- #1
- 19,437
- 10,007
- Author: George B. Arfken (Author), Hans J. Weber (Author), Frank E. Harris (Author)
- Title: Mathematical Methods for Physicists
- Amazon Link: https://www.amazon.com/dp/0123846544/?tag=pfamazon01-20
- Prerequisities: Calculus 1,2,3
Table of Contents:
Code:
[LIST]
[*] Preface
[*] Vector Analysis
[LIST]
[*] Definitions, Elementary Approach
[*] Rotation of the Coordinate Axes
[*] 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
[/LIST]
[*] Vector Analysis in Curved Coordinates and Tensors
[LIST]
[*] Orthogonal Coordinates in R^3
[*] 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
[/LIST]
[*] Determinants and Matrices
[LIST]
[*] Determinants
[*] Matrices
[*] Orthogonal Matrices
[*] Hermitian Matrices, Unitary Matrices
[*] Diagonalization of Matrices
[*] Normal Matrices
[*] Additional Readings
[/LIST]
[*] Group Theory
[LIST]
[*] 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
[/LIST]
[*] Infinite Series
[LIST]
[*] Fundamental Concepts
[*] Convergence Tests
[*] Alternating Series
[*] Algebra of Series
[*] Series of Functions
[*] Taylor's Expansion
[*] Power Series
[*] Elliptic Integrals
[*] Bernoulli Numbers, Euler-Maclaurin Formula
[*] Asymptotic Series
[*] Infinite Products
[*] Additional Readings
[/LIST]
[*] Functions of a Complex Variable I Analytic Properties, Mapping
[LIST]
[*] Complex Algebra
[*] Cauchy-Riemann Conditions
[*] Cauchy's Integral Theorem
[*] Cauchy's Integral Formula
[*] Laurent Expansion
[*] Singularities
[*] Mapping
[*] Conformal Mapping
[*] Additional Readings
[/LIST]
[*] Functions of a Complex Variable II
[LIST]
[*] Calculus of Residues
[*] Dispersion Relations
[*] Method of Steepest Descents
[*] Additional Readings
[/LIST]
[*] The Gamma Function (Factorial Function)
[LIST]
[*] Definitions, Simple Properties
[*] Digamma and Polygamma Functions
[*] Stirling's Series
[*] The Beta Function
[*] Incomplete Gamma Function
[*] Additional Readings
[/LIST]
[*] Differential Equations
[LIST]
[*] Partial Differential Equations
[*] First-Order Differential Equations
[*] Separation of Variables
[*] Singular Points
[*] Series Solutions—Frobeniusy Method
[*] A Second Solution
[*] Nonhomogeneous Equation—Green's Function
[*] Heat Flow, or Diffusion, PDF
[*] Additional Readings
[/LIST]
[*] Sturm-Liouville Theory—Orthogonal Functions
[LIST]
[*] Self-Adjoint ODEs
[*] Hermitian Operators
[*] Gram-Schmidt Orthogonalization
[*] Completeness of Eigenfunctions
[*] Green's Function—Eigenfunction Expansion
[*] Additional Readings
[/LIST]
[*] Bessel Functions
[LIST]
[*] Bessel Functions of the First Kind, J_v(x)
[*] Orthogonality
[*] Neumann Functions
[*] Hankel Functions
[*] Modified Bessel Functions, I_v(x) and K_v(x)
[*] Asymptotic Expansions
[*] Spherical Bessel Functions
[*] Additional Readings
[/LIST]
[*] Legendre Functions
[LIST]
[*] Generating Function
[*] Recurrence Relations
[*] Orthogonality
[*] Alternate Definitions
[*] Associated Legendre Functions
[*] Spherical Harmonics
[*] Orbital Angular Momentum Operators
[*] Addition Theorem for Spherical Harmonics
[*] Integrals of Three Y's
[*] Legendre Functions of the Second Kind
[*] Vector Spherical Harmonics
[*] Additional Readings
[/LIST]
[*] More Special Functions
[LIST]
[*] Hermite Functions
[*] Laguerre Functions
[*] Chebyshev Polynomials
[*] Hypergeometric Functions
[*] Confluent Hypergeometric Functions
[*] Mathieu Functions
[*] Additional Readings
[/LIST]
[*] Fourier Series
[LIST]
[*] General Properties
[*] Advantages, Uses of Fourier Series
[*] Applications of Fourier Series
[*] Properties of Fourier Series
[*] Gibbs Phenomenon
[*] Discrete Fourier Transform
[*] Fourier Expansions of Mathieu Functions
[*] Additional Readings
[/LIST]
[*] Integral Transforms
[LIST]
[*] Integral Transforms
[*] Development of the Fourier Integral
[*] Fourier Transforms—Inversion Theorem
[*] Fourier Transform of Derivatives
[*] Convolution Theorem
[*] Momentum Representation
[*] Transfer Functions
[*] Laplace Transforms
[*] Laplace Transform of Derivatives
[*] Other Properties
[*] Convolution (Faltungs) Theorem
[*] Inverse Laplace Transform
[*] Additional Readings
[/LIST]
[*] Integral Equations
[LIST]
[*] Introduction
[*] Integral Transforms, Generating Functions
[*] Neumann Series, Separable (Degenerate) Kernels
[*] Hilbert-Schmidt Theory
[*] Additional Readings
[/LIST]
[*] Calculus of Variations
[LIST]
[*] A Dependent and an Independent Variable
[*] Applications of the Euler Equation
[*] Several Dependent Variables
[*] Several Independent Variables
[*] Several Dependent and Independent Variables
[*] Lagrangian Multipliers
[*] Variation with Constraints
[*] Rayleigh-Ritz Variational Technique
[*] Additional Readings
[/LIST]
[*] Nonlinear Methods and Chaos
[LIST]
[*] Introduction
[*] The Logistic Map
[*] Sensitivity to Initial Conditions and Parameters
[*] Nonlinear Differential Equations
[*] Additional Readings
[/LIST]
[*] Probability
[LIST]
[*] Definitions, Simple Properties
[*] Random Variables
[*] Binomial Distribution
[*] Poisson Distribution
[*] Gauss'Normal Distribution
[*] Statistics
[*] Additional Readings
[/LIST]
[*] General References
[*] Index
[/LIST]
Last edited: