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物理学与偏微分方程  上  英文版
物理学与偏微分方程  上  英文版

物理学与偏微分方程 上 英文版PDF电子书下载

数理化

  • 电子书积分:11 积分如何计算积分?
  • 作 者:秦铁虎著
  • 出 版 社:北京:高等教育出版社
  • 出版年份:2012
  • ISBN:9787040346572
  • 页数:265 页
图书介绍:本书为英文版,由我社与美国工业与应用数学协会(SIAM,Society for Industrial and Applied Mathematics)共同合作出版,在国内外同时发行。本书力求在物理与偏微分方程之间架设一座桥梁,帮助从事应用偏微分方程学习、研究与教学的教师、研究生、高年级大学生及其他学科领域与应用部门的学者和研究工作者熟练掌握近代物理学中一些重要的基本方程,了解其来龙去脉及推导过程,理解现今国际上一些重要并常见的偏微分方程数学模型,从而可以更自觉地学习和运用,并会抓住一些有意义的问题开展研究工作。全书分上、下两册出版。上册共5章,从最基本的物理概念出发,分别介绍了电动力学、流体力学、磁流体力学、反应流体力学、弹性力学,重点介绍建立它们的基本方程的全过程,并对这些方程在数学上的结构与特征作简略的说明,还有选择地介绍了近年来国际上的一些最近的研究成果。
《物理学与偏微分方程 上 英文版》目录

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

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