Greenspan Computer-Oriented Mathematical Physics

1. Auflage 2016
ISBN: 978-1-4832-7884-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 178 Seiten, Web PDF

Computer-Oriented Mathematical Physics describes some mathematical models of classical physical phenomena, particularly the mechanics of particles. This book is composed of 12 chapters, and begins with an introduction to the link between mathematics and physics. The subsequent chapters deal with the concept of gravity, the theoretical foundations f classical physics as a mathematical science, and the principles of pendulum and other oscillators. These topics are followed by discussions of waves, vectors, gravitation, the body-problem, and discrete fluid models. The final chapters examine the phenomena of spinning tops and skaters, as well as the Galilean principle of relativity. This book is of value as an introductory textbook for math and physics university and advanced high school students.

Autoren/Hrsg.

Greenspan, Donald

Inhaltsverzeichnis

1;Front Cover;1
2;Computer-Oriented Mathematical Physics;4
3;Copyright Page
;5
4;Table of Contents;8
5;Preface;6
6;Chapter 1. Mathematical and Physical Sciences;10
6.1;1.1 INTRODUCTION;10
6.2;1.2 MATHEMATICAL SCIENCE;10
6.3;1.3 PHYSICAL SCIENCE;13
6.4;1.4 EXERCISES – CHAPTER 1;14
7;Chapter 2. Gravity;17
7.1;2.1 INTRODUCTION;17
7.2;2.2 A SIMPLE EXPERIMENT;17
7.3;2.3 VELOCITY;19
7.4;2.4 ACCELERATION;21
7.5;2.5 FURTHER EXPERIMENTS;22
7.6;2.6 A MATHEMATICAL MODEL;22
7.7;2.7 STILL FURTHER EXPERIMENTS;27
7.8;2.8 EXERCISES – CHAPTER 2;28
8;Chapter 3. Theoretical Physics as a Mathematical Science;30
8.1;3.1 INTRODUCTION;30
8.2;3.2 BASIC MATHEMATICAL CONCEPTS;30
8.3;3.3 BASIC PHYSICAL CONCEPTS;36
8.4;3.4 REMARKS;40
8.5;3.5 EXERCISES – CHAPTER 3;40
9;Chapter 4. The Pendulum and Other Oscillators;45
9.1;4.1 INTRODUCTION;45
9.2;4.2 A THEORETICAL PENDULUM;45
9.3;4.3 THE HARMONIC OSCILLATOR;49
9.4;4.4 HARMONIC MOTION;53
9.5;4.5 REMARKS;57
9.6;4.6 EXERCISES – CHAPTER 4;57
10;Chapter 5. Waves;59
10.1;5.1 INTRODUCTION;59
10.2;5.2 THE DISCRETE STRING;59
10.3;5.3 EXAMPLES;62
10.4;5.4 EXERCISES – CHAPTER 5;66
11;Chapter 6. Vectors;68
11.1;6.1 INTRODUCTION;68
11.2;6.2 TWO–DIMENSIONAL VECTORS;68
11.3;6.3 THREE DIMENSIONAL VECTORS;70
11.4;6.4 EXERCISES – CHAPTER 6;75
12;Chapter 7. Gravitation;78
12.1;7.1 INTRODUCTION;78
12.2;7.2 THE 1/r2 LAW;78
12.3;7.3 GRAVITATION;80
12.4;7.4 BASIC PLANAR CONCEPTS;82
12.5;7.5 PLANETARY MOTION AND DISCRETE GRAVITATION;84
12.6;7.6 NEWTON'S METHOD OF ITERATION;86
12.7;7.7 AN ORBIT EXAMPLE;91
12.8;7.8 GRAVITY REVISITED;93
12.9;7.9 ATTRACTION AND REPULSION;96
12.10;7.10 REMARKS;98
12.11;7.11 EXERCISES – CHAPTER 7;98
13;Chapter 8. The Three-Body Problem;101
13.1;8.1 INTRODUCTION;101
13.2;8.2 THE EQUATIONS OF MOTION;101
13.3;8.3 CONSERVATION OF ENERGY;103
13.4;8.4 SOLUTION OF THE DISCRETE THREE-BODY PROBLEM;104
13.5;8.5 THE OSCILLATORY NATURE OF PLANETARY PERIHELION MOTION;106
13.6;8.6 CENTER OF GRAVITY;110
13.7;8.7 CONSERVATION OF LINEAR MOMENTUM;112
13.8;8.8 CONSERVATION OF ANGULAR MOMENTUM;112
13.9;8.9 EXERCISES – CHAPTER 8;116
14;Chapter 9. The n-Body Problem;118
14.1;9.1 INTRODUCTION;118
14.2;9.2 DISCRETE n-BODY INTERACTION;118
14.3;9.3 THE SOLID STATE BUILDING BLOCK;119
14.4;9.4 FLOW OF HEAT IN A BAR;121
14.5;9.5 OSCILLATION OF AN ELASTIC BAR;123
14.6;9.6 EXERCISES – CHAPTER 9;126
15;Chapter 10. Discrete Fluid Models;127
15.1;10.1 INTRODUCTION;127
15.2;10.2 LAMINAR AND TURBULENT FLOWS;127
15.3;10.3 SHOCK WAVES;132
15.4;10.4 EXERCISES – CHAPTER 10;136
16;Chapter 11. Spinning Tops and Skaters;138
16.1;11.1 INTRODUCTION;138
16.2;11.2 THE SPINNING TOP;138
16.3;11.3 ANGULAR VELOCITY;139
16.4;11.4 THE SPINNING SKATER;141
16.5;11.5 EXERCISES – CHAPTER 11;145
17;Chapter 12. The Galilean Principle of Relativity;147
17.1;12.1 INTRODUCTION;147
17.2;12.2 THE GALILEAN PRINCIPLE;147
17.3;12.3 REMARKS;149
17.4;12.4 EXERCISES – CHAPTER 12;149
18;APPENDIX A;151
19;APPENDIX B;152
20;APPENDIX C;154
21;APPENDIX D;156
22;APPENDIX E;160
23;Answers to Selected Exercises;166
24;References and Sources for Further Reading;174
25;Index;176