Graduate Texts in Mathematics

Calculus Without Derivatives

Authors: Penot, Jean-Paul

  • Includes all necessary preliminary material
  • Introduces fundamental aspects of nonsmooth analysis that impact many applications
  • Presents a balanced picture of the most elementary attempts to replace a derivative with a one-sided generalized derivative called a subdifferential
  • Includes references, notes, exercises and supplements that will give the reader a thorough insight into the subject
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eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-4538-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-1-4614-4537-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-1-4899-8942-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
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About this Textbook

Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems.  Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. 

In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed.  The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.

About the authors

Jean-Paul Penot is an Emeritus Professor at Université Paris 6.  He has taught in Paris, Pau and Canada.

Reviews

“The book collects three different branches of analysis: differential calculus, convex analysis, and nonsmooth analysis. … What makes Penot’s work stand out is his path through the material and the clean and scholarly presentation. It is well suited for individual study or a classroom … . As preparation for the rough road ahead of us in the coming decades, it might be worth the investment.” (Russell Luke, SIAM Review, Vol. 57 (2), June, 2015)

“This very good book is an treatise on approximate calculus and justifies the author’s claim that the rules of this calculus are as important and useful as those for exact calculus. … The book is notable not only for its exposition but also for the notes at the end of each chapter explaining the historical and other relevant backgrounds of the material. There are many exercises throughout the book.” (Peter S. Bullen, Zentralblatt MATH, Vol. 1264, 2013)

“By collecting together a lot of results in nonsmooth analysis and presenting them in a coherent and accessible way, the author rendered a great service to the mathematical community. The book can be considered as an incentive for newcomers to enter this area of research … . The specialists will find also a lot of systematized information, and … the first three chapters can be used for independent graduate courses.” (S. Cobzaş¸ Studia Universitatis Babes-Bolyai, Mathematica, Vol. 58 (1), 2013)

Table of contents (7 chapters)

  • Metric and Topological Tools

    Penot, Jean-Paul

    Pages 1-115

  • Elements of Differential Calculus

    Penot, Jean-Paul

    Pages 117-186

  • Elements of Convex Analysis

    Penot, Jean-Paul

    Pages 187-261

  • Elementary and Viscosity Subdifferentials

    Penot, Jean-Paul

    Pages 263-356

  • Circa-Subdifferentials, Clarke Subdifferentials

    Penot, Jean-Paul

    Pages 357-405

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-4538-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-1-4614-4537-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-1-4899-8942-0
  • 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
Calculus Without Derivatives
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
266
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-4538-8
DOI
10.1007/978-1-4614-4538-8
Hardcover ISBN
978-1-4614-4537-1
Softcover ISBN
978-1-4899-8942-0
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XX, 524
Topics