Laplace Transform Ultimate Study Guide

How to do Laplace transforms! This 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.

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,
Q24, Laplace Transform of ln(t), 2:53:59,

[RationallyChallenged]

I fell asleep watching YouTube and woke up 2 hours and 40 minutes into this video… the most confusing way I’ve ever been woken up in my entire life.

[Albkiller]

My whole family has coronavirus me and my mother are fine for now my father had the lighter symptoms of the virus and furtunately he feels well now. Greetings from Italy
Ps you really mastered the double pen technique it's almost not visible to the human eye when you switch pens

[nilaymarathe]

When you have nothing to do during the lockdown.

Normal people:-I'm So

BPRP:-Laplace Transform Marathon GO GO GO!!!!

[VibingMath]

Whoaaa omg this video will be the bible of Laplace transform!!! It just contains eveything! And your effort is really much appreciated in preparing these series of non-stop marathon! Thank you man!

[James-okzo]

This is brilliant! Well done! Thank you for all your hard work! I am busy with my 2nd year electrical engineering degree, and would not be passing the mathematics without your videos.

[TheWisator]

47:45 When I took system theory course in university, my professor explained this property quite well. He described the dirac impulse as a rectangle with a width of 1/epsilon and a height of epsilon. For the limit of epsilon -> 0, this recantgle has a height of "infinity" and a width of zero, while the area (width * length) always remains 1.

[AndyGoth]

18:59 "Excuse my little brace"
*draws absolutely perfect brace*
"It's really hard for me to do that"

[arberithaqi]

Please do a Marathon for Differential Equations 2nd Order. Your Videos about Integral and Dervivatives helped me soooo much. Thank you for the hard and impressiv work. Greetings from Switzerland :)

[ben]

🤣🤣🤣 19:55 " 'i' don't like to be on bottom. 'i' like to be on top"
I died momentarily when you said that.

[luxeproultimate]

Is it weird to be a bit turned on by Laplace transforms?

[thevenin]

Yes, everyone needs to watch Mu Prime Math's video on Laplace.
For your next marathon, I think you should do 100 different proofs of Quadratic Reciprocity.

[yorusaka]

You are truly the GOAT of math communications

[warwick]

I remember bprp being one of my best resources for acing calculus 2 and a year later here we are with differential equations....Thank you for everything sir.

[benjaminbrady]

I personally feel like a master of laplace transforms and I will check for mistakes!

[aakolly]

I am a graduate student at CSULB and your videos are truly helpful.

[raptor]

Great video. I've enjoyed it very much despite I've never done Laplace transforms :)

Answers:
1x1=1
1*1=t


L{(1-cos t)/t}=ln((s^2+1)^(1/2)/s)
integral from 0 to infinty of (1-cos t)/(te^t)=ln 2^(1/2)

[ko]

i woke up in the morning to this playing - thanks for blessing my dreams blackpenredpen

[jarikosonen]

But a>s almost never occur, because 0<s<Inf is needed for it to work (all the frequencies must be there). But this is no problem because exponential circuit as that can not exists and is certainly undefined case nevertheless.
Also the t^n do not exist in real case.

[ozonewagle]

Holy Moly, Your teaching style is totally different and everything is quite clear. Thanks a lot.

[joesnickers]

Your voice is soothing, I am using this video as white noise while working on a flyer. I dont understand anything, but it lets me feel like I am doing something.