Physics and Partial Differential Equations, Volume II, proceeds directly from Volume I with five additional chapters that bridge physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines. Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models， which are described by partial differential equations (PDEs). The authors establish the funda mental equations for fields such as electrodynamics, fluid, dynamics, magnetohydrodynamics, and reacting fluid dynamics, elastic, thermoelastic and viscoelastic mechanics, the kinetic theory of gases , special relativity, and quantum mechanicsReaders who are more familiar with physics than mathematics will benefit from in depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics The book describes the mathematical structures and 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.Each chapter can be read independently and includes exercises and references. Used alone or in conjunction with Volume I， this book is appropriate as a textbook for upper-level undergraduate and graduate courses and can also serve as a reference for researchers in application areas that use PDEs and in physical and nrechanical disciplines.

Preface to the English Edition vii

Preface to the Chinese Edition ix

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 Waves 80

Exercises 84

Bibliography 86

8 Kinetic Theory of Gases 89

8.1 Introduction 89

8.2 BoltzmannEquation 90

8.3 Equilibrium State of Dilute Gases 102

8.4 ConservationLaws 109

8.5 Zero-OrderApproximation 114

8.6 First-OrderApproximation 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 Schrödinger 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 ofTensors 265

C.4 CovariantDerivatives ofTensors 266

Index 269

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