Mathematical methods for physicists.
| Main Author: | |
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| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Boston :
Elsevier,
2005.
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| Edition: | 6th ed. / |
| Subjects: |
Table of Contents:
- Cover
- Contents
- Preface
- Vector Analysis
- Definitions, Elementary Approach
- Rotation of the Coordinate Axes3
- Scalar or Dot Product
- Vector or Cross Product
- Triple Scalar Product, Triple Vector Product
- Gradient,
- Divergence,
- Curl, x
- Successive Applications of
- Vector Integration
- Gauss' Theorem
- Stokes' Theorem
- Potential Theory
- Gauss' Law, Poisson's Equation
- Dirac Delta Function
- Helmholtz's Theorem
- Additional Readings
- Vector Analysis in Curved Coordinates and Tensors
- Orthogonal Coordinates in R3
- Differential Vector Operators
- Special Coordinate Systems: Introduction
- Circular Cylinder Coordinates
- Spherical Polar Coordinates
- Tensor Analysis
- Contraction, Direct Product
- Quotient Rule
- Pseudotensors, Dual Tensors
- General Tensors
- Tensor Derivative Operators
- Additional Readings
- Determinants and Matrices
- Determinants
- Matrices
- Orthogonal Matrices
- Hermitian Matrices, Unitary Matrices
- Diagonalization of Matrices
- Normal Matrices
- Additional Readings
- Group Theory
- Introduction to Group Theory
- Generators of Continuous Groups
- Orbital Angular Momentum
- Angular Momentum Coupling
- Homogeneous Lorentz Group
- Lorentz Covariance of Maxwell's Equations
- Discrete Groups
- Differential Forms
- Additional Readings
- Infinite Series
- Fundamental Concepts
- Convergence Tests
- Alternating Series
- Algebra of Series
- Series of Functions
- Taylor's Eexpansion
- Power Series
- Elliptic Integrals
- Bernoulli Numbers, Euler-Maclaurin Formula
- Asymptotic Series
- Infinite Products
- Additional Readings
- Functions of a Complex Variable I: Analytic Properties, Mapping
- Complex Algebra
- Cauchy-Riemann Conditions
- Cauchy's Integral Theorem
- Cauchy's Integral Formula
- Laurent Expansion
- Singularities
- Mapping
- Conformal Mapping
- Additional Readings
- Functions of a Complex Variable II
- Calculus of Residues
- Dispersion Relations
- Method of Steepest Descents
- Additional Readings
- The Gamma Function (Factorial Function)
- Definitions, Simple Properties
- Digamma and Polygamma Functions
- Stirling's Series
- The Beta Function
- The Incomplete Gamma Functions and Related Functions
- Additional Readings
- Differential Equations
- Partial Differential Equations
- First-Order Differential Equations
- Separation of Variables
- Singular Points
- Series Solutions-Frobenius' Method
- A Second Solution
- Nonhomogeneous Equation-Green's Function
- Heat Flow, or Diffusion, PDE
- Additional Readings
- Sturm-Liouville Theory-Orthogonal Functions
- Self-aAjoint ODEs
- Hermitian Operators
- Gram-Sschmidt Orthogonalization
- Completeness of Eigenfunctions
- Green's Function-Eigenfunction Expansion
- Additional Readings
- Bessel Functions
- Bessel Functions of the First Kind, Jnu(x)
- Orthogonality
- Neumann Functions, Bessel Functions of th.