Existence And Property Of Laplace Transform
Existence And Property Of Laplace transforms : Existence Of Laplace Transforms : In order to discuss the theorem on existence of transform we need the following definition . Definition : A function f(t) is said to be piecewise continuous in a finite range a≤t≤b , if it is possible to divide the range into a finite number of sub-intervals such that f(t) is continuous inside each sub-interval and approaches finite values as t approaches either end of any interval from the interior. Theorem : Let f(t) be a function which is piecewise continuous on every finite interval in the range t≥0 and satisfies |f(t)|≤Me^αt , for all t≥0 .........(1) and for some constants α and M . Then the Laplace transform of f(t) exists for all p>α . Proof : Since f(t)...