Linear and Nonlinear Functional Analysis with Applications

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9781611972580: Linear and Nonlinear Functional Analysis with Applications
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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.

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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.

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Book Description Society for Industrial Applied Mathematics,U.S., United States, 2013. Hardback. Condition: New. Language: English . Brand New Book. Functional analysis occupies a central position in modern mathematics, and has powerful applications in many other branches of the subject. This book provides a thorough and self-contained introduction to the basic aspects of both linear and nonlinear functional analysis. Most of the major results are accompanied by complete proofs, and illustrated with a variety of applications to numerical analysis, optimisation theory, and partial differential equations. As well as covering a vast amount of foundational material, historical notes and many original references are included to help the reader explore the genesis of some important results. This book is intended for advanced undergraduates, graduate students, and researchers. With illustrations and over 400 problems, it is ideal for both teaching and self-study. Seller Inventory # AAN9781611972580

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Book Description Society for Industrial Applied Mathematics,U.S., United States, 2013. Hardback. Condition: New. Language: English . Brand New Book. Functional analysis occupies a central position in modern mathematics, and has powerful applications in many other branches of the subject. This book provides a thorough and self-contained introduction to the basic aspects of both linear and nonlinear functional analysis. Most of the major results are accompanied by complete proofs, and illustrated with a variety of applications to numerical analysis, optimisation theory, and partial differential equations. As well as covering a vast amount of foundational material, historical notes and many original references are included to help the reader explore the genesis of some important results. This book is intended for advanced undergraduates, graduate students, and researchers. With illustrations and over 400 problems, it is ideal for both teaching and self-study. Seller Inventory # AAN9781611972580

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