Up to this point in the book, we have derived time response solutions of LTI systems only for relatively simple input functions $$u(t)$$. The convolution integral will permit us to derive time response solutions for any physically realistic input function $$u(t)$$, and even to compute time response solutions if $$u(t)$$ is given in numerical form rather than equation form. The general convolution transform and its inverse, the convolution integral, are defined and described in this chapter, and application of the convolution integral is illustrated specifically for 1st order systems.