This brief provides an elementary introduction to the theory of piecewise differentiable
functions with an emphasis on differentiable equations. In the first chapter two sample
problems are used to motivate the study of this theory. The presentation is then developed
using two basic tools for the analysis of piecewise differentiable functions: the Bouligand
derivative as the nonsmooth analogue of the classical derivative concept and the theory of
piecewise affine functions as the combinatorial tool for the study of this approximation
function. In the end the results are combined to develop inverse and implicit function
theorems for piecewise differentiable equations. This Introduction to Piecewise Differentiable
Equations will serve graduate students and researchers alike. The reader is assumed to be
familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.
