Laplace transform of the unit step function | Laplace transform | Khan Academy

Introduction to the unit step function and its Laplace Transform

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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.

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[asemnafiz]

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!

[Sk-pguv]

Its amazing how you and my professor teach the same exact thing but with you it just magically makes SO MUCH SENSE!

[ranXXX]

To the author of this video, Man! For the first time I actually actually appreciate the luxury of Youtube, 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!!!

[hans_____]

It's like you actually WANT us to understand!! None of my other "teachers" ever seem to feel that Thank you sir for your excellence and your love for your fellow man.

[khanacademy]

The quality is only bad the first few minutes after the video is uploaded (while it is being processed). Re-watch it again in a few minutes.

[rajnglavol]

who ever did this thank you very much, learned LaPlace and step functions couple years ago and this is great material to refresh your memory!!

[xXguzmanXx]

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)}?

[sarvagyabhatnagar]

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.

[biller]

Somebody give this champion an award or something!

[ueiwqoak]

Why is the laplace of f(x) = laplace f(t) when x = t-c ? Why does that seem wrong to me?

[AymanRSaleh]

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.

[icwhatudont]

grandfather use to say, "don't bore others with the details, just show them the baby"

[SimeonHanks]

I swear you've got an amazing talent. I can't pin it down, but you are so easy to learn from. Thank you Sal.

[alexwhb]

you are a teaching god. Thank you so much for this video. It was so helpful.

[fuahuahuatime]

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. 

[badwolf]

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.

[MuhammadSalman-gvmx]

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

[quadrinhosmonica]

At 21:30 why didn't Sal back substitute x = (t-c)? He just ignored it, went along and used a "t" inside the laplace transform symbol

[demovseverybody]

When i am a dad, I'll name my 1st Male kid "Sal" cause you are a legend to all, i am honored to have learn t all that i know from you?!!

[Mirmida]

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!