Mathematical Methods for Physicists/
Arfken,George B
Mathematical Methods for Physicists/ by George B.Arfken and Hans J.Weber - 5th ed. - San Diego : Harcourt/Academic Press, 2001. - xiv,1112p. ill. ; 25 cm.
Includes bibliographical references and index.
1 Vector Analysis 1 --
1.1 Definitions,Elementary Approach--
1.2 Rotation of the Coordinate Axes --
1.3 Scalar or Dot Product --
1.4 Vector or Cross Product 19 --
1.5 Triple Scalar Product, Triple Vector Product 27 --
1.6 Gradient, [down triangle, open] 35 --
1.7 Divergence, [down triangle, open] 40 --
1.8 Curl, [down triangle, open] x 44 --
1.9 Successive Applications of [down triangle, open] 51 --
1.10 Vector Integration 55 --
1.11 Gauss's Theorem 61 --
1.12 Stokes's Theorem 65 --
1.13 Potential Theory 69 --
1.14 Gauss's Law, Poisson's Equation 80 --
1.15 Dirac Delta Function 84 --
1.16 Helmholtz's Theorem 96 -- 2 Curved Coordinates, Tensors --
2.1 Orthogonal Coordinates --
2.2 Differential Vector Operators --
2.3 Special Coordinate Systems: Introduction --
2.4 Circular Cylindrical Coordinates --
2.5 Spherical Polar Coordinates --
2.6 Tensor Analysis --
2.7 Contraction, Direct Product --
2.8 Quotient Rule --
2.9 Pseudotensors, Dual Tensors --
2.10 Non-Cartesian Tensors --
2.11 Tensor Derivative Operators-- 3 Determinants and Matrices --
3.1 Determinants --
3.2 Matrices --
3.3 Orthogonal Matrices --
3.4 Hermitian Matrices, Unitary Matrices --
3.5 Diagonalization of Matrices --
3.6 Normal Matrices -- 4 Group Theory --
4.1 Introduction to Group Theory --
4.2 Generators of Continuous Groups --
4.3 Orbital Angular Momentum --
4.4 Angular Momentum Coupling --
4.5 Homogeneous Lorentz Group --
4.6 Lorentz Covariance of Maxwell's Equations --
4.7 Discrete Groups -- 5 Infinite Series --
5.2 Convergence Tests --
5.3 Alternating Series --
5.4 Algebra of Series --
5.5 Series of Functions --
5.6 Taylor's Expansion --
5.7 Power Series --
5.8 Elliptic Integrals --
5.9 Bernoulli Numbers, Euler-Maclaurin Formula --
5.10 Asymptotic Series --
5.11 Infinite Products-- 6 Functions of a Complex Variable I--
6.1 Complex Algebra--
6.2 Cauchy-Riemann Conditions --
6.3 Cauchy's Integral Theorem --
6.4 Cauchy's Integral Formula --
6.5 Laurent Expansion --
6.6 Mapping --
6.7 Conformal Mapping -- 7 Functions of a Complex Variable II --
7.1 Singularities --
7.2 Calculus of Residues--
7.3 Dispersion Relations --
7.4 Method of Steepest Descents -- 8 Differential Equations --
8.1 Partial Differential Equations--
8.2 First-Order Differential Equations --
8.3 Separation of Variables --
8.4 Singular Points --
8.5 Series Solutions--Frobenius's Method --
8.6 A Second Solution --
8.7 Nonhomogeneous Equation--Green's Function --
8.8 Numerical Solutions -- 9 Sturm-Liouville Theory --
9.1 Self-Adjoint ODEs --
9.2 Hermitian Operators --
9.3 Gram-Schmidt Orthogonalization --
9.4 Completeness of Eigenfunctions --
9.5 Green's Function--Eigenfunction Expansion -- 10 Gamma-Factorial Function --
10.1 Definitions, Simple Properties --
10.2 Digamma and Polygamma Functions --
10.3 Stirling's Series --
10.4 Beta Function --
10.5 Incomplete Gamma Function -- 11 Bessel Functions --
11.1 Bessel Functions of the First Kind J[subscript v](x) --
11.2 Orthogonality --
11.3 Neumann Functions, Bessel Functions of the Second Kind --
11.4 Hankel Functions --
11.5 Modified Bessel Functions I[subscript v](x) and K[subscript v](x) --
11.6 Asymptotic Expansions --
11.7 Spherical Bessel Functions -- 12 Legendre Functions --
12.1 Generating Function --
12.2 Recurrence Relations --
12.3 Orthogonality --
12.4 Alternate Definitions --
12.5 Associated Legendre Functions--
