Laplace Transform of a periodic function

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  1. Math Problems Solved Craig Faulhaber
  2. differential
  3. equations
  4. Laplace Transform
  5. Periodic Function
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This was very helpful, thank you!  I have a question about your u substitution though.  It seems each term in your expanded Laplace integral uses a different u-substitution (I will dub them u1=t, u2=t-T, u3=t-2T, etc.).  You then say that after some algebraic manipulation, you end up with the same integral in each term.  Due to the periodicity of the function, I realize that f(u1)=f(u2)=f(u3)=...=f(u), but I don't see how the e^(-su) factors in the integrals of each term are equivalent, which it seems would be necessary to factor the integral out of each term.  Towards the end (around 4:55) you substitute u=t back into the equation, but only the first term of the expanded integral used that substitution.  Again, that's fine for f(u), but can you comment as to why that works given  Thanks!

tylernichol
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How do you take the inverse laplace of the periodic function?

supersejethomas