 3D region of integration 17:27 3-Find curl 22:22 4-Identify conservative vector function 32:01 5-Line integral"
YouTube Link 2024-11-28T01:18Z 11.8K followers, [---] engagements
"Practice with convergence tests (Calc 2; Lecture 30; Spring 25) * Review and practice with tests for convergence For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-04-16T15:27Z 12.9K followers, [---] engagements
"Examples in Calc [--] class on April [--] [----] (day before Exam 3) For more information visit: https://www.calc2.org Presented by Steve Butler: https://www.stevebutler.org"
YouTube Link 2025-04-30T15:41Z 13.1K followers, [---] engagements
"Augmented matrices (Finite math; Lecture 21; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1127556008 * Introduced matrices particularly augmented matrices and how they can relate to systems of equations. * Translate manipulation of systems of equations to row operations. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-15T15:15Z 14.2K followers, [--] engagements
"Partial derivatives (Calc 3; Lecture 2-2; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1123002745 We talk about importance of simplifying for a few minutes. We then get into the main topic of the day which is partial derivatives including notation and higher order derivatives. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-09-29T21:01Z 14.1K followers, [---] engagements
"Applications for Taylor series (Part 3) (Calc 2; Lecture 38; Spring 25) * Applications for Taylor series ** Finding indeterminates For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-05-09T15:15Z 13.2K followers, [---] engagements
"Linear inequalities (Finite math; Lecture 28; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1133177159 * Introduction to linear inequalities. * Bit of practice with word problems. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-11-03T16:15Z 14.4K followers, [--] engagements
"Comments made in Calc [--] class on February [--] [----] (day before Exam 1) For more information visit: https://www.calc2.org Presented by Steve Butler: https://www.stevebutler.org"
YouTube Link 2025-02-19T16:26Z 12.5K followers, [---] engagements
"Matrix inverse; Identity matrix (Finite math; Lecture 25; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1130945068 * Identity matrix acting like "1" in multiplication of matrices. * Matrix inverses. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-27T15:16Z 14.4K followers, [--] engagements
"Integration in polar coordinates (Calc 3; Lecture 3-3; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1131070677 * Integrating in polar coordinates; including (re)writing integrals in polar coordinates. * The three parts to every integral problem. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-27T20:40Z 14.4K followers, [---] engagements
"Conditional probability and independence (Finite math; Lecture 37; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1143134866 * Conditional probability * Probability trees * Independence Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-12-03T16:23Z 15.1K followers, [---] engagements
"(Spectral; Fall 23) [--] - A few more comments about Laplacian; introduction to signless Laplacian Course site: https://www.stevebutler.org/spectral2023 Presenter: https://www.stevebutler.org/ We give a few additional comments about the Laplacian matrix including why is the product of the nonzero eigenvalues an integer why do we call it the Laplacian what is spectral partitioning and spectral graph drawing. We then introduce the signless Laplacian matrix which is the optimistic version of the Laplacian Q=D+A and discuss a few basic properties"
YouTube Link 2023-10-18T20:36Z 14.6K followers, [---] engagements
"Integration in cylindrical and spherical coordinates (Calc 3; Lecture 3-6; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1133277054 * Finish discussing applications particularly inertia. * Discuss integration in cylindrical and spherical coordinates. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-11-03T21:46Z 14.4K followers, [---] engagements
"Properties of the gradient; tangent planes to implicit surfaces (Calc 3; Lecture 2-5; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1124996830 * Some practice with directional derivative * Properties of the gradient (greatest increase / decrease) * Tangent plane to implicit surface For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-06T22:06Z 14.3K followers, [---] engagements
"Lagrange multipliers -- bonus problem (Calc 3; Lecture 2-9; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1128345396 * One more problem done using Lagrange multiplier method for solving constrained optimization. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-17T20:42Z 14.2K followers, [--] engagements
"Introduction to probability (Finite math; Lecture 34; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1137749915 * Sample spaces; events * Probability Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-11-17T16:48Z 15.1K followers, [---] engagements
"Stokes' Theorem (Calc 3; Lecture 3-15; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1145019471 * Stokes' Theorem For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-12-09T20:41Z 15.1K followers, [---] engagements
"Standard deviation (Finite math; Lecture 40; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1145324028 * Standard deviation Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-12-10T16:44Z 15.1K followers, [---] engagements
