經(jīng)典數(shù)學(xué)物理方程

內(nèi)容概要

本書是數(shù)學(xué)物理方程課程的英文教材，共10章，內(nèi)容包括：緒論、數(shù)學(xué)模型與定解問題、二階線性偏微分方程的分類和化簡(jiǎn)、特征線積分法、分離變量法、本征值問題與特殊函數(shù)、高維邊值問題、積分變換法、調(diào)和函數(shù)的基本性質(zhì)、格林函數(shù)及其應(yīng)用等.    本書可作為高等學(xué)校理工科(非數(shù)學(xué)專業(yè))本科生和研究生的公共專業(yè)或技術(shù)基礎(chǔ)課英文教材，也可供科技工作者參考。

書籍目錄

Chapter 1 Introduction  1.1 Equations of mathematical physics  1.2 Basic concept and definition  1.3 Linear operator  ExercisesChapter 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 superpositionChapter 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  ExercisesChapter 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  ExercisesChapter 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  ExercisesChapter 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  ExercisesChapter 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  ExercisesChapter 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  ExercisesChapter 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 theoremChapter 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 integralSupplement  ExercisesSelected answers for exercisesAppendix AAppendix BAppendix C

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