Mathematical Physics

Robert Carroll (Eds.)0444704434, 9780444704436, 9780080872636

An introduction to the important areas of mathematical physics, this volume starts with basic ideas and proceeds (sometimes rapidly) to a more sophisticated level, often to the context of current research. All of the necessary functional analysis and differential geometry is included, along with basic calculus of variations and partial differential equations (linear and nonlinear). An introduction to classical and quantum mechanics is given with topics in Feynman integrals, gauge fields, geometric quantization, attractors for PDE, Ginzburg-Landau Equations in superconductivity, Navier-Stokes equations, soliton theory, inverse problems and ill-posed problems, scattering theory, convex analysis, variational inequalities, nonlinear semigroups, etc. Contents: 1. Classical Ideas and Problems. Introduction. Some Preliminary Variational Ideas. Various Differential Equations and Their Origins. Linear Second Order PDE. Further Topics in the Calculus of Variations. Spectral Theory for Ordinary Differential Operators, Transmutation, and Inverse Problems. Introduction to Classical Mechanics. Introduction to Quantum Mechanics. Weak Problems in PDE. Some Nonlinear PDE.

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Table of contents :
Content:
Editor
Page ii

Edited by
Page iii

Copyright page
Page iv

Preface
Pages v-viii

Chapter 1 Classical Ideas and Problems
Pages 1-98

Chapter 2 Scattering Theory and Solitons
Pages 99-225

Chapter 3 Some Nonlinear Analysis; Some Geometric Formalism
Pages 227-309

Appendix A Introduction to Linear Functional Analysis
Pages 311-327

Appendix B Selected Topics in Functional Analysis
Pages 329-349

Appendix C Introduction to Differential Geometry
Pages 351-375

References Review Article
Pages 377-391

Index
Pages 393-399