Advanced Methods of Mathematical Physics

R.S. Kaushal and D. Parashar

ISBN 10: 0849309530 / ISBN 13: 9780849309533

Editore: Narosa, 2000

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Dati bibliografici

• Titolo: Advanced Methods of Mathematical Physics
• Editore: Narosa
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0849309530
• ISBN 13: 9780849309533
• Rilegatura: Hard Cover
• Condizione: As New
• Condizione della sovraccoperta: Very Good
• Cataloghi dei venditori:
  • Mathematics
  • Physics

Descrizione articolo

Riassunto

In an introductory style with many examples, Advanced Methods of Mathematical Physics presents some of the concepts, methods, and tools that form the core of mathematical physics. The material covers two main broad categories of topics: 1) abstract topics, such as groups, topology, integral equations, and stochasticity, and 2) the methods of nonlinear dynamics.

Contenuti

GENERAL INTRODUCTION
THEORY OF FINITE GROUPS
A Brief Review of Set Theory
Abstract Groups
Homomorphisms
Group Representations
Introduction to Continuous Groups
Applications to Physical Problems
RUDIMENTS OF TOPOLOGY AND DIFFERENTIAL GEOMETRY
Preliminaries
Metric Spaces
Topological Spaces
Compactness
Connectedness
Homotopy
Essentials of Differential Geometry
INTEGRAL EQUATIONS, STURM-LIOUVILLE THEORY AND GREEN'S FUNCTIONS
Terminology and Definitions
Solution of Integral Equations
Sturm-Liouville Theory
The Green's Functions
Applications to Physics Problems
STOCHASTIC PROCESSES AND STOCHASTIC DIFFERENTIAL EQUATIONS
Random Variable and Distribution Function of Random Variables
Numerical Characteristics of Random Variables: Moments of the Distribution Function
Stochastic Processes: Markov Process
Stochastic Differential Equations: An Introduction
Applications to Physical Problems
METHODS OF NONLINEAR DYNAMICS I: PHASE PORTRAITS
A Brief Survey of Nonlinear Operators and Differential Equations
Solution of Nonlinear Differential Equations: Existence and Uniqueness Theorems
Critical Point Analysis of Differential Equations
Nonlinear Systems in the Plane
METHODS OF NONLINEAR DYNAMICS II: STABILITY AND BIFURCATION
Stability of Critical Points and Liapunov Functions
Limit Cycle
Index of a Critical Point and Bendixson Criterion for Periodic Solutions
Bifurcation and Structural Stability
Applications to Physical Problems
SOME NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS
Van der Pol Equation
Solitary-Wave Solutions of Nonlinear Differential Equations
Solitary-Wave Solution of Nonlinear Schrodinger Equation
Application to Physical Problems
SOME NONLINEAR INTEGRAL EQUATIONS AND THEIR SOLUTIONS
Inverse Scattering Transform Method
Backlund Transformation and the Solution of KdV Equation
The Lax Pair Method
Hirota's Method of Bilinear Derivatives
Painleve' Property and Painleve' Transcendents
Kadomstev-Petviashvili (KP) Equation and Its Solutions
Solution of Some Nonlinear Integral Equations
EXACT SOLUTION OF SOME NONLINEAR DIFFERENTIAL EQUATIONS
Riccati Equation
Exact Solution of Some Other NLODEs
Nonlinear diffusion Equations
Exact Solution of Some Other NLPDEs
Applications to Physical Problems
SYMMETRIES OF DIFFERENTIAL EQUATIONS
Symmetry Groups of Differential Equations: An Introduction
Extended Transformations or Prolongations
Extended Infinitesimal Transformations
Invariance of an Ordinary Differential Equation
Invariance of a Partial Differential Equation
Symmetry Groups and Conservation Laws
Noether's Theorem and Lie-Backlund Symmetries
NORMAL MODES IN NONLINEAR DYNAMICAL SYSTEMS
Normal Modes of Linear Systems: A Brief Survey
Normal Modes of Nonlinear Systems: A Simple Generalization
Types of Mode Interactions: A Group Theoretic Approach
Bushes of Modes for a Dynamical System
Dynamical Bush Equations: Normal Forms Theory
APPENDIX: SOME NUMERICAL ASPECTS OF NONLINEAR DYNAMICAL SYSEMS VIS-À-VIS CHAOS