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Preface to Third Edition | |
Preface to Second Edition | |
Preface to First Edition | |
Preliminaries | |
Heat Conduction | |
Diffusion | |
Reaction-Diffusion Problems | |
The Impulse-Momentum Law: The Motion of Rods and Strings | |
Alternative Formulations of Physical Problems | |
Notes on Convergence | |
The Lebesgue Integral | |
Green's Functions (Intuitive Ideas) | |
Introduction and General Comments | |
The Finite Rod | |
Maximum Principle | |
Examples of Green's Functions | |
The Theory of Distributions | |
Basic Ideas, Definitions, Examples | |
Convergence of Sequences and Series of Distributions | |
Fourier Series | |
Fourier Transforms and Integrals | |
Differential Equations in Distributions | |
Weak Derivatives and Sobolev Spaces | |
One-Dimensional Boundary Value Problems | |
Review | |
Boundary Value Problems for Second-Order Equations | |
Boundary Value Problems for Equations of Order | |
Alternative Theorems | |
Modified Green?s Functions | |
Hilbert and Banach Spaces | |
Functions and Transformations | |
Linear Spaces | |
Metric Spaces, Normed Linear Spaces, Banach Spaces | |
Contractions and the Banach Fixed-Point Theorem | |
Hilbert Spaces, the Projection Theorem | |
Separable Hilbert Spaces and Orthonormal Bases | |
Linear Functionals, the Riesz Representation Theorem | |
The Hahn-Banach Theorem, Reflexive Banach Spaces | |
Operator Theory | |
Basic Ideas and Examples | |
Closed Operators | |
Invertibility--the State of an Operator | |
Adjoint Operators | |
Solvability Conditions | |
The Spectrum of an Operator | |
Compact Operators | |
Extremal Properties of Operators | |
The Banach-Schauder and Banach-Steinhaus Theorems | |
Integral Equations 353 | |
Introduction | |
Fredholm Integral Equations | |
The Spectrum of a Self-Adjoint Compact Operator | |
The Inhomogeneous Equation | |
Variational Principles And Related Approximation Methods | |
Spectral Theory of Second-Order Differential Operators | |
Introduction; The Regular Problem | |
Weyl's Classification of Singular Problems | |
Spectral Problems with a Continuous Spectrum | |
Partial Differential Equations | |
Classification Of Partial Differential Equations | |
Typical Well-Posed Problems for Hyperbolic and Parabolic Equations | |
Elliptic Equations | |
Variational Principles for Inhomogeneous Problems | |
The Lax-Milgram Theorem | |
Nonlinear Problems | |
Introduction and Basic Fixed-Point Techniques | |
Branching Theory | |
Perturbation Theory for Linear Problems | |
Techniques For Nonlinear Problems | |
The Stability of the Steady State | |
Approximation Theory and Methods | |
Nonlinear Analysis Tools for Banach Spaces | |
Best and Near-Best Approximation in Banach Spaces | |
Overview of Sobolev and Besov Spaces | |
Applications to Elliptic Partial Differential Equations | |
Finite Element and Related Discretization Methods | |
Iterative Methods for Discretized Linear Equations | |
Methods for Nonlinear Equations | |
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