INDICE: Preface to Third Edition. Preface to Second Edition. Preface to First Edition. 0 Preliminaries. 1 Heat Conduction. 2 Diffusion. 3 Reaction-Diffusion Problems. 4 The Impulse-Momentum Law: The Motion of Rods and Strings. 5 Alternative Formulations of Physical Problems. 6 Notes on Convergence. 7 The Lebesgue Integral. 1 Greens Functions (Intuitive Ideas). 1 Introduction and General Comments. 2 The Finite Rod. 3 Maximum Principle. 4 Examples of Greens Functions. 2 The Theory of Distributions. 1 Basic Ideas, Definitions, Examples. 2 Convergence of Sequences and Series of Distributions. 3 Fourier Series. 4 Fourier Transforms and Integrals. 5 Differential Equations in Distributions. 6 WeakDerivatives and Sobolev Spaces. 3 One-Dimensional Boundary Value Problems. 1 Review. 2 Boundary Value Problems for Second-Order Equations. 3 Boundary ValueProblems for Equations of Order. 4 Alternative Theorems. 5 Modified Green?s Functions. 4 Hilbert and Banach Spaces. 1 Functions and Transformations. 2 Linear Spaces. 3 Metric Spaces, Normed Linear Spaces, Banach Spaces. 4 Contractions and the Banach Fixed-Point Theorem. 5 Hilbert Spaces, the Projection Theorem. 6 Separable Hilbert Spaces and Orthonormal Bases. 7 Linear Functionals, the Riesz Representation Theorem. 8 The Hahn-Banach Theorem, Reflexive Banach Spaces. 5 Operator Theory. 1 Basic Ideas and Examples. 2 Closed Operators. 3 Invertibility--the State of an Operator. 4 Adjoint Operators. 5 Solvability Conditions. 6 The Spectrum of an Operator. 7 Compact Operators. 8 Extremal Propertiesof Operators. 9 The Banach-Schauder and Banach-Steinhaus Theorems. 6 IntegralEquations 353. 1 Introduction. 2 Fredholm Integral Equations. 3 The Spectrum of a Self-Adjoint Compact Operator. 4 The Inhomogeneous Equation. 5 Variational Principles And Related Approximation Methods. 7 Spectral Theory of Second-Order Differential Operators. 1 Introduction; The Regular Problem. 2 Weyls Classification of Singular Problems. 3 Spectral Problems with a Continuous Spectrum. 8 Partial Differential Equations. 1 Classification Of Partial Differential Equations. 2 Typical Well-Posed Problems for Hyperbolic and Parabolic Equations. 3 Elliptic Equations. 4 Variational Principles for Inhomogeneous Problems. 5The Lax-Milgram Theorem. 9 Nonlinear Problems. 1 Introduction and Basic Fixed-Point Techniques. 2 Branching Theory. 3 Perturbation Theory for Linear Problems. 4 Techniques For Nonlinear Problems. 5 The Stability of the Steady State. 10 Approximation Theory and Methods. 1 Nonlinear Analysis Tools for Banach Spaces. 2 Best and Near-Best Approximation in Banach Spaces. 3 Overview of Sobolev and Besov Spaces. 4 Applications to Elliptic Partial Differential Equations.5 Finite Element and Related Discretization Methods. 6 Iterative Methods for Discretized Linear Equations. 7 Methods for Nonl
- ISBN: 978-0-470-60970-5
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 930
- Fecha Publicación: 23/12/2010
- Nº Volúmenes: 1
- Idioma: Inglés
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