The Dirac Delta 'Function': How to model an impulse or infinite spike

In this introduction to the Dirac Delta Function we'll see how we can deal with something happening instantaneously like a hammer hit. We will model this impulse with a 'function' that is infinite at one point and zero everywhere else. But such a thing isn't really a function! Sometimes we called it a functional or a generalized function. Regardless, it is defined by its pleasing properties such as what happens when you integrate the dirac delta function multiplied by another function. It can also be thought of as the derivative of the step function. In our next video we will study the Laplace Transform of the Dirac Delta Function and see how we can use it when studying differential equations.

Watch the rest of the Laplace Transform series in my Differential Equations playlist here:    • Laplace Transforms and Solving ODEs  

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