物理学与偏微分方程 下 英文PDF电子书下载

6 Thermoelasticity 1

6.1 Introduction 1

6.2 The Conservation Law of Energy and the Entropy Inequality 2

6.3 Constitutive Relations in Thermoelasticity 9

6.4 System of Thermoelastodynamics and Its Mathematical Structure 17

6.5 Propagation of Acceleration Waves 27

Exercises 32

Bibliography 34

7 Viscoelasticity 35

7.1 Introduction 35

7.2 Constitutive Equations of Viscoelastic Materials and the Dissipation Inequality 40

7.3 System of Viscoelastodynamics and Its Well-Posed Problems 61

7.4 Singularity of the Kernel and the Propagation of Linear Waves 72

7.5 Propagation of Acceleration Wayes 80

Exercises 84

Bibliography 86

8 Kinetic Theory of Gases 89

8.1 Introduction 89

8.2 Boltzmann Equation 90

8.3 Equilibrium State of Dilute Gases 102

8.4 Conservation Laws 109

8.5 Zero-Order Approximation 114

8.6 First-Order Approximation 117

8.7 Vlasov Equation and Related Coupled Systems 127

Exercises 139

Bibliography 140

9 Special Relativity and Relativistic Fluid Dynamics 141

9.1 Introduction 141

9.2 Fundamental Principles in Special Relativity；the Lorentz Transformation 144

9.3 Space-Time Theory in Special Relativity 152

9.4 Relativistic Dynamics 160

9.5 Relativistic Fluid Dynamics 169

9.6 Mathematical Structure of the System of Relativistic Fluid Dynamics 177

9.7 System of Relativistic Magnetohydrodynamics 187

Exercises 198

Bibliography 201

10 Quantum Mechanics 203

10.1 Establishment of Quantum Mechanics 203

10.2 Schr?dinger Equation and Wave Function 211

10.3 Introduction to the Fundamental Principles of Quantum Mechanics 228

10.4 Relativistic Quantum Mechanics and the Dirac Equation 233

Exercises 257

Bibliography 259

Appendix C Tensors in Minkowski Four-Space-Time 261

C.1 Minkowski Four-Space-Time and the Lorentz Transformation 261

C.2 Tensors in Minkowski Four-Space-Time 263

C.3 Operations of Tensors 265

C.4 Covariant Derivatives of Tensors 266

Index 269