"Integration by parts (Calc 2; Lecture 13; Spring 25) * Introduction to the techniques of integration portion of the course. * Integration by parts For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-24T17:30Z 12.6K followers, [---] engagements
"Triple integrals (Calc 3; Lecture 3-4; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1131862739 * Setting up integrals over solids (=triple integrals). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-29T21:39Z 14.4K followers, [---] engagements
"Bayes' formula and Expected value (Finite math; Lecture 38; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1143881421 * Bayes formula * Expected value Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-12-05T16:07Z 15.1K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1120453466 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:56 1-Average rate of change of a function 4:17 2-Finding tangent lines perpendicular to given line 7:34 3-Vertical and horizontal asymptotes 12:02 4-Making a function continuous 18:25 5-Testing types of discontinuity 22:01 6-Applying product and chain rules 26:59 7-Using the limit definition of"
YouTube Link 2025-09-20T17:49Z 14.5K followers, [----] engagements
"Solving systems (Finite math; Lecture 27; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1132549190 * Solving systems using matrices. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-31T15:26Z 14.4K followers, [--] engagements
"Changing order of integration (Calc 3; Lecture 3-2; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1128990217 * Using bounds to find the region and vice-versa. * Changing order of integration (from dx dy to dy dx and vice versa). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-20T20:51Z 14.3K followers, [---] engagements
"Sets (Finite math; Lecture 31; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1135449088 * Sets Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-11-10T18:24Z 15.1K followers, [---] engagements
"Linear programming (Finite math; Lecture 30; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1134690892 * Linear programming (test the corners) Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-11-07T18:08Z 14.4K followers, [--] engagements
"Vector-valued functions; grad div and curl (Calc 3; Lecture 3-9; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1135514550 * Vector-valued functions. * Gradient (grad) Divergence (div) and Curl (curl). For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-11-10T21:40Z 15.1K followers, [---] engagements
"More practice with Stokes' Theorem and Gauss's Divergence Theorem (Calc 3; Lecture 3-17; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1146075363 * More practice with Stokes' Theorem and Gauss's Divergence Theorem * Four variations of the Fundamental Theorem of Calculus For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-12-12T21:50Z 15.1K followers, [---] engagements
"Two equations and two unknowns (Finite math; Lecture 20; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1126868599 * Start working on systems of equations with the classic of two equations with two unknowns. * Solving by graphing substitution elimination Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-13T15:11Z 14.5K followers, [---] engagements
"Surface area (Calc 3; Lecture 3-13; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1138718900 * More about Green's Theorem * Area of surfaces For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-11-19T23:37Z 15.1K followers, [---] engagements
"Gauss-Jordan elimination (Finite math; Lecture 22; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1128903266 * Reduced form of matrices. * Gauss-Jordan elimination. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-20T15:48Z 14.4K followers, [---] engagements
"Practice 2-A problems for Calculus [--] (Fall 2025) -- partial derivatives and friends Vimeo (ad-free) link to same video: https://vimeo.com/1123936930 A set of problems that cover material from the first week of the second block for Calculus [--] (e.g. multivariable functions partial derivatives implicit differentiation chain rule gradient). For more information including scanned copies of the material: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:35 1-Find domain; give level surface 9:42 2-Sketch and label level curves 18:52 3-Steepest descent 29:52"
YouTube Link 2025-10-02T15:49Z 14.3K followers, [----] engagements
"Tangent lines and area for polar (Calc 2; Lecture 11; Spring 25) * We go through how to find tangent lines for polar curves by reducing to parametric. * We work through how to find area in polar curves which boils down to finding wedges and adding many wedges together. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-14T16:43Z 12.5K followers, [---] engagements
"Odds (Finite math; Lecture 36; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1139363471 * Odds Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-11-21T16:06Z 15.1K followers, [--] engagements
"Matrix inverse practice; solving systems (Finite math; Lecture 26; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1131728260 * More practice with inverses of matrices. * Solving systems using matrices. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-29T15:18Z 14.4K followers, [--] engagements
