Calculus Without Derivatives
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Calculus Without Derivatives

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Jean-Paul Penot
963 g
244x167x38 mm
266, Graduate Texts in Mathematics

Here is a wide-ranging introduction to the foundations of nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. Covers recent progress and methods of implementation, especially in optimization problems.
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
Preface.- 1 Metric and Topological Tools.- 2 Elements of Differential Calculus.- 3 Elements of Convex Analysis.- 4 Elementary and Viscosity Subdifferentials.- 5 Circa-Subdifferentials, Clarke Subdifferentials.- 6 Limiting Subdifferentials.- 7 Graded Subdifferentials, Ioffe Subdifferentials.- References.- Index.
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.

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