This brief""providesanelementaryintroduction 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 developedusingtwo 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."
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