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[@blackpenredpen](/creator/youtube/blackpenredpen)
"How to do epsilon-delta proofs (ultimate calculus guide)"  
[YouTube Link](https://youtube.com/watch?v=AfrnYS5S8VE) [@blackpenredpen](/creator/youtube/blackpenredpen) 2023-09-02T05:09Z 1.4M followers, 204.5K engagements


"how to easily write the epsilon-delta proofs for limits"  
[YouTube Link](https://youtube.com/watch?v=4pRMej3DnEM) [@blackpenredpen](/creator/youtube/blackpenredpen) 2020-11-17T22:00Z 1.4M followers, 374.5K engagements


"Its not joke its rigorous enough for physics 😂"  
[YouTube Link](https://youtube.com/watch?v=6JVsIwVQcpg) [@blackpenredpen](/creator/youtube/blackpenredpen) 2025-09-27T12:00Z 1.4M followers, 155.2K engagements


"My first abstract algebra problem in XX years"  
[YouTube Link](https://youtube.com/watch?v=EgO3GwZ07EA) [@blackpenredpen](/creator/youtube/blackpenredpen) 2025-09-18T11:58Z 1.4M followers, 100.4K engagements


"You me and my first International Math Olympiad problem"  
[YouTube Link](https://youtube.com/watch?v=QNPq4VKD7ic) [@blackpenredpen](/creator/youtube/blackpenredpen) 2020-04-10T22:07Z 1.4M followers, 645.4K engagements


"epsilon-N definition for a limit at infinity (introduction & how to write the proof)"  
[YouTube Link](https://youtube.com/watch?v=9JMFLzHtljA) [@blackpenredpen](/creator/youtube/blackpenredpen) 2023-08-23T10:00Z 1.4M followers, 101.3K engagements


"exact value of sin(3 degrees)"  
[YouTube Link](https://youtube.com/watch?v=GldJWGojFcs) [@blackpenredpen](/creator/youtube/blackpenredpen) 2019-06-05T19:42Z 1.4M followers, 457.2K engagements


"Euler's Method (introduction & example)"  
[YouTube Link](https://youtube.com/watch?v=Pm_JWX6DI1I) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-10-18T16:00Z 1.4M followers, 134.7K engagements


"So you want to prove the cubic formula (from scratch)"  
[YouTube Link](https://youtube.com/watch?v=ULsPhWmqhyc) [@blackpenredpen](/creator/youtube/blackpenredpen) 2023-04-18T17:12Z 1.4M followers, 418K engagements


"fast way to do partial fraction for integrals calculus X tutorial"  
[YouTube Link](https://youtube.com/watch?v=aF4o_c46VnI) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-02-28T08:24Z 1.4M followers, 167.3K engagements


"Ultimate Trig Identity Study Guide"  
[YouTube Link](https://youtube.com/watch?v=crlbRkEZAdw) [@blackpenredpen](/creator/youtube/blackpenredpen) 2023-09-05T14:14Z 1.4M followers, 95.8K engagements


"100 series convergence tests (no food no water no stop)"  
[YouTube Link](https://youtube.com/watch?v=jTuTEcwvkP4) [@blackpenredpen](/creator/youtube/blackpenredpen) 2019-05-06T23:56Z 1.4M followers, 3.6M engagements


"3 factoring tricks that you probably didnt know"  
[YouTube Link](https://youtube.com/watch?v=lWymNeIjA20) [@blackpenredpen](/creator/youtube/blackpenredpen) 2022-09-18T11:00Z 1.4M followers, 168.7K engagements


"What Integration Technique Should I Use (trig sub u sub DI method partial fractions) calculus 2"  
[YouTube Link](https://youtube.com/watch?v=M5MaGUO0JDs) [@blackpenredpen](/creator/youtube/blackpenredpen) 2019-02-19T18:52Z 1.4M followers, 1.7M engagements


