The first volume of the Chinese edition of this book waspublished in July 1997， and the second volume was published in June2000. In July 2000， upon the readers' request， we corrected severaltypographical errors and republished the first volume.
In this edition， minor typographical errors are corrected， and asmall paragraph has been added to section 5.5.4 in Chapter 5， whilethe remaining text is unchanged.
We would like to take this opportunity to express our sincerethanks to our teachers，friends， and readers for their encouragementand support.
Now available in English for the first time， Physics andPartial Differential Equations， Volumel bridges physics and appliedmathematics in a manner that is easily accessible to readers withan undergraduate-level background in these disciplines. Readers who are more familiar with mathematics than physics willdiscover the connection between various physical and mechanicaldisciplines and their related mathematical models， which aredescribed by partial differential equations （PDEs）. The authorsestablish the funda-mental equations for fields such as electrodynamics; fluid dynamics， magnetohydrodynamics， and reacting fluiddynamics; elastic， thermoelastic， and viscoelastic mechanics; the kinetic theory of gases; special relativity; and quantum mechanics. Readers who are more familiar with physics than mathematics willbenefit from in-depth explanations of how PDEs work as effectivemathematical tools to more clearly express and present the basicconcepts of physics. The book describes the mathematical structuresand features of these PDEs， including the types and basic characteristics of the equations， the behavior of solutions， and some commonly used approaches to solving PDEs.
Tatsien Li is a Professor in the School of MathematicalSciences at Fudan University in Shanghai. He is a member of theChinese Academy of Saences and a foreign member of the FrenchAcademy of Sciences.
Tiehu Qin is a Professor in the School of Mathematical Sciencesat Fudan University in Shanghai.
Preface to the English Edition
Preface to the Clunese Edition
1 Electrodynanucs
1.1 Introduction
1.2 Preliminaries
1.3 Maxwell's Equations in a Vacuum; Lorentz Force
1.4 Electromagnetic Energy and Momentum; Conservation andTransformation Laws of Energy and Momentum
1.5 Mathematical Structure of Maxwell's Equations; Wave Effect ofElectromagnetic Fields
1.6 Scalar Potential and Vector Potential of an ElectromagneticField
1.7 Maxwell's Equations in a Medium
1.8 Electrostatic Fields and Magnetostatic Fields
1.9 Darwin Model
Exercises
Bibliography
Preface to the English Edition
Preface to the Clunese Edition
1 Electrodynanucs
1.1 Introduction
1.2 Preliminaries
1.3 Maxwell's Equations in a Vacuum; Lorentz Force
1.4 Electromagnetic Energy and Momentum; Conservation andTransformation Laws of Energy and Momentum
1.5 Mathematical Structure of Maxwell's Equations; Wave Effect ofElectromagnetic Fields
1.6 Scalar Potential and Vector Potential of an ElectromagneticField
1.7 Maxwell's Equations in a Medium
1.8 Electrostatic Fields and Magnetostatic Fields
1.9 Darwin Model
Exercises
Bibliography
2 Fluid Dynamics
2.1 System of ldealFluid Dynamics
2.2 System of Viscous Fluid Dynamics
2.3 Navier-Stokes Equations
2.4 Shock Waves
2.5 System of One-Dimensional F1uid Dynamics inLagrangianRepresentation
Exercises
Bibliography
3 Magnetohydrodynamics
3.1 Plasma
3.2 System of Magnetohydrodynamics
3.3 System of Magnetohydrodynamics When theConductivity lnfinite
3.4 Mathematical Structure of Magnetohydrodynamics System
3.5 System of One-Dimensional Magnetohydrodynamics
Exercises
Bibliography
4 Reacting Fluid Dynamics
4.1 Introduction
4.2 System of Reacting Fluid Dynamics
4.3 System of One-Dimensional Reacting Fluid Dynamics
Exercises
Bibliography
5 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 andDeformation
5.5 System of Elastodynanucs 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; Intemal 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
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