物理学中的数学方法（英文版）简介，目录书摘

2020-02-07 21:28 来源：京东作者：京东

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内容简介:　　《物理学中的数学方法（英文版）》主要适用于物理、工程研究生，也适用于高年级学生和学生。
　　《物理学中的数学方法（英文版）》包括以下几个领域的知识：Hilbert空间，微分函数的微分方程，狄拉克函数，数学物理中的格林函数，积分方程，数论在物理学中的应用，基础多维空间和非欧几里得空间中的方程。
　　《物理学中的数学方法（英文版）》解释了这些概念，并详细推导了公式，包含大量的练习有益于读者。

作者简介:

目录:Introduction
Preface
Chapter 1 Variational Method
1．1． Functional and Its Extremal Problems
1．1．1． The conception of functional
1．1．2． The extremes of functionals
1．2． The Variational of Functionals and the Simplest Euler Equation
1．2．1． The variational of functionals
1．2．2． The simplest Euler equation
1．3． The Cases of Multifunctions and Multivariates
1．3．1． Multifunctions
1．3．2． Multivariates
1．4． Functional Extremes under Certain Conditions
1．4．1． Isoperimetric problem
1．4．2． Geodesic problem
1．5． Natural Boundary Conditions
1．6． Variational Principle
1．6．1． Variational principle of classical mechanics
1．6．2． Variational principle of quantummechanics
1．7． The Applications of the Variational Method in Physics
1．7．1． The applications in classical physics
1．7．2． The applications in quantum mechanics
Exercises

Chapter 2 Hilbert Space
2．1． Linear Space， Inner Product Spaceand Hilbert Space
2．1．1． Linear space
2．1．2． Inner product space
2．1．3． Hilbert space
2．2． Operators in Inner Product Spaces
2．2．1． Operators and adjoint operators
2．2．2． Self-adjoint operators
2．2．3． The alternative theorem for the solutions of linear algebraic equations
2．3． Complete Set of Orthonormal Functions
2．3．1． Three kinds of convergences
2．3．2． The completeness of a set of functions
2．3．3． N-dimensional space and Hilbert function space
2．3．4． Orthogonal polynomials
2．4． Polynomial Approximation
2．4．1． Weierstrass theorem
2．4．2． Polynomial approximation
Exercises

Chapter 3 Linear Ordinary Differential Equations of Second Order
3．1． General Theory
3．1．1． The existence and uniqueness of solutions
3．1．2． The structure of solutions of homogeneous equations
3．1．3． The solutions of inhomogeneous equations
3．2． Sturm-Liouville Eigenvalue Problem
3．2．1． The form of Sturm-LiouviUe equations
……
Chapter 4 Bessel Functions
Chapter 5 The Dirac Delta Function
Chapter 6 Green's Function
Chapter 7 Norm
Chapter 8 Integral Equations
Chapter 9 Application of Number Theory in Inverse Problems in Physics
Chapter 10 Fundamental Equations in Spaces with Arbitrary Dimensions
References
Answers of Selected Exercises
Author Index
Subject Index