"100 integrals (world record)"  
[YouTube Link](https://youtube.com/watch?v=dgm4-3-Iv3s) [@blackpenredpen](/creator/youtube/blackpenredpen) 2019-03-03T17:00Z 1.4M followers, 12.5M engagements


"The Limit (do not use L'Hospital rule)"  
[YouTube Link](https://youtube.com/watch?v=mZiPdyHyUvE) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-12-08T21:10Z 1.4M followers, 739K engagements


"integral of sin(x)/x from X to inf by Feynman's Technique"  
[YouTube Link](https://youtube.com/watch?v=s1zhYD4x6mY) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-08-20T18:30Z 1.4M followers, 1.3M engagements


"integration by parts DI method VERY EASY"  
[YouTube Link](https://youtube.com/watch?v=2I-_SV8cwsw) [@blackpenredpen](/creator/youtube/blackpenredpen) 2016-02-20T09:59Z 1.4M followers, 1.8M engagements


"solve differential equation with substitution"  
[YouTube Link](https://youtube.com/watch?v=3d8j_r2L16w) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-02-14T08:35Z 1.4M followers, 157.8K engagements


"First Order Linear Differential Equation & Integrating Factor (introduction & example)"  
[YouTube Link](https://youtube.com/watch?v=DJsjZ5aYK_g) [@blackpenredpen](/creator/youtube/blackpenredpen) 2016-12-31T03:11Z 1.4M followers, 697K engagements


"epsilon-delta definition ultimate introduction"  
[YouTube Link](https://youtube.com/watch?v=DdtEQk_DHQs) [@blackpenredpen](/creator/youtube/blackpenredpen) 2022-01-15T12:00Z 1.4M followers, 505.4K engagements


"MIT integration bee qualifier test"  
[YouTube Link](https://youtube.com/watch?v=E61uz0Yn8dM) [@blackpenredpen](/creator/youtube/blackpenredpen) 2021-08-21T13:00Z 1.4M followers, 398.7K engagements


"Eulers identity proof for calculus X students"  
[YouTube Link](https://youtube.com/watch?v=Jqt67tJCiwQ) [@blackpenredpen](/creator/youtube/blackpenredpen) 2021-11-22T11:00Z 1.4M followers, 165.6K engagements


"How to epsilon-delta #shorts"  
[YouTube Link](https://youtube.com/watch?v=KSEwLfuYeJg) [@blackpenredpen](/creator/youtube/blackpenredpen) 2020-11-10T02:29Z 1.4M followers, 191.9K engagements


"100 calculus limits (ft epsilon-delta definition and Riemann sum limits )"  
[YouTube Link](https://youtube.com/watch?v=TglD4Y6lmQk) [@blackpenredpen](/creator/youtube/blackpenredpen) 2022-08-12T15:00Z 1.4M followers, 786.8K engagements


"Factoring a trinomial (what I learned in Taiwan vs in US)"  
[YouTube Link](https://youtube.com/watch?v=VaisiQxuTVY) [@blackpenredpen](/creator/youtube/blackpenredpen) 2025-08-13T13:22Z 1.4M followers, 51.4K engagements


"how Laplace solved the Gaussian integral"  
[YouTube Link](https://youtube.com/watch?v=tCPQSobqFh4) [@blackpenredpen](/creator/youtube/blackpenredpen) 2022-10-24T19:08Z 1.4M followers, 850.9K engagements


"Is dy/dx a fraction"  
[YouTube Link](https://youtube.com/watch?v=u-I3kF3Drkk) [@blackpenredpen](/creator/youtube/blackpenredpen) 2019-08-09T16:52Z 1.4M followers, 212.3K engagements


"Convert degrees minutes and seconds (dms) into decimal degrees"  
[YouTube Link](https://youtube.com/watch?v=wM-RHMAzPb0) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-02-12T05:00Z 1.4M followers, 116.1K engagements


"Convert decimal degrees to degrees minutes and seconds (dms)"  
[YouTube Link](https://youtube.com/watch?v=M0AHuWJjeSo) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-02-12T05:00Z 1.4M followers, 97K engagements


