Ultimate Inverse Laplace Transform Study Guide

[@blackpenredpen]

Laplace Transform Ultimate Study Guide: kzbin.info/www/bejne/nKXRoYCVh7RjgMU

[@MuhammedmehdiTaqsh]

Sir can you show us how we can calculate inverse Laplace transform by using integral relation L^-1=1/2πi*integral(f(s).e^s*t.ds)

[@drpeyam]

At first I thought you were gonna do the Laplace video but in reverse 😂

[@blackpenredpen]

I should have just done that...

[@jacobharris5894]

That would be a meta video lol.

[@frozenmoon998]

These marathon videos are becoming my most favourite thing to watch!

[@blackpenredpen]

Thanks, glad to hear!!

[@mathalysisworld6693]

same @svetozar

[@MathswithMuneer]

Hello from a math teacher in Pakistan. I am glad to see teachers taking initiatives and helping students in their problems. I am positive our videos are a great source of help for them. Good work

[@vibhupandya6103]

The hell dude. I just started the original laplace marathon. And ALREADY?

[@blackpenredpen]

😂

[@Giovanni12332]

These marathons are great, your effort with the worksheet, timestamps, and everything else is greatly appreciated. Helped me out so much.

[@tombartimtim1725]

It would be nice a double and triple integrals marathon!!

[@jacobharris5894]

I second this. Although maybe like 50 instead of 100.

[@thecritiquer9407]

also a fourier transformation series marathon.

[@ContentMIN]

yeah, fourier series marathon@@thecritiquer9407

[@OwelleUwaleke]

The beauty of all these videos is that you can watch again, again and again until you come to grasp the concept

[@hevanderdacosta3211]

Now we just need a fourier and inverse fourier transform marathon.

[@daniloalmeida744]

Yes, Please!

[@aashsyed1277]

Wheres Fourier series and inverse Fourier series?

[@twapewaxoliswa3313]

Exactly

[@joshuaokeke2726]

Finally!!!!!! Someone that understands, S and 5 can be really confusing especially if your handwriting is as bad as mine

[@FaranAiki]

Yeah, but why we use 's' not 'f' or 'g'?

[@MrPanzerTanzer]

@@FaranAiki Because the original inventor used s and f and g are reserved for functions.

[@quantumsoul3495]

you can use cursive s, you will no longer confuse them

[@Shailendra2819962]

“Is this heaven?” - “No this is a Inverse Laplace marathon” “Hm, fair enough”

[@blackpenredpen]

lol

[@thevenin26]

Can't I just play the other Laplace video in reverse? :-)

[@blackpenredpen]

Hahaha that should work too!

[@markjosephaala2254]

😂😂 witty

[@sgems13]

It would sound wird

[@lih3391]

@@sgems13 thats the last of their worries lol

[@carultch]

Another way to solve the convolution of multiple trig functions: Based on the degree in the denominator for (s^2 + w^2)^n, the value of (n - 1) tells you how many times you'll eventually multiply trig by t. So you form a linear combination of t^k*sin(w*t) and t^k*cos(w*t), where w is the angular frequency, and k is a power that builds from 0 to (n-1). You then find corresponding Laplace transforms to each of these terms, and add up a linear combination with unknown coefficients, to equate to the original transform. Use the function parity property of convolution, you can eliminate half of the terms, and have half as many unknowns to solve for. f_odd(t) conv g_odd(t) = odd function f_even(t) conv g_even(t) = odd function f_odd(t) conv g_even(t) = even function If expecting odd functions, this means you can eliminate all t^even * cos(w*t) terms and t^odd * sin(w*t) terms. Vice versa, if you are expecting even functions. Then you proceed with solving for the unknown coefficients.

[@blackpenredpen]

All the s's are in red. How do you distinguish your s and your 5?

[@lopkobor6916]

blackpenredpen Can you do Fourier Transforms?

[@JB-ym4up]

Not without a green pen.

[@jagatiello6900]

Haha Steve, i had exact the same "trouble" distinguishing between the 5 and the s back in the university...my workaround method was writing the s with some horns added in both its ends, you can't imagine how fancy they look...

[@blackpenredpen]

Can you tweet me a picture of how it looks like?

[@jagatiello6900]

@@blackpenredpen don't have tw account, sent u to ur gmail instead

[@holyshit922]

19 Here we can be tricky and build difference of squares from linear factor of denominator Then we will get constant term if we combine difference of squares with the other factor of denominator We will get 13=(s^2+9)-(s+2)(s-2) If we replace numerator by 1/13((s^2+9)-(s+2)(s-2)) we will have nice cancelling 20 16=s^4-(s^2-4)(s^2+4) and we have nice cancelling If we know hyperbolic functions we dont need partial fractions

[@blackpenredpen]

Ahhhh so good!

