Applications to mathematical physics
著者
書誌事項
Applications to mathematical physics
（Nonlinear functional analysis and its applications / Eberhard Zeidler, 4）
Springer-Verlag, 1997
corrected 2nd printing
- : us
- : gw
- : softcover
- タイトル別名
-
Vorlesungen über nichtlineare Funktionalanalysis
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注記
Includes bibliographies and indexes
"Originally published by Springer-Verlag New York Inc. in 1988" on softcover
"Softcover reprint of the hardcover 1st edition 1988" on softcover
内容説明・目次
- 巻冊次
-
: us ISBN 9780387964997
内容説明
The fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text.
目次
- Preface
- Preface to Second Corrected Printing
- Translator's Preface
- Introduction: Mathematics and Physics
- APPLICATIONS IN MECHANICS: Basic Equations of Point Mechanics
- Dualism Between Wave and Particle, Preview of Quantum Theory, and Elementary Particles
- APPLICATIONS IN ELASTICITY THEORY: Elastoplastic Wire
- Basic Equations of Nonlinear Elasticity Theory
- Monotone Potential Operators and a Class of Models with Nonlinear Hooke's Law, Duality and Plasticity, and Polyconvexity
- Variational Inequalities and the Signorini Problem for Nonlinear Material
- Bifurcation for Variational Inequalities
- Pseudomonotone Operators, Bifurcation, and the von K rm n Plate Equations
- Convex Analysis, Maximal Monotone Operators, and Elasto-Viscoplastic Material with Linear Hardening and Hysteresis
- APPLICATIONS IN THERMODYNAMICS: Phenomenological Thermodynamics of Quasi-Equilibrium and Equilibrium States
- Statistical Physics
- Continuation with Respect to a Parameter and a Radiation Problem of Carleman
- APPLICATIONS IN HYDRODYNAMICS: Basic Equations of Hydrodynamics
- Bifurcation and Permanent Gravitational Waves
- Viscoud Fluids and the Navier-Stokes Equations
- MANIFOLDS AND THEIR APPLICATIONS: Banach Manifolds
- Classical Surface
- 巻冊次
-
: softcover ISBN 9781461289265
内容説明
The fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text.
目次
- Preface
- Preface to Second Corrected Printing
- Translator's Preface
- Introduction: Mathematics and Physics
- APPLICATIONS IN MECHANICS: Basic Equations of Point Mechanics
- Dualism Between Wave and Particle, Preview of Quantum Theory, and Elementary Particles
- APPLICATIONS IN ELASTICITY THEORY: Elastoplastic Wire
- Basic Equations of Nonlinear Elasticity Theory
- Monotone Potential Operators and a Class of Models with Nonlinear Hooke's Law, Duality and Plasticity, and Polyconvexity
- Variational Inequalities and the Signorini Problem for Nonlinear Material
- Bifurcation for Variational Inequalities
- Pseudomonotone Operators, Bifurcation, and the von K rm n Plate Equations
- Convex Analysis, Maximal Monotone Operators, and Elasto-Viscoplastic Material with Linear Hardening and Hysteresis
- APPLICATIONS IN THERMODYNAMICS: Phenomenological Thermodynamics of Quasi-Equilibrium and Equilibrium States
- Statistical Physics
- Continuation with Respect to a Parameter and a Radiation Problem of Carleman
- APPLICATIONS IN HYDRODYNAMICS: Basic Equations of Hydrodynamics
- Bifurcation and Permanent Gravitational Waves
- Viscoud Fluids and the Navier-Stokes Equations
- MANIFOLDS AND THEIR APPLICATIONS: Banach Manifolds
- Classical Surface
- 巻冊次
-
: gw ISBN 9783540964995
内容説明
This is the fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics and numerical analysis. The presentation is self-contained and should be accessible to the non-specialist. It attempts to combine classical and modern ideas and to build a bridge between the language and thoughts of physicists and mathematicians. This corrected printing is fully revised and contains a new section of additional references along with many exercises. Topics covered in this volume include: applications to mechanics; elasticity; plasticity; hydrodynamics; thermodynamics; statistical physics; and special and general relativity, including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained.
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