Equations of classical mathematical physics(经典数学物理方程)
发布日期:2006-12-31 浏览次
[内容提要]： 本书是数学物理方程课程的英文教材，共10章，内容包括：绪论、数学模型与定解问题、二阶线性偏微分方程的分类和化简、特征线积分法、分离变量法、本征值问题与特殊函数、高维边值问题、积分变换法、调和函数的基本性质、格林函数及其应用等.
本书可作为高等学校理工科(非数学专业)本科生和研究生的公共专业或技术基础课英文教材，也可供科技工作者参考。
[目录]：
Chapter 1 Introduction
1.1 Equations of mathematical physics
1.2 Basic concept and definition
1.3 Linear operator
Exercises
Chapter 2 Mathematical models and problems for defining solutions
2.1 Typical equations
2.2 String oscillation
2.3 Membrane oscillation
2.4 Heat conduction in solid
2.5 Gravitation potential
2.6 The conditions and problems for defining solutions
2.7 Principle of superposition
Chapter 3 Classification and simplification for linear partialdifferential equations of second order
3.1 Linear second order partial differential equations with two variables
3.2 Simplification and standard forms
3.3 Examples
Exercises
Chapter 4 Integral method on characteristics
4.1 D'Alembert formula of Cauchy problem for string oscillation
4.2 Small oscillations of semi-infinite and finite strings with rigidly fixed or free ends，method of prolongation
4.3 Three-dimensional wave equation
4.4 The method for descending dimension
4.5 Cauchy problem for non-homogeneous wave equation
4.6 Integral method on characteristics for second order hyperbolic equations with two variables
Exercises
Chapter 5 The method of separating variables on finite region
5.1 Separation of variables
5.2 The process by separation of variables for solving mixed problem on string oscillation
5.3 The application of the method on separating variables
5.4 Non-homogeneous problems
5.5 Uniqueness of the solutions for two mixed problems
Exercises
Chapter 6 Eigenvalue problems and special functions
6.1 Sturm-Liouville problem
6.2 Eigenfunctions
6.3 The boundary value problem of ordinary differential equation and Green function
6.4 The construction of Green function
6.5 Eigenvalue problem and Green function
6.6 Bessel function
6.7 Singular Sturm-Liouville problem
6.8 Legendre function
Exercises
Chapter 7 Multidimensional boundary value problems
7.1 Dirichlet problem in cube
7.2 Dirichlet problem in cylindrical body
7.3 Boundary value problems in a sphere
7.4 Membrane oscillation on rectangular region
7.5 Heat conduction on rectangular plate
7.6 Wave in three-dimensional cube
7.7 Heat conduction in cube
7.8 The problem on hydrogen atom
7.9 Forced vibration on membrane
Exercises
Chapter 8 Integral transformations
8.1 Fourier integral transformation
8.2 The properties of Fourier transformation
8.3 Application of Fourier integral transformation
8.4 Laplace integral transformation
8.5 Application of Laplace integral transformation
Exercises
Chapter 9 Basic properties of harmonic functions
9.1 Convex，linear，and concave functions in R1
9.2 Superhamonic，harmonic，and subharmonic functions in multidimen-sional regions
9.3 Hopf lemma and strong maximum principle
9.4 Green formulas，uniqueness theorems
9.5 Integral identity，mean value theorem，inverse mean value theorem
Chapter 10 Green function and their application to PDEs
10.1 Definition and main properties concerning Laplace operator
10.2 The method of superposition of sources and sinks
10.3 Poisson integral
Supplement
Exercises
Selected answers for exercises
Appendix A
Appendix B
Appendix C
【关闭】
新书报道