[@abdulmajeedghareeb]

I have just found ur channel today and hands down ur already one of my favorite teachers on youtube. I wish i knew about u earlier. Ive been studying for some hours now and this is something i didnt do in a very long time. Your videos are very informative and very entertaining.

[@The1RandomFool]

Coming back and re-watching this video a couple years later, it occurs to me that on question 20 and other hard partial fraction decomposition problems the residue theorem from complex analysis can be used to help with it. You'd just have to calculate a couple derivatives for building up the powers of s, and the rest is fine.

[@anarbay24]

I am taking differential equations in MIT and literally, you are saving my time with excellent exercises. Our book is just awful. Just imagine, some of your exercises appeared in my midterm exam

[@lindsaywaterman2010]

This expression could have been written as 1/8[1/(s^2-4 -2) -1/(s^2+4)] and then 1/16[2/(s^2-4 -2) -2/(s^2+4)]. The Laplace Transform would , therefore be 1/16[Sinh(2t) -Sin(2t)], which is what Black Pen Red Pen got but in a convoluted way.

[@Amine-gz7gq]

I've just finished the Laplace Transform Ultimate Study Guide video now I'm going to start watching this one, it's going to take me a while like the other one because I have other things to do.

[@ChanceGrey-t5v]

Thank you thank you thank you! I would be lost in college without your videos!

[@kirbo722]

I, once again, deeply thank you bprp! This was EXTREMELY helpful! ❤

[@federicopagano6590]

Number 16 no need to do that to find C and D You just have to multiply bt (s^2+4) both sides and then evaluate at s=2i It will follow -1/8 =C(2i) +D Immediately D=-1/8 and C=0 1/(s-2)(s+2)=1/(s^-4) evaluated at s=2i equals -1/8

[@luisgarza4244]

Love the way you teach. Fast but informative.

[@The1RandomFool]

I really like these marathons.

[@blackpenredpen]

Thanks!

[@XgamersXdimensions]

Maybe next could be some linear algebra videos? Ideas could be marathon on: finding Inverses, Eigenvectors, eigenvalues of matrices?

[@Zeusbeer]

For question 12 you can really easily simplify the partial fractions by letting some w = s^2 and then doing the partial fractions on w, and then later substituting s back in. edit: A simular trick can be used for Q16, where you can split up (s^4-16) into (s^2+4)(s^2-4) and again let w = s^2, do the partial fraction, reverse into the s world, then you can simplify it all down into 1/16(sinh(t) - sin(t))

[@jonacasals5]

I respect you so much. Right now I cant understand this topic, but I will comeback.

[@luisf6060]

Example (16) A=1/4 ; B=-1/4 ; C=0 ; D=-1 . Thanks !!!

[@holyshit922]

Residues are alternative way to partial fraction decomposition In fact complex partial fractions decomposition works better Residues are more comfortable also for inverse Z transform

[@Vladimir064Mr]

Thank you, this quarantine has led me to study differential equations on my own, thanks from Honduras

[@snipergranola6359]

Solution of partial differential eq using Laplace and Fourier transtorm

[@alperyasin710]

Sir i appreciate you. You are the best! Greetings from Turkey.

[@notpistooo]

Hii, thank you bprp for these marathon videos. It is very helpful even after 3 years and it will stay helpful. I would like to point that i couldn't open the file, which is not a big problem because we have the functions in the video and the description, but still it would be nicer to have them printed. Thank uu again

[@farhanaferdous3581]

Thanks blackpenredpen....take care and best wishes from Bangladesh 🇧🇩🇧🇩🇧🇩

[@banderfargoyl]

An inverse Laplace marathon? Man, there must be a lock-down! 😂

[@Bayonettamachinekill]

incredible was able to find error in the work we did thanks so much.

[@igarciaasua9]

Do you guys know a marathon video of differential equations? I have to retake them for a subject and these videos are very useful

[@啟瑞-f4n]

You are a great teacher!❤❤❤

[@eswyatt]

A higher order differential equations marathon would make a complete set!

[@Marcox385]

Getting bored with the quarantine bprp? Ye, me neither

[@lopkobor6916]

Everyone's saying that they're all bored while we're just chilling at home doing maths

[@aleks456]

can't imagine that this was posted 9 months ago now..

