Linear and Nonlinear Functional Analysis with Applications - Hardcover

Ciarlet, Philippe G.

Hardcover

ISBN 10: 1611972582 ISBN 13: 9781611972580

Publisher: Society for Industrial and Applied Mathematics, 2013

Synopsis

This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory.

This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.

Audience: Linear and Nonlinear Functional Analysis with Applications is intended for advanced undergraduates, graduate students, and researchers and is ideal for teaching or self-study.

Contents: Preface; Chapter 1: Real analysis and theory of functions: A quick review; Chapter 2: Normed vector spaces; Chapter 3: Banach spaces; Chapter 4: Inner-product spaces and Hilbert spaces; Chapter 5: The great theorems of linear functional analysis; Chapter 6: Linear partial differential equations; Chapter 7: Differential calculus in normed vector spaces; Chapter 8: Differential geometry in Rn; Chapter 9: The great theorems of nonlinear functional analysis; Bibliographical notes; Bibliography; Main notations; Index.

About this title

Book Description

A thorough and self-contained introduction to linear and nonlinear functional analysis, with applications to numerical analysis, optimisation, and partial differential equations. The book presents a vast amount of foundational material, suitable for advanced undergraduates, along with historical notes, illustrations, and over 400 problems to help the reader explore the subject.

About the Author

Philippe G. Ciarlet began his academic career at the Université Pierre et Marie Curie, Paris, in 1974, and moved to City University of Hong Kong in 2002. He is a member of eight academies, including the French Academy of Sciences and the Chinese Academy of Sciences and of the Hong Kong Institution of Science, and he is a Fellow of SIAM and the AMS. Ciarlet is the recipient of a Grand Prize from the French Academy of Sciences and a Humboldt Research Award, as well as many other awards. He is Doctor Honoris Causa, or Honorary Professor, at eight universities and the author of 190 research papers and 15 books.

Edition details

• Publisher: Society for Industrial and Applied Mathematics
• Publication date: 2013
• ISBN 10: 1611972582
• ISBN 13: 9781611972580
• Binding: Hardcover
• Language: English
• Number of pages: 840