"Laplace Transform: Translation Theorem in s"  
[YouTube Link](https://youtube.com/watch?v=shVLuccijfU) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-04-14T03:13Z 1.4M followers, 46.4K engagements


"Solving polynomial equations but they get increasingly awesome"  
[YouTube Link](https://youtube.com/watch?v=-EDdRZcgLa4) [@blackpenredpen](/creator/youtube/blackpenredpen) 2022-06-01T11:00Z 1.4M followers, 1.3M engagements


"Arc Length (formula explained)"  
[YouTube Link](https://youtube.com/watch?v=PK7HZiFG_VI) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-10-27T08:12Z 1.4M followers, 258.8K engagements


"i did another XXX integrals"  
[YouTube Link](https://youtube.com/watch?v=SOJlKFiQJ4U) [@blackpenredpen](/creator/youtube/blackpenredpen) 2022-12-25T11:53Z 1.4M followers, 176.4K engagements


"the most famous Ramanujan sum 1+2+3+.=-1/12"  
[YouTube Link](https://youtube.com/watch?v=U_g_OZLt4OU) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-12-28T21:09Z 1.4M followers, 379.8K engagements


"how do we know the derivative of ln(x) is 1/x (the definition & implicit differentiation)"  
[YouTube Link](https://youtube.com/watch?v=Xc1YdpWcKsQ) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-09-25T14:30Z 1.4M followers, 789.5K engagements


"how is eex=1 solvable"  
[YouTube Link](https://youtube.com/watch?v=ckc9F0VjZ3k) [@blackpenredpen](/creator/youtube/blackpenredpen) 2023-09-25T07:38Z 1.4M followers, 786K engagements


"Why is the derivative of ex equal to ex"  
[YouTube Link](https://youtube.com/watch?v=oBlHiX6vrQY) [@blackpenredpen](/creator/youtube/blackpenredpen) 2021-08-08T08:40Z 1.4M followers, 441.3K engagements


"Solving x=sqrt(x-1/x)+sqrt(1-1/x) Math Stack Exchange"  
[YouTube Link](https://youtube.com/watch?v=x-IHueYbzuQ) [@blackpenredpen](/creator/youtube/blackpenredpen) 2024-11-19T08:44Z 1.4M followers, 95.4K engagements


"integral of ln(x) from X to 1"  
[YouTube Link](https://youtube.com/watch?v=5RhbrPAlx2E) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-01-17T18:45Z 1.4M followers, 285.7K engagements


"Pell's equation (Introduction & example) ft. @octopuskeng"  
[YouTube Link](https://youtube.com/watch?v=9WP8jMSwRDw) [@blackpenredpen](/creator/youtube/blackpenredpen) 2024-12-30T11:32Z 1.4M followers, 24.8K engagements


"Multiplication & Division in Base 2"  
[YouTube Link](https://youtube.com/watch?v=BnchEbti5t0) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-09-29T21:46Z 1.4M followers, 55.2K engagements


"Sum of 1/n3 Believe In Integrals"  
[YouTube Link](https://youtube.com/watch?v=Gfnfmut6zP0) [@blackpenredpen](/creator/youtube/blackpenredpen) 2019-05-17T16:00Z 1.4M followers, 96.8K engagements


"Ultimate Inverse Laplace Transform Tutorial"  
[YouTube Link](https://youtube.com/watch?v=Gx6yQcmLuH8) [@blackpenredpen](/creator/youtube/blackpenredpen) 2020-03-28T20:05Z 1.4M followers, 242.1K engagements


"solving a cubic equation by completing the cube"  
[YouTube Link](https://youtube.com/watch?v=Jz-Z0jfs2V4) [@blackpenredpen](/creator/youtube/blackpenredpen) 2020-05-25T17:06Z 1.4M followers, 125.6K engagements


