MATHEMATICAL METHODS FOR PHYSICISTS A COMPREHENSIVE GUIDE SEVENTH EDITION2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

MATHEMATICAL METHODS FOR PHYSICISTS A COMPREHENSIVE GUIDE SEVENTH EDITIONPDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

1 Mathematical Preliminaries1

1.1 Infinite Series1

1.2 Series of Functions21

1.3 Binomial Theorem33

1.4 Mathematical Induction40

1.5 Operations on Series Expansions of Functions41

1.6 Some Important Series45

1.7 Vectors46

1.8 Complex Numbers and Functions53

1.9 Derivatives and Extrema62

1.10 Evaluation of Integrals65

1.11 Dirac Delta Function75

Additional Readings82

2 Determinants and Matrices83

2.1 Determinants83

2.2 Matrices95

Additional Readings121

3 Vector Analysis123

3.1 Review of Basic Properties124

3.2 Vectors in 3-D Space126

3.3 Coordinate Transformations133

3.4 Rotations in IR 3139

3.5 Differential Vector Operators143

3.6 Differential Vector Operators： Further Properties153

3.7 Vector Integration159

3.8 Integral Theorems164

3.9 Potential Theory170

3.10 Curvilinear Coordinates182

Additional Readings203

4 Tensors and Differential Forms205

4.1 Tensor Analysis205

4.2 Pseudotensors， Dual Tensors215

4.3 Tensors in General Coordinates218

4.4 Jacobians227

4.5 Differential Forms232

4.6 Differentiating Forms238

4.7 Integrating Forms243

Additional Readings249

5 Vector Spaces251

5.1 Vectors in Function Spaces251

5.2 Gram-Schmidt Orthogonalization269

5.3 Operators275

5.4 Self-Adjoint Operators283

5.5 Unitary Operators287

5.6 Transformations of Operators292

5.7 Invariants294

5.8 Summary—Vector Space Notation296

Additional Readings297

6 Eigenvalue Problems299

6.1 Eigenvalue Equations299

6.2 Matrix Eigenvalue Problems301

6.3 Hermitian Eigenvalue Problems310

6.4 Hermitian Matrix Diagonalization311

6.5 Normal Matrices319

Additional Readings328

7 Ordinary Differential Equations329

7.1 Introduction329

7.2 First-Order Equations331

7.3 ODEs with Constant Coefficients342

7.4 Second-Order Linear ODEs343

7.5 Series Solutions Frobenius’ Method346

7.6 Other Solutions358

7.7 Inhomogeneous Linear ODEs375

7.8 Nonlinear Differential Equations377

Additional Readings380

8 Sturm-Liouville Theory381

8.1 Introduction381

8.2 Hermitian Operators384

8.3 ODE Eigenvalue Problems389

8.4 Variation Method395

8.5 Summary， Eigenvalue Problems398

Additional Readings399

9 Partial Differential Equations401

9.1 Introduction401

9.2 First-Order Equations403

9.3 Second-Order Equations409

9.4 Separation of Variables414

9.5 Laplace and Poisson Equations433

9.6 Wave Equation435

9.7 Heat-Flow， or Diffusion PDE437

9.8 Summary444

Additional Readings445

10 Green’s Functions447

10.1 One-Dimensional Problems448

10.2 Problems in Two and Three Dimensions459

Additional Readings467

11 Complex Variable Theory469

11.1 Complex Variables and Functions470

11.2 Cauchy-Riemann Conditions471

11.3 Cauchy’s Integral Theorem477

11.4 Cauchy’s Integral Formula486

11.5 Laurent Expansion492

11.6 Singularities497

11.7 Calculus of Residues509

11.8 Evaluation of Deffinite Integrals522

11.9 Evaluation of Sums544

11.10 Miscellaneous Topics547

Additional Readings550

12 Further Topics in Analysis551

12.1 Orthogonal Polynomials551

12.2 Bernoulli Numbers560

12.3 Euler-Maclaurin Integration Formula567

12.4 Dirichlet Series571

12.5 Infinite Products574

12.6 Asymptotic Series577

12.7 Method of Steepest Descents585

12.8 Dispersion Relations591

Additional Readings598

13 Gamma Function599

13.1 Definitions， Properties599

13.2 Digamma and Polygamma Functions610

13.3 The Beta Function617

13.4 Stirling’s Series622

13.5 Riemann Zeta Function626

13.6 Other Related Functions633

Additional Readings641

14 Bessel Functions643

14.1 Bessel Functions of the First Kind， Jv （x）643

14.2 Orthogonality661

14.3 Neumann Functions， Bessel Functions of the Second Kind667

14.4 Hankel Functions674

14.5 Modified Bessel Functions， Iv （x） and Kv （x）680

14.6 Asymptotic Expansions688

14.7 Spherical Bessel Functions698

Additional Readings713

15 Legendre Functions715

15.1 Legendre Polynomials716

15.2 Orthogonality724

15.3 Physical Interpretation of Generating Function736

15.4 Associated Legendre Equation741

15.5 Spherical Harmonics756

15.6 Legendre Functions of the Second Kind766

Additional Readings771

16 Angular Momentum773

16.1 Angular Momentum Operators774

16.2 Angular Momentum Coupling784

16.3 Spherical Tensors796

16.4 Vector Spherical Harmonics809

Additional Readings814

17 Group Theory815

17.1 Introduction to Group Theory815

17.2 Representation of Groups821

17.3 Symmetry and Physics826

17.4 Discrete Groups830

17.5 Direct Products837

17.6 Symmetric Group840

17.7 Continuous Groups845

17.8 Lorentz Group862

17.9 Lorentz Covariance of Maxwell’s Equations866

17.10 Space Groups869

Additional Readings870

18 More Special Functions871

18.1 Hermite Functions871

18.2 Applications ofHermite Functions878

18.3 Laguerre Functions889

18.4 Chebyshev Polynomials899

18.5 Hypergeometric Functions911

18.6 Confluent Hypergeometric Functions917

18.7 Dilogarithm923

18.8 Elliptic Integrals927

Additional Readings932

19 Fourier Series935

19.1 General Properties935

19.2 Applications of Fourier Series949

19.3 Gibbs Phenomenon957

Additional Readings962

20 Integral Transforms963

20.1 Introduction963

20.2 Fourier Transform966

20.3 Properties of Fourier Transforms980

20.4 Fourier Convolution Theorem985

20.5 Signal-Processing Applications997

20.6 Discrete Fourier Transform1002

20.7 Laplace Transforms1008

20.8 Properties of Laplace Transforms1016

20.9 Laplace Convolution Theorem1034

20.10 Inverse Laplace Transform1038

Additional Readings1045

21 Integral Equations1047

21.1 Introduction1047

21.2 Some Special Methods1053

21.3 Neumann Series1064

21.4 Hilbert-Schmidt Theory1069

Additional Readings1079

22 Calculus of Variations1081

22.1 Euler Equation1081

22.2 More General Variations1096

22.3 Constrained Minima/Maxima1107

22.4 Variation with Constraints1111

Additional Readings1124

23 Probability and Statistics1125

23.1 Probability： Definitions， Simple Properties1126

23.2 Random Variables1134

23.3 Binomial Distribution1148

23.4 Poisson Distribution1151

23.5 Gauss’ Normal Distribution1155

23.6 Transformations ofRandom Variables1159

23.7 Statistics1165

Additional Readings1179

Index1181