This example computes the convolution of two triangle functions, i.e. y(t) = x(t)*x(t) where x(t) are triangle signals and * is the convolution operator.
The convolution integral is systematically evaluated by sketching the convolution integral integrands for each case of interest as a function of time "t". Each case provides a portion of the desired convolution for some portion of time. The final answer for y(t) is a piecewise-defined polynomial in "t".