"Line integrals -- an introduction (Calc 3; Lecture 3-10; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1136268979 * Line integrals For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-11-12T21:56Z 15.1K followers, [---] engagements
"More practice with probability (Finite math; Lecture 35; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1138583906 * Empirical probability * Union intersection and complement Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-11-19T16:57Z 15.1K followers, [--] engagements
"Applications (Calc 3; Lecture 3-5; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1132638458 * Applications in physics mass moment and a touch of inertia. For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-10-31T20:44Z 14.4K followers, [---] engagements
"Practice for Exam [--] = Matrices and Linear Equations (Finite math; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1134095791 A walkthrough of a practice exam for the third exam dealing with the topics of matrices and linear equations. These problems are slight variations of the posted practice exam. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.businessmath.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 1-This is"
YouTube Link 2025-11-06T05:01Z 14.4K followers, [---] engagements
"Algebra review (Diff. Eq.; Lecture 1-2; Spring 2026) Vimeo (ad-free) link to same video: https://vimeo.com/1157413275 * Review of algebra tools that will show up in the course For more information: https://www.calc4.org/spring-2026 Presenter: Steve Butler (https://www.stevebutler.org/) differential equations differential equations"
YouTube Link 2026-01-23T01:46Z 15.1K followers, [---] engagements
"Systems of linear inequalities (Finite math; Lecture 29; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1133917745 * Systems of linear inequalities. * Bounded vs unbounded. * Corner points Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-11-05T17:46Z 14.4K followers, [--] engagements
"Calc [--] Final walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1146397506 A walk-through of the solutions for the Final of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:44 1-Find point where tangent line passes through 3:48 2-Motion of a particle 6:21 3-Find equation y satisfies 11:49 4-Dealing with sum notation 14:26 5-Finding properties of function from graph 19:24 6-Integration using substitution 25:42 7-Second derivative of an inverse 32:09 8-Using"
YouTube Link 2025-12-14T21:08Z 15.1K followers, [----] engagements
"(DiffEQ Fall 23) [--] - Higher order ODEs; Wronskian We start into higher order ODEs. We discuss linear ODEs superposition Wronskian and some basic solutions to constant coefficient linear homogeneous ODEs. More information: https://www.calc4.org/flipped-fall-2023 Presenter: https://www.stevebutler.org/ 0:00 Introduction to higher order ODEs 3:49 Superposition for linear ODEs 14:41 Example (using superposition) 22:18 Wronskian 27:48 Example (computing Wronskian) 31:44 Constant coefficient linear homogeneous ODEs 36:10 Example (finding solution to second-order ODE)"
YouTube Link 2023-09-10T18:05Z 14.6K followers, [----] engagements
"Solutions to practice exam [--] (Calc 3; Fall 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1142768957 The one where we walk through the solutions of practice Exam [--] from Fall [----] Calc [--] (aka multivariable class). Presenter: Steve Butler (https://www.stevebutler.org/) Additional materials: https://www.calc3.org 0:00 Intro 0:52 1-Find a divergence 5:02 2-Orient curve for Green's Theorem 14:37 3-Integrate by changing order of integration 24:17 4-Switching between spherical and cylindrical integration 36:34 5-Identify a conservative function 43:48 6-Set up integral to find flux"
YouTube Link 2025-12-03T21:00Z 15.1K followers, [----] engagements
"Practice for Exam [--] = Functions and financial math (Finite math; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1126053363 A walkthrough of a practice exam for the first exam dealing with the topics of algebra and lines. These problems are slight variations of the posted practice exam. This is NOT the test but is a good way to practice for the test. For best results you should practice as many problems as you can from a wide variety of sources. For more information: https://www.businessmath.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro & [--] 1:59"
YouTube Link 2025-10-10T01:25Z 14.2K followers, [----] engagements
"Counting (Finite math; Lecture 32; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1136169749 * Counting; addition and multiplication Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-11-12T16:54Z 15.1K followers, [---] engagements
"Verifying solutions (Diff. Eq.; Lecture 1-3; Spring 2026) Vimeo (ad-free) link to same video: https://vimeo.com/1158509697 * Verifying solutions * Plugging in and setting parameters to make a solution * Initial condition problems * Word problems and differential equations * Existence and uniqueness For more information: https://www.calc4.org/spring-2026 Presenter: Steve Butler (https://www.stevebutler.org/) differential equations differential equations"
YouTube Link 2026-01-26T18:30Z 15.1K followers, [---] engagements
