李大潜和秦铁虎编著的《物理学与偏微分方程上》内容介绍:The fundamental equations in many important physical and mechanical disciplines are partial differential equations. Although the names of these equations are well known,and although a considerable amount of research has been done on these equations, it is not an easy task to comprehensively and profoundly understand the related physical and mechanical background.
Preface to the English Edition
Preface to the Chinese Edition
1 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
2 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
3 Magnetohydrodynamies
3.1 Plasma
3.2 System of Magnetohydrodynamics
3.3 System of Magnetohydrodynamics When the
Conductivity σ Is Infinite
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 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