12.6G Spherical Harmonics --
12.7 Orbital Angular Momentum Operators --
12.8 Addition Theorem for Spherical Harmonics --
12.9 Integrals of Three Ys --
12.10 Legendre Functions of the Second Kind --
12.11 Vector Spherical Harmonics -- 13 Special Functions --
13.1 Hermite Functions --
13.2 Laguerre Functions --
13.3 Chebyshev Polynomials --
13.4 Hypergeometric Functions --
13.5 Confluent Hypergeometric Functions-- 14 Fourier Series --
14.1 General Properties--
14.2 Advantages, Uses of Fouries Series--
14.3 Applications of Fourier Series --
14.4 Properties of Fourier Series --
14.5 Gibbs Phenomenon --
14.6 Discrete Fourier Transform -- 15 Integral Transforms--
15.1 Integral Transforms --
15.2 Development of the Fourier Integral --
15.3 Fourier Transforms--Inversion Theorem --
15.4 Fourier Transform of Derivatives 920 --
15.5 Convolution Theorem 924 --
15.6 Momentum Representation 928 --
15.7 Transfer Functions 935 --
15.8 Laplace Transforms 938 --
15.9 Laplace Transform of Derivatives 946 --
15.10 Other Properties 953 --
15.11 Convolution or Faltungs Theorem 965 --
15.12 Inverse Laplace Transform 969 -- 16 Integral Equations --
16.2 Integral Transforms, Generating Functions --
16.3 Neumann Series, Separable Kernels --
16.4 Hilbert-Schmidt Theory -- 17 Calculus of Variations --
17.1 A Dependent and an Independent Variable --
17.2 Applications of the Euler Equation --
17.3 Several Dependent Variables --
17.4 Several Independent Variables --
17.5 Several Dependent and Independent Variables --
17.6 Lagrangian Multipliers --
17.7 Variation With Constraints --
17.8 Rayleigh-Ritz Variational Technique -- 18 Nonlinear Methods and Chaos --
18.2 Logistic Map --
18.3 Sensitivity to Initial Conditions --
18.4 Nonlinear Differential Equations --
8178670712
Mathematics.
Mathematical physics
510 / ARF/M
Mathematical Methods for Physicists/ by George B.Arfken and Hans J.Weber - 5th ed. - San Diego : Harcourt/Academic Press, 2001. - xiv,1112p. ill. ; 25 cm.
Includes bibliographical references and index.
1 Vector Analysis 1 --
1.1 Definitions,Elementary Approach--
1.2 Rotation of the Coordinate Axes --
1.3 Scalar or Dot Product --
1.4 Vector or Cross Product 19 --
1.5 Triple Scalar Product, Triple Vector Product 27 --
1.6 Gradient, [down triangle, open] 35 --
1.7 Divergence, [down triangle, open] 40 --
1.8 Curl, [down triangle, open] x 44 --
1.9 Successive Applications of [down triangle, open] 51 --
1.10 Vector Integration 55 --
1.11 Gauss's Theorem 61 --
1.12 Stokes's Theorem 65 --
1.13 Potential Theory 69 --
1.14 Gauss's Law, Poisson's Equation 80 --
1.15 Dirac Delta Function 84 --
1.16 Helmholtz's Theorem 96 -- 2 Curved Coordinates, Tensors --
2.1 Orthogonal Coordinates --
2.2 Differential Vector Operators --
2.3 Special Coordinate Systems: Introduction --
2.4 Circular Cylindrical Coordinates --
2.5 Spherical Polar Coordinates --
2.6 Tensor Analysis --
2.7 Contraction, Direct Product --
2.8 Quotient Rule --
2.9 Pseudotensors, Dual Tensors --
2.10 Non-Cartesian Tensors --
2.11 Tensor Derivative Operators-- 3 Determinants and Matrices --
3.1 Determinants --
3.2 Matrices --
3.3 Orthogonal Matrices --
3.4 Hermitian Matrices, Unitary Matrices --
3.5 Diagonalization of Matrices --
3.6 Normal Matrices -- 4 Group Theory --
4.1 Introduction to Group Theory --
4.2 Generators of Continuous Groups --
4.3 Orbital Angular Momentum --
4.4 Angular Momentum Coupling --
4.5 Homogeneous Lorentz Group --
4.6 Lorentz Covariance of Maxwell's Equations --
4.7 Discrete Groups -- 5 Infinite Series --
5.2 Convergence Tests --
5.3 Alternating Series --
5.4 Algebra of Series --
