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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