[@Marcox385]

@@aleks456 I can't handle this anymore, I've passed calc 2 and 3 since then but this is enough

[@aleks456]

@@Marcox385 Same bro. Let's just hold on and wait for this to finish!

[@Subhajit03-n6j]

Exciting!!

[@guiencarnacao6918]

You are the best, thank you so much :D

[@paologrisanti7865]

I was additcted to marathon's race (done 3) now I am addict to your marathon 👍 From Italy with love!

[@jarikosonen4079]

It looks like the (6) case the cos(t-π/2) can be also sin(t)... In the (7) case cos(t)-sin(t) can be sqrt(2)*sin(π/4-t)... This should be possibly simplified in the t-domain. (10) delta(t-a) correct, but maybe then mistake before the inverse laplace if this is result. The delta is more practical in s-domain than in t-domain... (26) Try inverse laplace of s^2/(s^2+a^2)... How to make this? Why result is different for L^-1{1-a^2/(s^2+a^2)} versus L^-1{s/(s^2+i×a)} ∗ L^-1{s/(s^2-i×a)} (∗ = convolution)? Can this prove that convolution theorem and other inverse laplace can differ? Is correct answer -a×sin(a×t) ? Maybe is it possible to reconfigure the transformation to present the frequencies reference point at t=0- (zero minus) so that resulted delta(0) would be delta(0-) and then by using laplace validity for t>=0 removing this delta-function?

[@muhamadfaisalbinrachmanmoe5228]

I love u sirrrrrr❤❤i love the way u teach us.its easy to understand

[@milagros070728]

THANK YOU SO MUCH

[@downtwojames5441]

You're a champ! This helped a ton. Thanks!

[@bassjunias439]

Video still useful today. Thanks teacher! But @blackpenredpen Can you also do fourier transform please?

[@arberithaqi]

Next Video: Differential Equation 2nd Order (btw. keep up with the great content, love it!)

[@mahibulhaque5952]

You are great I like this channel more than other ...

[@QuranReact1]

Well done !! I gotta ask a question : for Q15, F(S) doesn't converge to 0 when s goes to infinity, therefore we can't use differentiation, right ?

[@QuranReact1]

oh srry, right ln(1)=0. My bad.

[@laurentwatteau8835]

For #16, the result could have been written as (1/16)[sinh(2t)-sin(2t)], which makes more sense to me.

[@chris-hj2qd]

Awesome working through the struggle

[@WilsonWolAguekNgot]

My favorite teacher

[@wryanihad]

In minite 48 your solution Is correct But i solve it by adding (s²+1-s²) twic

[@1ereliguejeunessetennisdet708]

你回来了曹老师👍

[@blackpenredpen]

Thanks!!

[@emanuellandeholm5657]

Who's teacher cao? Is that bprp?

[@lawandeconomics1]

Your video was badly needed! Most books and sources just blow through one example…forgetting that perfect practice makes perfect! Thanks!

[@blackpenredpen]

Glad to help 😃

[@piyushgupta1811]

Thanks!

[@torcida214]

hello, thanks for the videos! Did you do any via the Fourier Transform? Something similar to the Laplace? thank you

[@rotomflux]

I love the beginning, I also mess up my 5's and s's

[@gradientattack]

Thank you Mathematic Marathons GOD!!!, we appreciate your big brain, but there are a topic, Limits, can you give us a marathon about it? (I'm learn English, I speak spanish )

[@sinr2688]

this is a good video for me to practice my engineering math ：))

[@dishant4222]

Amazing & thanks

[@anirudhnarasimhan7307]

Thanks for keeping my quarantine filled. Love from India😍

[@aymen_sahnoun]

thanks ... is there a marathon for fourier ?

[@blackpenredpen]

We have to call up dr. Peyam for this! Lol

[@aymen_sahnoun]

@@blackpenredpen is it really harder than Laplace and it's inverse and power series and the all mighty integral Marathon !??

[@comingshoon2717]

aqui, en pleno verano practicando, para no olvidarse de esto... un cracj bprp... saludos :)

[@blaugios]

According to f(t-a)*u(t-a) = iLapace{e^(-as)F(s)} , for a=0, all inverse Laplace transforms should be multiplied by u(t), am I right?

[@ssdd9911]

1:08:43 i realised it is possible to use cover up by substituting s^2=u and A and C is automatically 0

[@aymanalgeria7302]

That was too much fun . Isn't it

[@julianmldc]

AMAZING AS ALWAYS

[@MathswithMuneer]

José Julián Maldonado Camacho indeed

[@blackscreen4033]

You got some stamina!

