物理学与偏微分方程（上册 英文版）

物理学与偏微分方程（上册 英文版）
作者：秦铁虎 著
出版时间：2012年版
内容简介
本书为英文版，由我社与美国工业与应用数学协会（SIAM，Society for Industrial and Applied Mathematics）共同合作出版，在国内外同时发行。
本书力求在物理与偏微分方程之间架设一座桥梁，帮助从事应用偏微分方程学习、研究与教学的教师、研究生、高年级大学生及其他学科领域与应用部门的学者和研究工作者熟练掌握近代物理学中一些重要的基本方程，了解其来龙去脉及推导过程，理解现今国际上一些重要并常见的偏微分方程数学模型，从而可以更自觉地学习和运用，并会抓住一些有意义的问题开展研究工作。
全书分上、下两册出版。上册共5章，从最基本的物理概念出发，分别介绍了电动力学、流体力学、磁流体力学、反应流体力学、弹性力学，重点介绍建立它们的基本方程的全过程，并对这些方程在数学上的结构与特征作简略的说明，还有选择地介绍了近年来国际上的一些最近的研究成果。
目录
Preface to the English Edition
Preface to the Chinese Edition
Electrodynamics
1.1 Introduction
1.2 Preliminaries
1.3 Maxwell's Equations in a Vacuum; Lorentz Force
1.4 Electromagnetic Energy and Momentum; Conservation and
Transformation Laws of Energy and Momentum
1.5 Mathematical Structure of Maxwell's Equations; Wave Effect of
Electromagnetic Fields
1.6 Scalar Potential and Vector Potential of an Electromagnetic Field
1.7 Maxwell's Equations in a Medium
1.8 Electrostatic Fields and Magnetostatic Fields
1.9 Darwin Model
Exercises
Bibliography
Fluid Dynamics
2.1 System of Ideal Fluid Dynamics
2.2 System of Viscous Fluid Dynamics
2.3 Navier-Stokes Equations
2.4 Shock Waves
2.5 System of One-Dimensional Fluid Dynamics in
Lagrangian Representation
Exercises
Bibliography
Magnetohydrodynamics
3.1 Plasma
3.2 System of Magnetohydrodynamics
3.3 System of Magnetohydrodynamics When the
Conductivity a Is Infinite
3.4 Mathematical Structure of Magnetohydrodynamics System
3.5 System of One-Dimensional Magnetohydrodynamics
Exercises
Bibliography
Reacting Fluid Dynamics
4.1 Introduction
4.2 System of Reacting Fluid Dynamics
4.3 System of One-Dimensional Reacting Fluid Dynamics
Exercises
Bibliography
Elastic Mechanics
5.1 Introduction
5.2 Description of Deformation; Strain Tensor
5.3 Conservation Laws; Stress Tensor
5.4 Constitutive Equation: Relationship Between Stress and
Deformation
5.5 System of Elastodynamics and Its Mathematical Structure
5.6 Well-Posed Problems of the System of Elastostatics
Exercises
Bibliography
Appendix A Cartesian Tensor
A. 1 Definition of Tensor
A.2 Operations of Tensor
A.3 Invariants of the Second-Order Symmetric Tensor
A.4 Isotropic Tensor
A.5 Differentiation of Tensor
Appendix B Overview of Thermodynamics
B. 1 Objective of the Study of Thermodynamics
B.2 The First Law of Thermodynamics; Internal Energy
B.3 The Second Law of Thermodynamics; Entropy
B.4 Legendre Transform
B.5 Thermodynamic Functions
B.6 Expressions of Internal Energy and Entropy
Index