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Mathematics - Analysis | Calculus Without Derivatives

Calculus Without Derivatives

Series: Graduate Texts in Mathematics, Vol. 266

Penot, Jean-Paul

2013, XX, 524 p.

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  • 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

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.

Content Level » Graduate

Keywords » Clarke subdifferential - Newton Method - approximation - calculus of variations - coderivative - convex analysis - differential calculus - duality - elementary subdifferentials - error bounds - fuzzy calculus - limiting subdifferential - mathematical programming - nonsmooth analysis - normal cone - optimization - stability theory - tangent cone

Related subjects » Analysis - Applications - Mathematics

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