"Lambert W Function (domain range approximation solving equations derivative & integral)"  
[YouTube Link](https://youtube.com/watch?v=Qb7JITsbyKs) [@blackpenredpen](/creator/youtube/blackpenredpen) 2021-01-05T22:00Z 1.4M followers, 265.8K engagements


"integral of csc(x) the standard result calculus X tutorial"  
[YouTube Link](https://youtube.com/watch?v=byB0Vz3dcsE) [@blackpenredpen](/creator/youtube/blackpenredpen) 2015-02-13T04:55Z 1.4M followers, 195.9K engagements


"My First Stanford Math Tournament Problem"  
[YouTube Link](https://youtube.com/watch?v=gYAQg7xn-Xo) [@blackpenredpen](/creator/youtube/blackpenredpen) 2021-09-24T10:10Z 1.4M followers, 369.2K engagements


"My First Harvard MIT Math Tournament Problem"  
[YouTube Link](https://youtube.com/watch?v=jQuArBZO7PI) [@blackpenredpen](/creator/youtube/blackpenredpen) 2021-09-04T07:32Z 1.4M followers, 349.8K engagements


"Laplace transform of 1"  
[YouTube Link](https://youtube.com/watch?v=nGMEGbAkTfk) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-04-11T07:06Z 1.4M followers, 112.6K engagements


"Auxiliary equations with complex roots for 2nd order linear differential equations"  
[YouTube Link](https://youtube.com/watch?v=u-eQaef1EWw) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-03-15T00:05Z 1.4M followers, 90.3K engagements


"delta y vs. dy (differential)"  
[YouTube Link](https://youtube.com/watch?v=2ooWs_8hzxQ) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-08-01T16:55Z 1.4M followers, 300.9K engagements


"Math for fun sin(z)=2"  
[YouTube Link](https://youtube.com/watch?v=3C_XD_cCeeI) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-07-10T22:00Z 1.4M followers, 2M engagements


"solve differential with laplace transform sect 7.5#3"  
[YouTube Link](https://youtube.com/watch?v=6jW7FCyapXE) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-04-20T07:20Z 1.4M followers, 269K engagements


"ln(-2) yes possible but NOT real"  
[YouTube Link](https://youtube.com/watch?v=IX_23EWpF5U) [@blackpenredpen](/creator/youtube/blackpenredpen) 2019-01-30T06:01Z 1.4M followers, 449.7K engagements


"Introduction to the Gamma function & the Pi function (extending the factorial)"  
[YouTube Link](https://youtube.com/watch?v=L4Trz6pFut4) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-01-15T08:18Z 1.4M followers, 410.2K engagements


"integral of cos(ln(x)) integration by parts (w/ u-sub vs without u-sub)"  
[YouTube Link](https://youtube.com/watch?v=PthIehmcNKA) [@blackpenredpen](/creator/youtube/blackpenredpen) 2018-09-08T01:44Z 1.4M followers, 148.9K engagements


"the ultimate integral starter (u sub IBP trig sub partial fractions & more)"  
[YouTube Link](https://youtube.com/watch?v=XOUwIdufY9Y) [@blackpenredpen](/creator/youtube/blackpenredpen) 2019-09-14T18:02Z 1.4M followers, 1.2M engagements


"Laplace transform of f(t-a)u(t-a) the shifted unit step function"  
[YouTube Link](https://youtube.com/watch?v=_Ovz4u8FL9k) [@blackpenredpen](/creator/youtube/blackpenredpen) 2017-04-29T19:18Z 1.4M followers, 150.6K engagements


"I want all trig functions in one integral"  
[YouTube Link](https://youtube.com/watch?v=yAFImJwzw_g) [@blackpenredpen](/creator/youtube/blackpenredpen) 2023-10-14T07:15Z 1.4M followers, 810.8K engagements


"Why I don't teach LIATE (integration by parts trick)"  
[YouTube Link](https://youtube.com/watch?v=z33rYYUM4d8) [@blackpenredpen](/creator/youtube/blackpenredpen) 2021-09-08T17:08Z 1.4M followers, 421.8K engagements