《物理學家用的數學方法（第7版）》是2014年3月世界圖書出版公司出版的圖書，作者是(英)阿夫肯。
基本介紹
- 中文名：物理學家用的數學方法（第7版）
- 作者：(英)阿夫肯
- 出版社：世界圖書出版公司
- 出版時間：2014年3月
- ISBN：9787510070754
內容簡介,目錄,
內容簡介
阿夫肯著的《物理學家用的數學方法（第7版）（精）》是為具有研究生水平的讀者編寫的一部入門性工具書，語言簡練，結構流暢，可讀性很強，很受讀者歡迎，本書是第7版。本版全面介紹了物理學中常用數學方法，內容涉及物理學中用到的數學內容，包括矢量/張量分析，矩陣，群論，數列與複變函數，各種特殊函式，微分方程，傅立葉分析與積分變換，非線性方法，變分法和機率論等諸多領域，是從事物理學研究和教學人員的案頭必備書。 讀者對象：物理、數學及相關專業的研究生和科教工作者。
目錄
Preface
1 Mathematical Preliminaries
1.1 InfiniteSeries
1.2 Series ofFunctions
1.3 Binomial Theorem
1.4 Mathematical Induction
1.5 Operations on Series Expansions of Functions
1.6 Some Important Series
1.7 Vectors
1.8 Complex Numbers and Functions
1.9 Derivatives andExtrema
1.10 Evaluation oflntegrals
1.1 I Dirac Delta Function
AdditionaIReadings
2 Determinants and Matrices
2.1 Determinants
2.2 Matrices
AdditionaI Readings
3 Vector Analysis
3.1 Review ofBasic Properties
3.2 Vectors in 3-D Space
3.3 Coordinate Transformations
3.4 Rotations in IR3
3.5 Differential Vector Operators
3.6 Differential Vector Operators: Further Properties
3.7 Vectorlntegration
3.8 Integral Theorems
3.9 PotentiaITheory
3.10 Curvilinear Coordinates
AdditionaIReadings
4 Tensors and Differential Forms
4.1 TensorAnalysis
4.2 Pseudotensors, Dual Tensors
4.3 Tensors in General Coordinates
4.4 Jacobians
4.5 DifferentialForms
4.6 DifferentiatingForms
4.7 IntegratingForms
AdditionalReadings
5 Vector Spaces
5.1 Vectors in Function Spaces
5.2 Gram-Schmidt Orthogonalization
5.3 Operators
5.4 SelfAdjointOperators
5.5 Unitaty Operators
5.6 Transformations of Operators
5.7 Invariants
5.8 Summary-Vector Space Notation
AdditionaIReadings
6 Eigenvalue Problems
6.1 EigenvalueEquations
6.2 Matrix Eigenvalue Problems
6.3 Hermitian Eigenvalue Problems
6.4 Hermitian Matrix Diagonalization
6.5 NormaIMatrices
AdditionalReadings
7 Ordinary DifTerential Equations
7.1 Introduction
7.2 First-OrderEquations
7.3 ODEs with Constant Coefficients
7.4 Second-Order Linear ODEs
7.5 Series Solutions-Frobenius ' Method
7.6 OtherSolutions
7.7 Inhomogeneous Linear ODEs
7.8 Nonlinear Differential Equations
Additional Readings
8 Sturm-Liouville Theory
8.1 Introduction
8.2 Hermitian Operators
8.3 ODE Eigenvalue Problems
8.4 Variation Method
8.5 Summary, Eigenvalue Problems
Additional Readings
9 Partial Differential Equations
9.1 Introduction
9.2 First-Order Equations
9.3 Second-Order Equations
9.4 Separation of Variables
9.5 Laplace and Poisson Equations
9.6 Wave Equation
9.7 Heat-Flow, or Diffusion PDE
9.8 Summary
Additional Readings
10 Green's Functions
10.1 One-Dimensional Problems
10.2 Problems in Two and Three Dimensions
Additional Readings
11 Complex Variable Theory
11.1 Complex Variables and Functions
11.2 Cauchy-Riemann Conditions
11.3 Cauchy' s Integral Theorem
11.4 Cauchy' s Integral Formula
11.5 Laurent Expansion
11.6 Singularities
11.7 Calculus of Residues
11.8 Evaluation of Definite Integrals
11.9 Evaluation of Sums
11.10 Miscellaneous Topics
Additional Readings
12 Further Topics in Analysis
12.1 Orthogonal Polynomials
12.2 Bernoulli Numbers
12.3 Euler-Maclaurin Integration Formula
12.4 Dirichlet Series
12.5 Infinite Products
12.6 Asymptotic Series
12.7 Method of Steepest Descents
12.8 Dispersion Relations
Additional Readings
13 Gamma Function
13.1 Definitions, Properties
13.2 Digamma and Polygamma Functions
13.3 The Beta Function
13.4 Stirling's Series
13.5 Riemann Zeta Function
13.6 Other Related Functions
