Applied mathematical methods in theoretical physics /
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| Author / Creator: | Masujima, Michio, 1949- |
|---|---|
| Imprint: | Weinheim : Wiley-VCH, c2005. |
| Description: | xi, 377 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6287840 |
Table of Contents:
- Preface
- Introduction
- 1. Function Spaces, Linear Operators and Green's Functions
- 1.1. Function Spaces
- 1.2. Ortho normal System of Functions
- 1.3. Linear Operators
- 1.4. Eigen values and Eigen functions
- 1.5. The Fredholm Alternative
- 1.6. Self-adjoint Operators
- 1.7. Green's Functions for Differential Equations
- 1.8. Review of Complex Analysis
- 1.9. Review of Fourier Transform
- 2. Integral Equations and Green's Functions
- 2.1. Introduction to Integral Equations
- 2.2. Relationship of Integral Equations with Differential Equations and Green's Functions
- 2.3. Sturm-Liouville System
- 2.4. Green's Function for Time-Dependent Scattering Problem
- 2.5. Lippmann-Schwinger Equation
- 2.6. Problems for Chapter 2
- 3. Integral Equations of Volterra Type
- 3.1. Iterative Solution to Volterra Integral Equation of the Second Kind
- 3.2. Solvable cases of Volterra Integral Equation
- 3.3. Problems for Chapter 3
- 4. Integral Equations of the Fredholm Type
- 4.1. Iterative Solution to the Fredholm Integral Equation of the Second Kind
- 4.2. Resolvent Kernel
- 4.3. Pincherle-Goursat Kernel
- 4.4. Fredholm Theory for a Bounded Kernel
- 4.5. Solvable Example
- 4.6. Fredholm Integral Equation with a Translation Kernel
- 4.7. System of Fredholm Integral Equations of the Second Kind
- 4.8. Problems for Chapter 4
- 5. Hilbert-Schmidt Theory of Symmetric Kernel
- 5.1. Real and Symmetric Matrix
- 5.2. Real and Symmetric Kernel
- 5.3. Bounds on the Eigen values
- 5.4. Rayleigh Quotient
- 5.5. Completeness of Sturm-Liouville Eigen functions
- 5.6. Generalization of Hilbert-Schmidt Theory
- 5.7. Generalization of Sturm-Liouville System
- 5.8. Problems for Chapter 5
- 6. Singular Integral Equations of Cauchy Type
- 6.1. Hilbert Problem
- 6.2. Cauchy Integral Equation of the First Kind
- 6.3. Cauchy Integral Equation of the Second Kind
- 6.4. Carleman Integral Equation
- 6.5. Dispersion Relations
- 6.6. Problems for Chapter 6
- 7. Wiener-Hopf Method and Wiener-Hopf Integral Equation
- 7.1. The Wiener-Hopf Method for Partial Differential Equations
- 7.2. Homogeneous Wiener-Hopf Integral Equation of the Second Kind
- 7.3. General Decomposition Problem
- 7.4. Inhomogeneous Wiener-Hopf Integral Equation of the Second Kind
- 7.5. Toeplitz Matrix and Wiener-Hopf Sum Equation
- 7.6. Wiener-Hopf Integral Equation of the First Kind and Dual Integral Equations
- 7.7. Problems for Chapter 7
- 8. Nonlinear Integral Equations
- 8.1. Nonlinear Integral Equation of Volterra type
- 8.2. Nonlinear Integral Equation of Fredholm Type
- 8.3. Nonlinear Integral Equation of Hammerstein type
- 8.4. Problems for Chapter 8
- 9. Calculus of Variations: Fundamentals
- 9.1. Historical Background
- 9.2. Examples
- 9.3. Euler Equation
- 9.4. Generalization of the Basic Problems
- 9.5. More Examples
- 9.6. Differential Equations, Integral Equations, and Extremization of Integrals
- 9.7. The Second Variation
- 9.8. Weierstrass-Erdmann Corner Relation
- 9.9. Problems for Chapter 9
- 10. Calculus of Variations: Applications
- 10.1. Feynman's Action Principle in Quantum Mechanics
- 10.2. Feynman's Variational Principle in Quantum Statistical Mechanics
- 10.3. Schwinger-Dyson Equation in Quantum Field Theory
- 10.4. Schwinger-Dyson Equation in Quantum Statistical Mechanics
- 10.5. Weyl's Gauge P
