## UnkleRhaukus 2 years ago laplace transform of a periodic functions

1. UnkleRhaukus

2. Outkast3r09

What is this you're doing lol

3. UnkleRhaukus

i have taken the Laplace transform of some periodic functions i dont know how to check if i have done it right

4. UnkleRhaukus

i have used $\mathcal L\{f(x)\}=\int\limits_0^\infty f(x)e^{-px}\text dx$ $=\int\limits_0^\tau f(x)e^{-px}\text dx+\int\limits_\tau^{2\tau} f(x)e^{-px}\text dx+\int\limits_{2\tau}^{3\tau} f(x)e^{-px}\text dx+\dots$$=(1+e^{-p\tau}+e^{-2p\tau}+\dots)\int\limits_0^\tau f(z)e^{-pz}\text dz$$=\frac{1}{1-e^{-p\tau}}\int\limits_0^\tau f(z)e^{-pz}\text dz$

how do you type a document like that is it LaTex ,it looks great csry i cant help with the content but the presentation is fine hw do you create such a presentation

6. UnkleRhaukus

i have been using a program called TeXShop

7. tkhunny

How sure are you that it converges?

8. UnkleRhaukus

i dont know

9. malevolence19

As long as the function grows slower than Me^pt then it converges.

10. UnkleRhaukus

ok it converges because the slope is only positive or negative 1 , which is less slope than any exponential

11. malevolence19

Yeah, I'm not sure of the name of the theorem but I just went over that in one of my classes not too long ago.

12. UnkleRhaukus

geometric series?