1 Electrodynamics 1
1.1 Introduction 1
1.2 Preliminaries 2
1.3 Maxwell's Equations in a Vacuum;Lorentz Force 13
1.4 Electromagnetic Energy and Momentum;Conservation and Transformation Laws of Energy and Momentum 17
1.5 Mathematical Structure of Maxwell's Equations;Wave Effect of Electromagnetic Fields 22
1.6 Scalar Potential and Vector Potential of an Electromagnetic Field 31
1.7 Maxwell's Equations in a Medium 40
1.8 Electrostatic Fields and Magnetostatic Fields 48
1.9 Darwin Model 57
Exercises 65
Bibliography 67
2 Fluid Dynamics 69
2.1 System of Ideal Fluid Dynamics 69
2.2 System of Viscous Fluid Dynamics 90
2.3 Navier-Stokes Equations 105
2.4 Shock Waves 109
2.5 System of One-Dimensional Fluid Dynamics in Lagrangian Representation 120
Exercises 126
Bibliography 128
3 Magnetohydrodynamics 131
3.1 Plasma 131
3.2 System of Magnetohydrodynamics 133
3.3 System of Magnetohydrodynamics When the Conductivity σ Is Infinite 144
3.4 Mathematical Structure of Magnetohydrodynamics System 148
3.5 System of One-Dimensional Magnetohydrodynamics 152
Exercises 158
Bibliography 159
4 Reacting Fluid Dynamics 161
4.1 Introduction 161
4.2 System of Reacting Fluid Dynamics 162
4.3 System of One-Dimensional Reacting Fluid Dynamics 169
Exercises 172
Bibliography 173
5 Elastic Mechanics 175
5.1 Introduction 175
5.2 Description of Deformation;Strain Tensor 177
5.3 Conservation Laws;Stress Tensor 182
5.4 Constitutive Equation:Relationship Between Stress and Deformation 194
5.5 System of Elastodynamics and Its Mathematical Structure 207
5.6 Well-Posed Problems of the System of Elastostatics 224
Exercises 234
Bibliography 235
Appendix A Cartesian Tensor 237
A.1 Definition of Tensor 237
A.2 Operations of Tensor 239
A.3 Invariants of the Second-Order Symmetric Tensor 242
A.4 Isotropic Tensor 243
A.5 Differentiation of Tensor 247
Appendix B Overview of Thermodynamics 249
B.1 Objective of the Study of Thermodynamics 249
B.2 The First Law of Thermodynamics;Internal Energy 250
B.3 The Second Law of Thermodynamics;Entropy 250
B.4 Legendre Transform 253
B.5 Thermodynamic Functions 256
B.6 Expressions of Internal Energy and Entropy 258
Index 261