SpringerBriefs in Optimization

Introduction to Piecewise Differentiable Equations

Authors: Scholtes, Stefan

  • ​​​Introduces the theory of piecewise differentiable functions with an emphasis on piecewise differentiable equations Illustrates the relevance of the study via two sample problems

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  • ISBN 978-1-4614-4340-7
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Softcover $49.95
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  • ISBN 978-1-4614-4339-1
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About this book

​​​​​​​

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.

Reviews

From the reviews:

“The book is nicely written with a lucid yet rigorous presentation of the mathematical concepts and constructions involved. It does not require prerequisites far beyond multivariable calculus and basic linear algebra … . This book is a welcome addition to the bookshelf of anyone who is interested in polyhedral combinatorics and nonsmooth analysis, and applications to sensitivity analysis of variational inequalities.” (Asen L. Dontchev, Mathematical Reviews, January, 2013)

Table of contents (5 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-4340-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-4339-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Piecewise Differentiable Equations
Authors
Series Title
SpringerBriefs in Optimization
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Stefan Scholtes
eBook ISBN
978-1-4614-4340-7
DOI
10.1007/978-1-4614-4340-7
Softcover ISBN
978-1-4614-4339-1
Series ISSN
2190-8354
Edition Number
1
Number of Pages
X, 133
Topics