物理学家用的数学方法（第7版 英文影印版）
作 者： （英） 阿夫肯（Arfken,G.B.） 著
出版时间：2014
内容简介
This， the seventh edition of Mathematical Methods for Physicists， maintains the tradition set by the six previous editions and continues to have as its objective the presentation of all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. While the organization of this edition differs in some respects from that of its predecessors， the presentation style remains the same： Proofs are sketched for almost all the mathematical relations introduced in the book， and they are accompanied by examples that illustrate how the mathematics applies to real-world physics problems. Large numbers of exercises provide opportunities for the student to develop skill in the use of the mathematical concepts and also show a wide variety of contexts in which the mathematics is of practical use in physics.
目录
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
……
8 Sturm-Liouville Theory
9 Partial Differential Equations
10 Green's Functions
11 Complex Variable Theory
12 Further Topics in Analysis
13 GammaFunction
14 Bessel Functions
15 Legendre Functions
16 Angular Momentum
17 Group Theory
18 More Special Functions
19 Fourier Series
20 IntegraITransforms
21 IntegraIEquations
22 Calculus of Variations
23 Probability and Statistics
Index