[@خلفابراهيم-ض5س]

Thank you very much Steve...continuous..we are all love you ❤❤❤

[@MathswithMuneer]

خلف ابراهيم no doubt

[@blackpenredpen]

Thanks!!!

[@sarsoor1429]

That face expression switch at 34:45

[@stevenglowacki8576]

Whenever I got a problem that stated "s" as a variable, my first line on my answer was "Let s = t" or something like that. S looks way too similar to 5 to be used a variable name. For the same reason, I have crossed hand-written every z for a very long time so that they don't look like 2.

[@carultch]

Write a cursive s, to tell it apart from a 5.

[@jaredjones6570]

2:02:17 and 2:02:31 reveal that an infinitesimal amount of exhaustion has affected the dual-pen-wielding Jedi master.

[@rodwayworkor9202]

Next up : W Lambert Marathon

[@josammarenye4021]

I feel so unlucky not being your student. Your teaching is eloquent ☺️

[@williamfernandez4117]

OMG Love this video

[@charlesk5138]

I love you. thank you.

[@backtonature1923]

1:43:10

[@bludeat7398]

on problem 8... why not add and substract s^2 on top?

[@hari8568]

Hey can u do a marathon on z transform and inverse z transform

[@jeryipina2333]

for question 4 could you complete the square and use laplace of e^-at*sinhbt? or is that wrong

[@saisrirajnallam]

sir thank you very much for your greatest efforts sir.........❤❤❤

[@prashantswami8345]

😅

[@_witeK]

*Will you make a video with 100 limits ?*

[@TheTalmon18]

Dang I havent done laplace transforms since ODEs in my first year of uni. I graduated with an applied math bachelors back in 2016 but never had to do these again haha. Ive used the laplacian in PDEs many times but never these again😅. Blast from the past! Thanks for the video! Was able to do these since you mentioned LT is linear and with your note of what the laplace transform is its easy to go backwards Thank you!! Idk if Ill ever use this again (even in my masters when I start it) but it was fun to watch haha

[@viniciusps01]

Great!

[@koffisamuel9517]

thank you so much professor can you do the same with fourier transform ?please

[@ianmi4i727]

Wonderful 😊

[@snakesocks]

Hi bprp! The link to the file doesn't work. It takes me to your website but there's no file attached to the inverse Laplace title.

[@blackpenredpen]

Just updated. Thanks for letting me know.

[@saatee100]

Corona in belgium big deal, pff we have blackpenredpen 👍

[@blackpenredpen]

Thanks. And I wish you and your family safe and healthy.

[@siyuanruan3404]

Hello, sir, I have a question on inverse laplace transform, how can we inverse laplace transform sqrt(pi/4s^3)?

[@carultch]

Non-integer powers of t have a Laplace transform that uses a function that interpolates the factorials, called the Gamma function. So where L{t^n} = n!/s^(n + 1), the corresponding Laplace transform of non-integer powers of t is: L{t^p} = Gamma(p + 1)/s^(p +1) For reasons I can't explain, the Gamma function is offset from the factorials by a shift of 1. Your given transform is: sqrt(pi/(4*s^3)) which we can rewrite as sqrt(pi/4) * 1/s^(3/2) This means (p+1) = 3/2, implying that the power p = 1/2. We want Gamma(3/2) to appear upstairs, so we multiply by 1 in a fancy way to achieve this: sqrt(pi/4)/Gamma(3/2) * Gamma(3/2)/s^(3/2) Now we can take the inverse Laplace and get: sqrt(pi/4)/Gamma(3/2) * t^(1/2) Special cases of the Gamma function occur half way between integers, where: Gamma(n + 1/2) = (product of odds up to 2*n-1)/2^n * sqrt(pi) Gamma(3/2) = (product of odds up to 1)/2^1 * sqrt(pi) = 1/2*sqrt(pi) Thus: sqrt(pi/4)/(1/2*sqrt(pi)) = 1 And our result is: sqrt(t)

[@kulvirsharma6940]

Good morning sir

[@thomasfranzstockhammer7846]

Lg /amazing video's

[@froilanemeliano6551]

i would totally give a like to tell u how helpful u are ♥️

[@and12309]

don't you have to multiply u(t) to the whole expression when taking the inverse laplace, or at least note that t > 0?

[@xaviersson7047]

stay safe everyone

[@biscet6287]

Marathon for integration with residues?

[@akhileshray3478]

I am using this marathon for exam preparation 😂 thanks btw 😁👍