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Mathematical physics

Author: Robert W Carroll
Publisher: Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988.
Series: North-Holland mathematics studies, 152.; Notas de matemática (Rio de Janeiro, Brazil), no. 121.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Carroll, Robert Wayne, 1930-
Mathematical physics.
Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988
(DLC) 88011195
(OCoLC)17873809
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Robert W Carroll
ISBN: 9780444704436 0444704434 9780080872636 0080872638 1281793213 9781281793218
OCLC Number: 316566723
Description: 1 online resource (x, 399 pages) : illustrations.
Contents: Front Cover; Mathematical Physics; Copyright Page; PREFACE; CONTENTS; CHAPTER 1. CLASSICAL IDEAS AND PROBLEMS; CHAPTER 2. SCATTERING THEORY AND SOLITONS; CHAPTER 3. SOME NONLINER ANALYSIS: SOME GEOMETRIC FORMALISM; APPENDIX A. INTRODUCTION TO LINEAR FUNCTIONAL ANALYSIS; APPENDIX B. SELECTED TOPICS IN FUNCTIONAL ANALYSIS; APPENDIX C. INTRODUCTION TO DIFFERENTIAL GEOMETRY; REFERENCES; INDEX.
Series Title: North-Holland mathematics studies, 152.; Notas de matemática (Rio de Janeiro, Brazil), no. 121.
Responsibility: Robert Carroll.

Abstract:

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. Ill-Posed Problems and Regularization. 2. Scattering Theory and Solitons. Introduction. Scattering Theory I (Operator Theory). Scattering Theory II (3-D). Scattering Theory III (A Medley of Themes). Scattering Theory IV (Spectral Methods in 3-D). Systems and Half Line Problems. Relations between Potentials and Spectral Data. Introduction to Soliton Theory. Solitons via AKNS Systems. Soliton Theory (Hamiltonian Structure). Some Topics in Integrable Systems. 3. Some Nonlinear Analysis: Some Geometric Formalism. Introduction. Nonlinear Analysis. Monotone Operators. Topological Methods. Convex Analysis. Nonlinear Semigroups and Monotone Sets. Variational Inequalities. Quantum Field Theory. Gauge Fields (Physics). Gauge Fields (Mathematics) and Geometric Quantization. Appendices: Introduction to Linear Functional Analysis. Selected Topics in Functional Analysis. Introduction to Differential Geometry. References. Index.

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