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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