文件名称:
Mathematical Methods for Physicists 第六版
开发工具:
文件大小: 8mb
下载次数: 0
上传时间: 2010-09-12
详细说明： 1 Vector Analysis 1 1.1 Definitions, Elementary Approach 1 1.2 Rotation of the Coordinate Axes 7 1.3 Scalar or Dot Product 12 1.4 Vector or Cross Product 18 1.5 Triple Scalar Product, Triple Vector Product 25 1.6 Gradient, V 32 1.7 Divergence, V 38 1.8 Curl, Vx 43 1.9 Successive Applications of V 49 1.10 Vector Integration 54 1.11 Gauss' Theorem 60 1.12 Stokes' Theorem 64 1.13 Potential Theory 68 1.14 Gauss' Law, Poisson's Equation 79 1.15 Dirac Delta Function 83 1.16 Helmholtz's Theorem 95 Additional Readings 1 01 2 Vector Analysis in Curved Coordinates and Tensors 103 2.1 Orthogonal Coordinates in R3 103 2.2 Differential Vector Operators 110 2.3 Special Coordinate Systems: Introduction 114 2.4 Circular Cylinder Coordinates 115 2.5 Spherical Polar Coordinates 123 ν 2.6 Tensor Analysis 133 2.7 Contraction, Direct Product 139 2.8 Quotient Rule 141 2.9 Pseudotensors, Dual Tensors 142 2.10 General Tensors 151 2.11 Tensor Derivative Operators 160 Additional Readings 163 3 Determinants and Matrices 165 3.1 Determinants 165 3.2 Matrices 176 3.3 Orthogonal Matrices 195 3.4 Hermitian Matrices, Unitary Matrices 208 3.5 Diagonalization of Matrices 215 3.6 Normal Matrices 231 Additional Readings 239 4 Group Theory 241 4.1 Introduction to Group Theory 241 4.2 Generators of Continuous Groups 246 4.3 Orbital Angular Momentum 261 4.4 Angular Momentum Coupling 266 4.5 Homogeneous Lorentz Group 278 4.6 Lorentz Covariance of Maxwell's Equations 283 4.7 Discrete Groups 291 4.8 Differential Forms 304 Additional Readings 319 5 Infinite Series 321 5.1 Fundamental Concepts 321 5.2 Convergence Tests 325 5.3 Alternating Series 339 5.4 Algebra of Series 342 5.5 Series of Functions 348 5.6 Taylor's Expansion 352 5.7 Power Series 363 5.8 Elliptic Integrals 370 5.9 Bernoulli Numbers, Euler-Maclaurin Formula 376 5.10 Asymptotic Series 389 5.11 Infinite Products 396 Additional Readings 401 6 Functions of a Complex Variable I Analytic Properties, Mapping 403 6.1 Complex Algebra 404 6.2 Cauchy-Riemann Conditions 413 6.3 Cauchy's Integral Theorem 418 Contents vii 6.4 Cauchy's Integral Formula 425 6.5 Laurent Expansion 430 6.6 Singularities 438 6.7 Mapping 443 6.8 Conformal Mapping 451 Additional Readings 453 7 Functions of a Complex Variable II 455 7.1 Calculus of Residues 455 7.2 Dispersion Relations 482 7.3 Method of Steepest Descents 489 Additional Readings 497 8 The Gamma Function (Factorial Function) 499 8.1 Definitions, Simple Properties 499 8.2 Digamma and Polygamma Functions 510 8.3 Stirling's Series 516 8.4 The Beta Function 520 8.5 Incomplete Gamma Function 527 Additional Readings 533 9 Differential Equations 535 9.1 Partial Differential Equations 535 9.2 First-Order Differential Equations 543 9.3 Separation of Variables 554 9.4 Singular Points 562 9.5 Series Solutions—Frobeniusy Method 565 9.6 A Second Solution 578 9.7 Nonhomogeneous Equation—Green's Function 592 9.8 Heat Flow, or Diffusion, PDF 611 Additional Readings 618 10 Sturm-Liouville Theory—Orthogonal Functions 621 10.1 Self-Adjoint ODEs 622 10.2 Hermitian Operators 634 10.3 Gram-Schmidt Orthogonalization 642 10.4 Completeness of Eigenfunctions 649 10.5 