Theory of Distributions
In this course you will learn to do the impossible: to differentiate non-differentiable functions. We do this by introducing distributions, which is a larger class of objects than functions. All bounded functions are included in the class of distributions, all distributions are differentiable and conform to the ordinary rules of differentiation, and for differentiable functions the distribution derivative is the same as the ordinary derivative. Distributions also give us a way to generalize the Fourier transform. Distribution theory is of fundamental importance in modern analysis, especially in the theory of differential equations.