Mathematical methods for physicists
"Mathematical Methods for Physicists serves as both textbook and/or useful reference work. This renowned and well respected title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics and engineering. The mathematical relations are clearly illustrated and proven. It is a vital addition to the bookshelf of any serious student of physics and or research professional in the field."--Jacket
1 online resource (xii, 1182 pages) : illustrations
9780080470696, 9786610961146, 9781280961144, 0080470696, 661096114X, 1280961147
127114279
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
English