Additional Readings
14 Bessel Functions
14.1 Bessel Functions of the First Kind, ,Iv (x)
14.2 Orthogonality
14.3 Neumann Functions, Bessel Functions of the Second Kind
14.4 Hankel Functions
14.5 Modified Bessel Functions, Iv (x) and Kv (x)
14.6 Asymptotic Expansions
14.7 Spherical Bessel Functions
Additional Readings
15 Legendre Functions
15.1 Legendre Polynomials
15.2 Orthogonality
15.3 Physical Interpretation of Generating Function
15.4 Associated Legendre Equation
15.5 Spherical Harmonics
15.6 Legendre Functions of the Second Kind
Additional Readings
16 Angular Momentum
16.1 Angular Momentum Operators
16.2 Angular Momentum Coupling
16.3 Spherical Tensors
16.4 Vector Spherical Harmonics
Additional Readings
17 Group Theory
17.1 Introduction to Group Theory
17.2 Representation of Groups
17.3 Symmetry and Physics
17.4 Discrete Groups
17.5 Direct Products
17.6 Symmetric Group
17.7 Continuous Groups
17.8 Lorentz Group
17.9 Lorentz Covariance of Maxwell's Equations
17.10 Space Groups
Additional Readings
18 More Special Functions
18.1 Hermite Functions
18.2 Applications of Hermite Functions
18.3 Laguerre Functions
18.4 Chebyshev Polynomials
18.5 Hypergeometric Functions
18.6 Confluent Hypergeometric Functions
18.7 Dilogarithm
18.8 Elliptic Integrals
Additional Readings
19 Fourier Series
19.1 General Properties
19.2 Applications of Fourier Series
19.3 Gibbs Phenomenon
Additional Readings
20 Integral Transforms
20.1 Introduction
20.2 Fourier Transform
20.3 Properties of Fourier Transforms
20.4 Fourier Convolution Theorem
20.5 Signal-Processing Applications
20.6 Discrete Fourier Transform
20.7 Laplace Transforms
20.8 Properties of Laplace Transforms
20.9 Laplace Convolution Theorem
20.10 Inverse Laplace Transform
Additional Readings
21 Integral Equations
21.1 Introduction
21.2 Some Special Methods
21.3 Neumann Series
21.4 Hilbert-Schmidt Theory
Additional Readings
17.4 Discrete Groups
17.5 Direct Products
17.6 Symmetric Group
17.7 Continuous Groups
17.8 Lorentz Group
17.9 Lorentz Covariance of Maxwell's Equations
17.10 Space Groups
Additional Readings
18 More Special Functions
18.1 Hermite Functions
18.2 Applications of Hermite Functions
18.3 Laguerre Functions
18.4 Chebyshev Polynomials
18.5 Hypergeometric Functions
18.6 Confluent Hypergeometric Functions
18.7 Dilogarithm
18.8 Elliptic Integrals
Additional Readings
19 Fourier Series
19.1 General Properties
19.2 Applications of Fourier Series
19.3 Gibbs Phenomenon
Additional Readings
20 Integral Transforms
20.1 Introduction
20.2 Fourier Transform
20.3 Properties of Fourier Transforms
20.4 Fourier Convolution Theorem
20.5 Signal-Processing Applications
20.6 Discrete Fourier Transform
20.7 Laplace Transforms
20.8 Properties of Laplace Transforms
20.9 Laplace Convolution Theorem
20.10 Inverse Laplace Transform
Additional Readings
21 Integral Equations
21.1 Introduction
21.2 Some Special Methods
21.3 Neumann Series
21.4 Hilbert-Schmidt Theory
Additional Readings
22 Calculus of Variations
22.1 Euler Equation
22.2 More General Variations
22.3 Constrained Minima/Maxima
22.4 Variation with Constraints
Additional Readings
23 Probability and Statistics
23.1 Probability: Definitions, Simple Properties
23.2 Random Variables
23.3 Binomial Distribution
23.4 Poisson Distribution
23.5 Gauss' Normal Distribution
23.6 Transformations of Random Variables
23.7 Statistics
Additional Readings
Index
