Linear and Nonlinear Functional Analysis with Applications-行业好书-社会科学-太极之巅书单号

书刊介绍

内容简介

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.

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.

作品目录

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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