Zeidler E. Applied Functional Analysis: Applications to Mathematical Physics

Springer, 1999. — 507 p. — ISBN: 0387944427, 1461269105, 9781461208150The 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.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
AppendixHints for Further Reading
List of Symbols
List of Theorems
List of Most Important Definitions
Subject Index.