5.5 Series of Functions --
5.6 Taylor's Expansion --
5.7 Power Series --
5.8 Elliptic Integrals --
5.9 Bernoulli Numbers, Euler-Maclaurin Formula --
5.10 Asymptotic Series --
5.11 Infinite Products-- 6 Functions of a Complex Variable I--
6.1 Complex Algebra--
6.2 Cauchy-Riemann Conditions --
6.3 Cauchy's Integral Theorem --
6.4 Cauchy's Integral Formula --
6.5 Laurent Expansion --
6.6 Mapping --
6.7 Conformal Mapping -- 7 Functions of a Complex Variable II --
7.1 Singularities --
7.2 Calculus of Residues--
7.3 Dispersion Relations --
7.4 Method of Steepest Descents -- 8 Differential Equations --
8.1 Partial Differential Equations--
8.2 First-Order Differential Equations --
8.3 Separation of Variables --
8.4 Singular Points --
8.5 Series Solutions--Frobenius's Method --
8.6 A Second Solution --
8.7 Nonhomogeneous Equation--Green's Function --
8.8 Numerical Solutions -- 9 Sturm-Liouville Theory --
9.1 Self-Adjoint ODEs --
9.2 Hermitian Operators --
9.3 Gram-Schmidt Orthogonalization --
9.4 Completeness of Eigenfunctions --
9.5 Green's Function--Eigenfunction Expansion -- 10 Gamma-Factorial Function --
10.1 Definitions, Simple Properties --
10.2 Digamma and Polygamma Functions --
10.3 Stirling's Series --
10.4 Beta Function --
10.5 Incomplete Gamma Function -- 11 Bessel Functions --
11.1 Bessel Functions of the First Kind J[subscript v](x) --
11.2 Orthogonality --
11.3 Neumann Functions, Bessel Functions of the Second Kind --
11.4 Hankel Functions --
11.5 Modified Bessel Functions I[subscript v](x) and K[subscript v](x) --
11.6 Asymptotic Expansions --
11.7 Spherical Bessel Functions -- 12 Legendre Functions --
12.1 Generating Function --
12.2 Recurrence Relations --
12.3 Orthogonality --
12.4 Alternate Definitions --
12.5 Associated Legendre Functions--
12.6G Spherical Harmonics --
12.7 Orbital Angular Momentum Operators --
12.8 Addition Theorem for Spherical Harmonics --
12.9 Integrals of Three Ys --
12.10 Legendre Functions of the Second Kind --
12.11 Vector Spherical Harmonics -- 13 Special Functions --
13.1 Hermite Functions --
13.2 Laguerre Functions --
13.3 Chebyshev Polynomials --
13.4 Hypergeometric Functions --
13.5 Confluent Hypergeometric Functions-- 14 Fourier Series --
14.1 General Properties--
14.2 Advantages, Uses of Fouries Series--
14.3 Applications of Fourier Series --
14.4 Properties of Fourier Series --
14.5 Gibbs Phenomenon --
14.6 Discrete Fourier Transform -- 15 Integral Transforms--
15.1 Integral Transforms --
15.2 Development of the Fourier Integral --
15.3 Fourier Transforms--Inversion Theorem --
15.4 Fourier Transform of Derivatives 920 --
15.5 Convolution Theorem 924 --
15.6 Momentum Representation 928 --
15.7 Transfer Functions 935 --
15.8 Laplace Transforms 938 --
15.9 Laplace Transform of Derivatives 946 --
15.10 Other Properties 953 --
15.11 Convolution or Faltungs Theorem 965 --
15.12 Inverse Laplace Transform 969 -- 16 Integral Equations --
16.2 Integral Transforms, Generating Functions --
16.3 Neumann Series, Separable Kernels --
16.4 Hilbert-Schmidt Theory -- 17 Calculus of Variations --
17.1 A Dependent and an Independent Variable --
17.2 Applications of the Euler Equation --
17.3 Several Dependent Variables --
17.4 Several Independent Variables --
17.5 Several Dependent and Independent Variables --
17.6 Lagrangian Multipliers --
17.7 Variation With Constraints --
17.8 Rayleigh-Ritz Variational Technique -- 18 Nonlinear Methods and Chaos --
18.2 Logistic Map --
18.3 Sensitivity to Initial Conditions --
18.4 Nonlinear Differential Equations --
8178670712
Mathematics.
Mathematical physics
510 / ARF/M