数学物理(第1卷)(经典名著系列)(Mathematical Physics:A Modern Introduction to Its Foundations)
点此进入淘宝搜索页搜索分類: 图书,科学与自然,数学,综合,
品牌: 哈萨尼
基本信息·出版社：世界图书出版公司
·页码：549 页
·出版日期：2007年
·ISBN：9787506283052
·包装版本：第1版
·装帧：平装
·开本：16
·正文语种：英语
·丛书名：经典名著系列
·外文书名：Mathematical Physics:A Modern Introduction to Its Foundations
产品信息有问题吗？请帮我们更新产品信息。
内容简介如果说数学是大自然的语言，那么，物理学就是大自然的诗歌。数学是物理学的出色工具，数学是物理学唯一能够表达自己且不失真确性的语言。另外，数学在物理学中的应用也富有戏剧性的发展。
《数学物理(第1卷)》是为学习物理学的读者编写的数学基础教材，不仅如此，《数学物理(第1卷)》还对那些学习数学的人们非常有益，即可以将抽象思维化为活龙活现的应用。现有的数学物理方法著作，通常是像词典那样将诸如矩阵对角化、张量分析、Legendre多项式和各种各样的积分公式等汇集起来，很少强调主题的系统发展，因而缺乏生气；《数学物理(第1卷)》则不同，作者试图在形式和应用上、抽象化和具体问题上达到一种平衡，为了使内容编排最优化和自成一体，《数学物理(第1卷)》尽可能多地引入必要的数学形式，这自然包括大量的定量、性质、引理和推论的陈述和证明，以及丰富多样的练习题。同时，作者希望通过学习《数学物理(第1卷)》，读者能够很清楚地发现在物理学中使用数学思想及方法的威力和局限性，这些都是许多物理学和数学教程中很少能明确指出的。《数学物理(第1卷)》的另一个突出特点是，除了用较现代的方法处理经典的数学物理问题外，还引入了很多有较强物理应用意义的较现代的数学方法和思想，从涵盖的知识面来看，已远远超出通常数学物理方法教程的范围，因此可以供更大范围的读者来参考选用。值得一提的是，《数学物理(第1卷)》还将一些近现代的著名科学家的小传及照片穿插于全书各处，这使得《数学物理(第1卷)》生色不少。
《数学物理(第1卷)》的内容非常丰富，可作为物理系高年级学生、研究生和教师的参考书，也适合专门学习数学及对数学方法感兴趣的读者阅读。
目录
Preface
Note to the Reader
List of Symbols
0 Mathematical Preliminaries
0.1 Sets
0.2 Maps
0.3 Metric Spaces
0.4 Cardinality
0.5 Mathematical Induction
0.6 Problems
Ⅰ Finite-Dimensional Vector Spaces
1 Vectors and Transformations
1.1 Vector Spaces
1.2 Inner Product
1.3 Linear Transformations
1.4 Algebras
1.5 Problems
2 Operator Algebra
2.1 Algebra of L (V)
2.2 Derivatives of Functions of Operators
2.3Conjugation of Operators
2.4Hermitian and Unitary Operators
2.5Projection Operators
2.6Operators in Numerical Analysis
2.7Problems
3 Matrices: Operator Representations
3.1Matrices
3.2 Operations on Matrices
3.3Orthonormal Bases
3.4 Change of Basis and Similarity Transformation
3.5 The Determinant
3.6The Trace
3.7 Problems
4 Spectral Decomposition
4.1Direct Sums
4.2Invariant Subspaces
4.3Eigenvalues and Eigenvectors
4.4 Spectral Decomposition
4.5Functions of Operators
4.6 Polar Decomposition
4.7Real Vector Spaces
4.8Problems
Ⅱ Infinite-Dimensional Vector Spaces
5 Hilbert Spaces
5.1The Question of Convergence
5.2The Space of Square-Integrable Functions
5.3Problems
6 Generalized Functions
6.1Continuous Index
6.2 Generalized Functions
6.3Problems
7 Classical Orthogonal Polynomials
7.1General Properties
7.2 Classification
7.3Recurrence Relations
7.4 Examples of Classical Orthogonal Polynomials
7.5 Expansion in Terms of Orthogonal Polynomials
7.6 Generating Functions
7.7 Problems
8 F0urier Analysis
8.1 Fourier Series
8.2 The Fourier Transform
8.3 Problems
Ⅲ Complex Analysis
9 Complex Calculus
9.1 Complex Functions
9.2 Analytic Funcfions
9.3 Conformal Maps
9.4 Integration of Complex Functions
9.5 Derivafives as Integrals
9.6 Taylor and Laurent Series
9.7 Problems
10 Calculus of Residues
10.1 Residues
10.2 Class if I cation of I so lated Singularities
10.3 Evaluation ofDeftnite Integrals
10.4 Problems
11 Complex Analysis：A dvanced~opics
11.1 Meromorphic Functions
11.2 Multivalued Functions
11.3 Analytic Confinuation
11.4 The Gamma and Beta Functions
11.5 Method of Steepest Descent
11.6 Problems
Ⅳ Differential Equations
12 Separation of Variables in Spherical Coordinates
12.1 PDEs of Mathematical Physics
12.2 Separation of the Angular Part of the Laplacian
12.3 Construction of Eigenvalues of L2
12.4 Eigenvectors ofL2：Spherical Harmonics
12.5 Problems
13 Second-Order Linear Differential Equations
13.1 General Prope~ies of 0DEs
13.2 Existence and Uniqueness for First.Order DEs
13.3 General Properties Of SOLDEs
13.4 The Wronskian
13.5 Adioint Diflferential Operators
13.6 Power-Series Solutions of SOLDEs
13.7 SOLDEs with Constant Coefficients
13.8 The WKB Method
13.9 Numerical Solutions ofDEs
13.10 Problems
14 Complex Analysis Of SoLDEs
14.1 Analytic Prope~ies of Complex DEs
14.2 Complex SOLDEs
14.3 Fuchsian Difierential Equations
14.4 The HypergeometriC Function
14.5 Confluent Hypergeometric Functions
14.6 Problems
15 Integral Transforms and Differential Equations
15.1 Integral Representation of the Hypergeometric Function
15.2 Integral Representation of the Confluent Hypergeometrie Function
1 5.3 Integral Representation of Bessel Functions
15.4 Asymptotic Behavior Of Bessel Functions
15.5 Problems
Ⅴ Operators on Hilbert Spaces
16 An Introduction to Operator Theory
1 6.1 From Abstract to Integral and Differential 0perators
16.2 Bounded Opera torsin Hilbert Spaces
16.3 Spectra of Linear Operators
16.4 Compact Sets
16.5 Compact Operators
16.6 Spectrum of Compact Operators
16.7 Spectral Theorem for Compact Operators
16.8 Resolvents
16.9 Problems
17 Integral Equations
17.1 Classification
Ⅵ Green'S Functions
Ⅶ Groups and Manifolds
Ⅷ Lie Croups and Their Applications
Bibvliography
Index
……[看更多目录]