Green's Function—Eigenfunction Expansion 662 Additional Readings 674 11 Bessel Functions 675 11.1 Bessel Functions of the First Kind, Jv(x) 675 11.2 Orthogonality 694 11.3 Neumann Functions 699 11.4 Hankel Functions 707 11.5 Modified Bessel Functions, Iv(x) and Kv(x) 713 11.6 Asymptotic Expansions 719 11.7 Spherical Bessel Functions 725 Additional Readings 739 12 Legendre Functions 741 12.1 Generating Function 741 12.2 Recurrence Relations 749 12.3 Orthogonality 756 12.4 Alternate Definitions 767 12.5 Associated Legendre Functions 771 12.6 Spherical Harmonics 786 12.7 Orbital Angular Momentum Operators 793 12.8 Addition Theorem for Spherical Harmonics 797 12.9 Integrals of Three Y's 803 12.10 Legendre Functions of the Second Kind 806 12.11 Vector Spherical Harmonics 813 Additional Readings 816 13 More Special Functions 817 13.1 Hermite Functions 817 13.2 Laguerre Functions 837 13.3 Chebyshev Polynomials 848 13.4 Hypergeometric Functions 859 13.5 Confluent Hypergeometric Functions 863 13.6 Mathieu Functions 869 Additional Readings 879 14 Fourier Series 881 14.1 General Properties 881 14.2 Advantages, Uses of Fourier Series 888 14.3 Applications of Fourier Series 892 14.4 Properties of Fourier Series 903 14.5 Gibbs Phenomenon 910 14.6 Discrete Fourier Transform 914 14.7 Fourier Expansions of Mathieu Functions 919 Additional Readings 929 15 Integral Transforms 931 15.1 Integral Transforms 931 15.2 Development of the Fourier Integral 936 15.3 Fourier Transforms—Inversion Theorem 938 15.4 Fourier Transform of Derivatives 946 15.5 Convolution Theorem 951 15.6 Momentum Representation 955 15.7 Transfer Functions 961 15.8 Laplace Transforms 965 Contents ix 15.9 Laplace Transform of Derivatives 971 15.10 Other Properties 979 15.11 Convolution (Faltungs) Theorem 990 15.12 Inverse Laplace Transform 994 Additional Readings 1003 16 Integral Equations 1005 16.1 Introduction 1005 16.2 Integral Transforms, Generating Functions 1012 16.3 Neumann Series, Separable (Degenerate) Kernels 1018 16.4 Hilbert-Schmidt Theory 1029 Additional Readings 1036 17 Calculus of Variations 1037 17.1 A Dependent and an Independent Variable 1038 17.2 Applications of the Euler Equation 1044 17.3 Several Dependent Variables 1052 17.4 Several Independent Variables 1056 17.5 Several Dependent and Independent Variables 1058 17.6 Lagrangian Multipliers 1060 17.7 Variation with Constraints 1065 17.8 Rayleigh-Ritz Variational Technique 1072 Additional Readings 1076 18 Nonlinear Methods and Chaos 1079 18.1 Introduction 1079 18.2 The Logistic Map 1080 18.3 Sensitivity to Initial Conditions and Parameters 1085 18.4 Nonlinear Differential Equations 1088 Additional Readings 1107 19 Probability 1109 19.1 Definitions, Simple Properties 1109 19.2 Random Variables 1116 19.3 Binomial Distribution 1128 19.4 Poisson Distribution 1130 19.5 Gauss'Normal Distribution 1134 19.6 Statistics 1138 Additional Readings 1150 General References 1150 ...展开收缩
(系统自动生成,下载前可以参看下载内容)
下载文件列表
相关说明
- 本站资源为会员上传分享交流与学习,如有侵犯您的权益,请联系我们删除.
- 本站是交换下载平台，提供交流渠道，下载内容来自于网络，除下载问题外，其它问题请自行百度。
- 本站已设置防盗链，请勿用迅雷、QQ旋风等多线程下载软件下载资源，下载后用WinRAR最新版进行解压.
- 如果您发现内容无法下载，请稍后再次尝试；或者到消费记录里找到下载记录反馈给我们.
- 下载后发现下载的内容跟说明不相乎，请到消费记录里找到下载记录反馈给我们，经确认后退回积分.
- 如下载前有疑问，可以通过点击"提供者"的名字，查看对方的联系方式，联系对方咨询.
