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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