In this lecture, the Dirac Delta Function is introduced as a way to model impulse inputs, which are commonly used in physics and engineering. The impulse is defined as the integral of a constant force acting over a time interval, and the unit impulse is used to model this scenario. The Laplace transform of the unit impulse is calculated, and as the width of the impulse goes to zero, it approaches the Dirac Delta Function. This non-function is given properties such as having a Laplace transform of one and an integral of one over the entire real line. The convolution of a function with the Dirac Delta Function is also shown to be equal to the original function.
Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions -- Lecture 23. Moving on to other functions from the Laplace Transform.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.
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