Mathematical methods for Physicists by Arfken and Weber torrent

This book is the most preferred reference for maths required at the graduate level by physics students. In the djvu version here only first 15 chapters are present thus excluding the last three. however those absent are relatively unimportant as you will find out from the table of contents and are meant for a higher level.

Contents

1 Vector Analysis 1
1.1 Definitions, Elementary Approach 1
1.2 Rotation of the Coordinate Axes 8
1.3 Scalar or Dot Product 13
1.4 Vector or Cross Product 19
1.5 " Triple Scalar Product, Triple Vector Product ." 27
1.6 Gradient, V 35
1.7 Divergence, V- . 40
1.8 Curl, Vx 44
1.9 Successive Applications of V 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 103
2.1 Orthogonal Coordinates 103
2.2 Differential Vector Operators 108
2.3 Special Coordinate Systems: Introduction 113
2.4 Circular Cylindrical Coordinates 114
2.5 Spherical Polar Coordinates 121
2.6 Tensor Analysis 131
2.7 Contraction, Direct Product 137
2.8 Quotient Rule 139
2.9 Pseudotensors, Dual Tensors 141
2.10 Non-Cartesian Tensors 150
2.11 Tensor Derivative Operators 160

3 Determinants and Matrices 165
3.1 Determinants 165
3.2 Matrices 174
3.3 Orthogonal Matrices 192
3.4 Hermitian Matrices, Unitary Matrices 206
3.5 Diagonalization of Matrices 213
3.6 Normal Matrices . 227

4 Group Theory 237
4.1 Introduction to Group Theory 237
4.2 Generators of Continuous Groups 242
4.3 Orbital Angular Momentum 258
4.4 Angular Momentum Coupling 263
4.5 Homogeneous Lorentz Group 275
4.6 Lorentz Covariance of Maxwell's Equations 278
4.7 Discrete Groups 286

5 Infinite Series 303
5.1 Fundamental Concepts 303
5.2 Convergence Tests 306
5.3 Alternating Series 322
5.4 Algebra of Series 325
5.5 Series of Functions 329
5.6 Taylor's Expansion 334
5.7 Power Series . . . 346
5.8 Elliptic Integrals 354
5.9 Bernoulli Numbers, Euler-Maclaurin Formula 360
5.10 Asymptotic Series 373
5.11 Infinite Products 381

6 Functions of a Complex Variable I 389
6.1 Complex Algebra 390
6.2 Cauchy-Riemann Conditions . 399
6.3 Cauchy's Integral Theorem 404
6.4 Cauchy's Integral Formula 411
6.5 Laurent Expansion 416
6.6 Mapping 425
6.7 Conformal Mapping 434

7 Functions of a Complex Variable II 439
7.1 Singularities 439
7.2 Calculus of Residues 444
7.3 Dispersion Relations 469
7.4 Method of Steepest Descents 477

8 Differential Equations 487
8.1 Partial Differential Equations 487
8.2 First-Order Differential Equations 496
8.3 Separation of Variables 506
8.4 Singular Points 516
8.5 Series Solutions—Frobenius's Method 518
8.6 A Second Solution 533
8.7 Nonhomogeneous Equation — Green's Function 548
8.8 Numerical Solutions 567

9 Stnrm-Liouville Theory 575
9.1 Self-Adjoint ODEs 575
9.2 Hermitian Operators 588
9.3 Gram-Schmidt Orthogonalization 596
9.4 Completeness of Eigenfunctions 604
9.5 Green's Function — Eigenfunction Expansion 616

10 Gamma-Factorial Function 631
10.1 Definitions, Simple Properties 631
10.2 Digamma and Polygamma Functions . . 643
10.3 Stirling's Series 649
10.4 The Beta Function 654
10.5 Incomplete Gamma Function 660

11 Bessel Functions 669
11.1 Bessel Functions of the First Kind Jv (x) 669
11.2 Orthogonality 688
11.3 Neumann Functions, Bessel Functions of the Second Kind .... 694
11.4 Hankel Functions 702
11.5 Modified Bessel Functions Iv(x) and Kv(x) 709
11.6 Asymptotic Expansions 716
11.7 Spherical Bessel Functions 722

12 Legendre Functions 739
12.1 Generating Function 739
12.2 Recurrence Relations 748
12.3 Orthogonality 755
12.4 Alternate Definitions 767
12.5 Associated Legendre Functions 771
12.6 Spherical Harmonics 786
12.7 Orbital Angular Momentum Operators 792
12.8 The Addition Theorem for Spherical Harmonics 796
12.9 Integrals of Three Ys 802
12.10 Legendre Functions of the Second Kind 806
12.11 Vector Spherical Harmonics 813

13 Special Functions 817
13.1 Hermite Functions 817
13.2 Laguerre Functions 828
13.3 Chebyshev Polynomials 839
13.4 Hypergeometric Functions 850
13.5 Confluent Hypergeometric Functions 855

14 Fourier Series 863
14.1 General Properties 863
14.2 Advantages, Uses of Fourier Series 870
14.3 Applications of Fourier Series 874
14.4 Properties of Fourier Series 886
14.5 Gibbs Phenomenon 893
14.6 Discrete Fourier Transform 898

15 Integral Transforms 905
15.1 Integral Transforms 905
15.2 Development of the Fourier Integral 909
15.3 Fourier Transforms — Inversion Theorem 911
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 orFaltungs Theorem . 965
15.12 Inverse Laplace Transform 969


//ABSENT FROM BOOK//

16 Integral Equations 983
16.1 Introduction 983
16.2 Integral Transforms, Generating Functions 991
16.3 Neumann Series, Separable Kernels 997
16.4 Hilbert-Schmidt Theory 1009

17 Calculus of Variations 1017
17.1 A Dependent and an Independent Variable 1018
17.2 Applications of the Euler Equation 1023
17.3 Several Dependent Variables 1031
17.4 Several Independent Variables 1036
17.5 Several Dependent and Independent Variables 1038
17.6 Lagrangian Multipliers 1039
17.7 Variation With Constraints 1045
17.8 Rayleigh-Ritz Variational Technique 1052

18 Nonlinear Methods and Chaos 1059
18.1 Introduction 1059
18.2 The Logistic Map . 1060
18.3 Sensitivity to Initial Conditions 1064
18.4 Nonlinear Differential Equations 1068