Synopses & Reviews
The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.
Includes bibliographical references (p. -458) and index.
Table of Contents
Preface.- Prologue.- Banach Spaces and Fixed-Point Theorems.- Hilbert Spaces.- Orthogonality, and the Dirichlet Principle.- Hilbert Spaces and Generalized Fourier Series.- Eigenvalue Problems for Linear Compact Symmetric Operators.- Self-Adjoint Operators, the Friedrichs Extension and the Partial Differential Equations of Mathematical Physics.- Epilogue.- Appendix.- References.- Hints for Further Reading.- List of Symbols.- List of Theorems.- List of Most Important Definitions.- Subject Index.