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机械工业出版社
- ISBN：7111159101
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内容简介
本书讨论偏微分方程在工程技术科学与自然科学中的应用，讲授的内容是高级工程数学、自然科学范畴的数学方法中非常重要的部分。本书适合作为与傅里叶级数、正交函数和边值问题等相关的课程的教材，也可以作为学习格林函数、变换方法等的参考书，是一本非常好的应用数学入门书籍。
本书作者从事教学工作多年，积累了丰富的经验。本书注重应用、内容广泛、层次清晰，每章后均附有大量的习题，方便读者巩固所学到的知识。
本书作者从事教学工作多年，积累了丰富的经验。本书注重应用、内容广泛、层次清晰，每章后均附有大量的习题，方便读者巩固所学到的知识。
作者介绍
理醒德·哈伯曼 于麻省理工学院获得应用数学专业博士学位，现任南卫理公会大学数学系教授。他的主要研究方向包括奇异扰动方法、非线性动态系统、非线性波运动以及数学模型。
目录介绍
前言
1 Heat Equation
1.1 Introduction
1.2 Derivation of the Conduction of Heat
1.3 Boundary Conditions
1.4 Equilibrium Temperature Distribution
1.5 Derivation of the Heat Equation in Two or Three Dimensions
2 Method of Separation of Variables
2.1 Introduction
2.2 Linearity
2.3 Heat Equation with Zero Temperatures at Finite Ends
2.4 Worked Examples with the Heat Equation:Other Boundary Value
2.5 Laplace's Equation:solutions and Qualitative Properties
3 Fourier Series
3.1 Introduction
3.2 Statement of Convergence Theorem
3.3 Term-by-Term Kifferentiation of Fourier Series
3.4 Term-By-Term Integration of Fourier Series
3.6 Complex Form of Fourier Series
4 Vibrating Strings and Membranes
4.1 Introduction
4.2 Derivation of a Vertically Vibrating String
4.3 Boundary conditions
4.4 Vibrating Membrane
4.6 Reflection and Refraction of Electromagnetic
5 Sturm-Liouville Eigenvalue Problems
……
6 Finite Difference Numerical Methods for Partial Differential Equations
7 Partial Differential Equations with at Least Three Independent Variables
8 Nonhomogeneous Problems
9 Green's Functions for Time-Independent Problems
10 Infinite Domain Problems—Fourier Transform Solutions of Partial Differential Equations
11 Green's Functions for Wave and Heat Equations
12 The Method of Characteristics for Linear and Quasi-Linear Wave Equations
13 A Brief Introduction to Laplace Transform Solution of Partial Differential Equations
14 Topics: Dispersive Waves, Stability, Nonlinearity, and Perturbation Methods
Bibliography
Selected Answers to Starred Exercises
Index
1 Heat Equation
1.1 Introduction
1.2 Derivation of the Conduction of Heat
1.3 Boundary Conditions
1.4 Equilibrium Temperature Distribution
1.5 Derivation of the Heat Equation in Two or Three Dimensions
2 Method of Separation of Variables
2.1 Introduction
2.2 Linearity
2.3 Heat Equation with Zero Temperatures at Finite Ends
2.4 Worked Examples with the Heat Equation:Other Boundary Value
2.5 Laplace's Equation:solutions and Qualitative Properties
3 Fourier Series
3.1 Introduction
3.2 Statement of Convergence Theorem
3.3 Term-by-Term Kifferentiation of Fourier Series
3.4 Term-By-Term Integration of Fourier Series
3.6 Complex Form of Fourier Series
4 Vibrating Strings and Membranes
4.1 Introduction
4.2 Derivation of a Vertically Vibrating String
4.3 Boundary conditions
4.4 Vibrating Membrane
4.6 Reflection and Refraction of Electromagnetic
5 Sturm-Liouville Eigenvalue Problems
……
6 Finite Difference Numerical Methods for Partial Differential Equations
7 Partial Differential Equations with at Least Three Independent Variables
8 Nonhomogeneous Problems
9 Green's Functions for Time-Independent Problems
10 Infinite Domain Problems—Fourier Transform Solutions of Partial Differential Equations
11 Green's Functions for Wave and Heat Equations
12 The Method of Characteristics for Linear and Quasi-Linear Wave Equations
13 A Brief Introduction to Laplace Transform Solution of Partial Differential Equations
14 Topics: Dispersive Waves, Stability, Nonlinearity, and Perturbation Methods
Bibliography
Selected Answers to Starred Exercises
Index
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