"Diff Eq Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1139636229 A walk-through of the solutions for Exam [--] of Differential Equations administered in Spring [----]. For more information: https://www.calc4.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 1:06 1-Inverse Laplace (partial fractions) 9:54 2-Laplace transform of piecewise function 19:03 3-Finding some inverse Laplace expressions 32:33 4-Set up and solve diff. eq. with delta 47:29 5-Find first few terms in series solution 56:00 6-Find recurrence relation of series solution"
YouTube Link 2025-11-22T16:15Z 15.1K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1138200604 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:43 1-Grad div curl 3:32 2-Set up volume in cylindrical 12:08 3-Find potential function 14:40 4-Make sure function is conservative 17:36 5-Green's Theorem problem 21:10 6-Surface area of paraboloid 29:42 7-Line integral (put in terms of t) 35:03 8-Substitution / change of variables 46:33"
YouTube Link 2025-11-18T19:09Z 15.1K followers, [----] engagements
"Calculus [--] -- Limits with infinity -- Overview Presenter: Steve Butler (http://mathbutler.org) Course website: http://calc1.org 0:00 Introduction 1:15 Limits with infinity 6:19 Horizontal asymptotes 13:36 Vertical asymptotes"
YouTube Link 2020-06-10T23:45Z 14.3K followers, [----] engagements
"Calc [--] Final walkthrough (Fall 2024) Vimeo (ad-free) link to same video: https://vimeo.com/1146397327 A walk-through of the solutions for the Final of Calculus [--] administered in Fall [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:51 1-Limit of indeterminant (L'Hospital) 2:32 2-Limit definition of derivative 5:30 3-Product rule 6:59 4-Motion of a particle 9:53 5-Derivative rules (be careful with constants) 13:41 6-Absolute maximum 17:36 7-Using algebra to do an integral 21:05 8-Integration using substitution 25:14"
YouTube Link 2025-12-14T21:08Z 15.1K followers, [---] engagements
"Calc [--] Final walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1146637590 A walk-through of the solutions for the Final of Calculus [--] administered in Spring [----]. For more information: https://www.calc3.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:47 1-Angle between planes 5:01 2-Use linearization (tangent planes) to estimate 10:13 3-Identify quadric surfaces 15:56 4-Find max rate of change (magnitude of gradient) 20:15 5-Find average of a function 26:26 6-Distance between centers 29:14 7-Find projection of vectors 32:03 8-Find speed"
YouTube Link 2025-12-15T16:58Z 15.1K followers, [----] engagements
"Applications of Gauss-Jordan and matrices (Finite math; Lecture 23; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1129567314 * Applications with Gauss-Jordan elimination. * Adding/scaling/comparing matrices (work entry-by-entry). Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-22T15:27Z 14.3K followers, [--] engagements
"Green's Theorem (Calc 3; Lecture 3-12; Fall 25) Vimeo (ad-free) link to same video: https://vimeo.com/1137857757 * More practice with conservative line integrals and finding potential functions * Green's Theorem * Practice with Green's Theorem For more information: https://www.calc3.org/fall-25 Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-11-17T21:47Z 15.1K followers, [---] engagements
"Calc [--] Exam [--] walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1138190176 A walk-through of the solutions for Exam [--] of Calculus [--] administered in Spring [----]. For more information: https://www.calc1.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:40 1-L'Hospital 2:47 2-Evaluate indefinite integral 5:33 3-Mean Value Theorem 7:57 4-Riemann sum (left endpoints) 10:18 5-Substitution 13:29 6-Fundamental Theorem of Calculus 18:13 7-Newton's Method (finding roots) 25:27 8-Area of a region (slice horizontally) 32:32 9-Integrals using"
YouTube Link 2025-11-18T19:09Z 15.1K followers, [---] engagements
"Arc length for polar curves (Calc 2; Lecture 12; Spring 25) * We go through how to find arc length for polar curves (spoiler we do it by linking back to parametric curves). For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/)"
YouTube Link 2025-02-17T16:50Z 12.5K followers, [---] engagements
"Matrix multiplication (Finite math; Lecture 24; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1130258433 * Different view of what a matrix represents. * Matrix multiplication. Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-24T15:26Z 14.3K followers, [--] engagements
"Calc [--] Final walkthrough (Spring 2025) Vimeo (ad-free) link to same video: https://vimeo.com/1146815456 A walk-through of the solutions for the Final of Calculus [--] administered in Spring [----]. For more information: https://www.calc2.org/ Presenter: Steve Butler (https://www.stevebutler.org/) 0:00 Intro 0:58 1-Trapezoid rule 5:08 2-Center of mass of wire (1D) 12:12 3-Improper integral 15:17 4-Sum of geometric series 19:58 5-Direct comparison test 23:10 6-Center of power series 25:38 7-Find sum of geometric series 29:01 8-Find coefficient in Taylor series 34:16 9-Find length of parametric curve"
YouTube Link 2025-12-16T04:15Z 15.1K followers, [---] engagements
"Annual Percentage Yield = APY (Finite math; Lecture 17; Fall 25) Vimeo (ad-free) link to the same video: https://vimeo.com/1124244003 * Annual Percentage Yield (APY) -- The answer to the question what would be the equivalent if we just donated once a year Course site: https://www.businessmath.org/fall-25 Presenter: https://www.stevebutler.org"
YouTube Link 2025-10-03T15:12Z 14.3K followers, [--] engagements
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