Laplace Transform Study Guide 📘

Learn all the Laplace transforms you need for your differential equation class. This tutorial video includes the Laplace transform of derivatives, Laplace transform of e^(at), Laplace transform of t^n, Laplace transform of sin(bt) & cost(bt), and Laplace transform of hyperbolic functions. Laplace transform properties such as the shift theorem or the convolution theorem. Some special Laplace transforms will be included such as the Laplace transform of the unit step function, Laplace transform of the Dirac Delta function, Laplace transform of sin(t)/t, Laplace transform of the first and second derivative of the function, Laplace transform of ln(t), and more.

Inverse Laplace Marathon: 👉 https://youtu.be/Gx6yQcmLuH8
Laplace for you t-shirt: 👉 https://amzn.to/3MV933x
File: 👉https://www.patreon.com/posts/files-to-laplace-95154820?

0:00 start
Q1, Laplace Transform of e^(at), 1:16,
Q2, Laplace Transform of t^n, 6:14,
Q3, Q4, Laplace Transform of sin(bt) & cost(bt), 17:51,
Q5, Laplace Transform of sinh(bt), 24:05,
Q6, Laplace Transform of cosh(bt), 28:33,
Q7, Laplace Transform of the unit step function U(t-a), 32:00,
Q8, Laplace Transform of Window function, 39:05,
Q9, Laplace Transform of Dirac Delta function, 43:56,
Q10, Laplace Transform of f(t-a)u(t-a) and f(t)u(t-a), 51:58,
Q11, Laplace Transform of (t-2)^2*u(t-2) and t^2*u(t-2), 1:04:17,
Q12, Laplace Transform of f(at), 1:09:43,
Q13, Laplace Transform of e^(at)*f(t), 1:19:26,
Q14, Laplace Transform of t^3*e^(2t), 1:23:05,
Q14*, Laplace Transform of e^(3t)*cos(2t), 1:25:58,
Q15, Laplace Transform of t*f(t), 1:28:29, ft. Feynman’s trick, Leibniz rule, differentiation under the integral sign
Q16, Laplace Transform of t*sin(bt), 1:35:45
Extension: Laplace Transform of t^n*f(t), 1:38:19
Q14 again, 1:41:06
Q17, Laplace Transform of f(t)/t, 1:45:55
Q18, Laplace Transform of sin(t)/t, 2:01:30
Honorable mentions: 2:04:03, integral of sin(t)/t from 0 to inf, integral of e^(-t)sin(t)/t from 0 to inf, integral of sin(e^x) from -inf to inf
Q19, Laplace Transform of f'(t), 2:10:33
Q20, Laplace Transform of f''(t), 2:16:26
Q21, Laplace Transform of integral of f(v), 2:22:25
Q22, Convolution theorem, 2:28:11,
**a small mistake in the video: [thanks to Franscious Cummings] 2:35:16 U(t-v). t is the number and v is the variable
Honorable mentions, Laplace Transform of sin(t)cos(t) vs sin(t)*cos(t), 2:44:05
Q23, Laplace Transform of sqrt(t), 2:46:40,
Gamma & Pi functions: https://youtu.be/L4Trz6pFut4
(1/2)! = sqrt(pi)/2, https://youtu.be/dBmApl6gkII
Q24, Laplace Transform of ln(t), 2:53:59,

Dr. P: integral of e^(-x)*ln(x) from 0 to inf, https://youtu.be/80_fNEflUdw
Mu Prime Math: Why Laplace transform can solve differential equations: https://youtu.be/ofvkZXgbIxE
Chester: Generalized Dirichlet Integral, https://youtu.be/ug4LeeIJN68