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Mathematical Methods for Physicists/ by George B.Arfken and Hans J.Weber

By:

Arfken,George B

Contributor(s):

Weber,Hans J

Material type: Text

TextPublication details: San Diego : Harcourt/Academic Press, 2001.Edition: 5th edDescription: xiv,1112p. ill. ; 25 cmISBN:

8178670712

Subject(s):

DDC classification:

510 ARF/M

Contents:

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 --

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Book	Study Centre Alappuzha, University of Kerala	Study Centre Alappuzha, University of Kerala	510 ARF/M (Browse shelf(Opens below))	Available		USCA3536

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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 --

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