经典数学物理方程

"Chapter1Introduction

1.1Equationsofnmthematiealphysics

1.2Basicconceptanddefinition

1.3Linearoperator

Exercises

Chapter2Mathematicalmodelsandproblemsfordefiningsolutions

2.1Typicalequations

2.2Stringoscillation

2.3Membraneoscillation

2.4Heatconductioninsolid

2.5Gravitationpotential

2.6Theconditionsandproblemsfordefiningsolutions

2.7Principleofsuperposition

Chapter3Classificationandsimplificationforlinearpartial

differentialequationsofsecondorder

3.1Linearsecondorderpartialdifferentialequationswithtwovariables

3.2Simplificationandstandardforms

3.3Examples

Exercises

Chapter4Integralmethodoncharacteristics

4.1D’AlembertformulaofCauchyproblemforstringoscillation’

4.2Smalloscillationsofsemi-infiniteandfinitestringswithrigidly

fixedorfreeends,methodofprolongation

4.3Three-dimensionalwaveequation

4.4Themethodfordescendingdimension

4.5Cauchyproblemfornon-homogeneouswaveequation

4.6Integralmethodoncharacteristicsforsecondorderhyperbolic

equationswithtwovariables

Exercises

Chapter5Themethodofseparatingvariablesonfiniteregion

5.1Separationofvariables

5.2Theprocessbyseparationofvariablesforsolvingmixedproblel

onstringoscillation

5.3Theapplicationofthemethodonseparatingvariables

5.4Non-homogeneousproblems

5.5Uniquenessofthesolutionsfortwomixedproblems

Exercises

Chapter6Eigenvalueproblemsandspecialfunctions

6.1Sturm-Liouvilleproblem

6.2Eigenfunctions

6.3Theboundaryvalueproblemofordinarydifferentialequation

andGreenfunction

6.4TheconstructionofGreenfunction

6.5EigenvalueproblemandGreenfunction

6.6Besselfunction

6.7SingularSturm-Liouvilleproblem

6.8Legendrefunction

Exercises

Chapter7Multidimensionalboundaryvalueproblems

7,1Dirichletproblemincube7.2Dirichletproblemincylindricalbody

7.3Boundaryvalueproblemsinasphere

7.4Membraneoscillationonrectangularregion

7.5Heatconductiononrectangularplate

7.6Waveinthree-dimensionalcube

7.7Heatconductionincube

7.8Theproblemonhydrogenatom

7.9Forcedvibrationonmembrane

Exercises

Chapter8Integraltransformations

8.1Fourierintegraltransformation

8.2ThepropertiesofFouriertransformation

8.3ApplicationofFourierintegraltransformation

8.4Laplaceintegraltransformation

8.5ApplicationofLaplaceintegraltransformation

Exercises

Chapter9Basicpropertiesofharmonicfunctions

9.1Convex,linear,andconcavefunctionsinR1

9.2Superhamonic,harmonic,andsubharmonicfunctionsinmultidimen-

sionalregions

9.3Hopflemmaandstrongmaximumprinciple

9.4Greenformulas,uniquenesstheorems

9.5Integralidentity,meanvaluetheorem,inversemeanvaluetheorem

Chapter10GreenfunctionandtheirapplicationtoPDEs

10.1DefinitionandmainpropertiesconcerningLaplace

operator

10.2Themethodofsuperpositionofsourcesandsinks

10.3Poissonintegral

Supplement

Exercises

Selectedanswersforexercises

AppendixA

AppendixB

AppendixC

"

"　　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菇专业或技术基础课英文教材，也可供科技工作者参考。　　"