Which genius came up with this stuff! Sometimes when I go through something like this I can't help but to wonder how the first mathematician came up with it in the first place!
To the author of this video, Man! For the first time I actually actually appreciate the luxury of RU-vid, but it is particularly because of your life saving effort that I shall one day be able to boast that I know math. Not because I learnt it in school, but because I watched your videos. I thank you from the bottom of my heart!!!
It's like you actually WANT us to understand!! None of my other "teachers" ever seem to feel that way....... Thank you sir for your excellence and your love for your fellow man.
Good explanation, but I feel that 23:00 is just a little bit misleading. The reason why is because the laplace of the shifted function isn't simply the laplace of the unshifted function. *There's an extra step* where you have to find the unshifted function by using manipulations such that you get the original function again.
Why is the laplace transform L{u(t)f(t-c)} equal to e^(-cs)*L{f(t)} where f(t) is the unshifted function and not equal to e^(-cs)*L{f(t-c)} where f(t-c) is the shifted function? When you worked out the integral with the variable x, you got as an answer that L{u(t)f(t-c)}=e^(-cs)*L{f(x)} and since x=t-c, shouldn't L{u(t)f(t-c)}, when you substitute (t-c) back for x, be equal to e^(-cs)*L{f(t-c)} instead of e^(-cs)*L{f(t)}?
You are my hero sir. I watched your videos last year in my ode and pde class, and thought I'd never need this stuff again. This is the second time you've made me actually understand laplace.
I didn't understand how you went from f(x) to f(t) from 19:00 to L(f(t)) at 21:33. The Laplace of f(x) should be L(f(x)) where x = t-c, however, the final answer includes the Laplace of f(t). Shouldn't it be Laplace of (t-c)? Greatly appreciate any help.
Awsummm Workkkk Sir, U know What Our Instructor Was Doing these things, Like things Are moving In air , But u Did, Insert those Concepts For What I was Thinking Thnx Again
Man, i just wanna say a big thank you from brazil! i really dont go to class cause the teacher kinda sucks, and i started studying 4 days before my calculus 4 exam. i was rageing like hell cause i couldn't understanding a lot of stuff by myself, but then i found your videos... you sir, made me get a 8.5 in 10! and i atudy at one of the hardest universities of the country. thank you so much!
Can anyone explain the missing step of how f(t-c) = f(t) ??? I was following this course with no problems up until this point. It clearly confused a lot of other people too.
I think the argument he made was Kind of weird. You could substitute back, But there is no point. The point is that it doesn’t matter What you call the integrering variable, since it will go away when you integrate. Its still a Laplace-Transform if its x you are integrating instead of t, its still a function og s. Kinda like ∫₀² ax³ dx = ∫₀² as³ ds = 4a its still the same, even tho we use different variables to integrate
***** I took the Civil Engineering one (structural)... I did not see any laplace transforms.... Im guessing they only have it there for other engr majors which heavily rely on this kind of concept....
Hi Sal Thanks for the videos, could you please explain how did you assume F(X) is equal to F(t) in the end of the video because earlier you said x = t-c ? Thanks again.
I would suggest watching the mit differential equations and then watch this videos, you would get a way better understanding with two or three different points.
This is amazing!!!!, This is what our future is all about.(Actually present as well). Thank you. Thank you very much who ever you are sir!!!. PS.: You Just Made Me Love Laplace all over again.
Mr Sal I love your work, in this video I kinda disagree with how u simplified Laplace of the step function, u replaced x=t at the end but we know that X=t+c please help me out here
this is an absolutely amazing explanation!!....but why do we shift the function to the right and multiply it by unit step function, what is the purpose of that?
* Thanks a lot, for introducing this new -- (shifted) "unit step function" * shifted is my own annotation, as i think _μ_zero_ or just *μ* is a more fundamental function, with the general _μ_c_ being shifted to right by +c i.e. the *μ( t - c )* Anyways: * this step fxn eases alot the task of defining functions which are stepped at only a few (say 1-3) points like the fxns for absolute, or signum, or other such * eases a lot - or at least provides a new way to think about ... * other than that, i don't think it helps much for other *periodically partwise functions* like floor, ceiling, fractional-part, modulus, remainder, etc.
he explained before that at the end the answer would be as the same to take the laplace transofrm of the unshifted function (in this case sin t) instead of the shifted function, check a few mins back before this sin t example, u will find out
Thanks a lot. I was never formally introduced to step functions and my diffeq book gave a very poor introduction to them. I got it figured out now, thanks =)
at got a suggestion for u if u dnt mind...at 4:46 u say it's here quite often i saw in ur videos u say here and there it's not always helpful to relate whr u are talking abt....so cud u pls luk into dis mattr snd try 2 brng out a solnt for it thnk u guys
