Calculus Without Derivatives

Graduate Texts in Mathematics #266

by Jean-Paul Penot

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.

Genres: Mathematics

544 pages, Hardcover

First published November 9, 2012

Reviews

[Nattapon Chotsisuparat · Rating 5 out of 5]

Calculus Without Derivatives by Jean-Paul Penot. At first, I thought this book would only focus on integration and wouldn’t have derivatives just as the title suggests. I expected integrations like integration by parts or substitution by U. But no it’s not Calculus I, II, or even advanced calculus you may have studied in your undergrad years. This book has no mercy on you it’s really tough. It starts with sets and order, followed by set-valued mappings, the Ekeland Variational Principle, the Decrease Principle, Differential Calculus, Subderivatives, Subdifferentials and so on. I have to confess, I got filtered by the very first problem about proving Tykhonov’s theorem for the product of two spaces. Good times, worth every penny.