Monday Math 106

The Laplace Transform
Part 7: Periodic functions

Let us consider a general periodic function f(x), with period T, and its Laplace transform. From the definition of the Laplace transform,
.
Now, dividing up the region of integration into (infinitely many) intervals of length T, we get
.
Next, on each integral term, we perform the substitution u=tnT, which gives us
.

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One Response to “Monday Math 106”

  1. Monday Math 111 « Twisted One 151's Weblog Says:

    […] consider the square wave with period 2π given by . As this is a periodic function, we use our periodic function Laplace transform , where T is the period. For our current function, this gives us: . Possibly related posts: […]

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