Computer-Oriented Mathematical Physics
- 1st Edition - April 11, 2015
- Author: Donald Greenspan
- Language: English
- Hardback ISBN:9 7 8 - 0 - 0 8 - 0 2 6 4 7 1 - 4
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 4 5 0 - 2
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 8 8 4 - 1
Computer-Oriented Mathematical Physics describes some mathematical models of classical physical phenomena, particularly the mechanics of particles. This book is composed of 12… Read more
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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.
Chapter 1 Mathematical and Physical Sciences
1.1 Introduction
1.2 Mathematical Science
1.3 Physical Science
1.4 Exercises
Chapter 2 Gravity
2.1 Introduction
2.2 A Simple Experiment
2.3 Velocity
2.4 Acceleration
2.5 Further Experiments
2.6 A Mathematical Model
2.7 Still Further Experiments
2.8 Exercises
Chapter 3 Theoretical Physics as a Mathematical Science
3.1 Introduction
3.2 Basic Mathematical Concepts
3.3 Basic Physical Concepts
3.4 Remarks
3.5 Exercises
Chapter 4 The Pendulum and Other Oscillators
4.1 Introduction
4.2 A Theoretical Pendulum
4.3 The Harmonic Oscillator
4.4 Harmonic Motion
4.5 Remarks
4.6 Exercises
Chapter 5 Waves
5.1 Introduction
5.2 The Discrete String
5.3 Examples
5.4 Exercises
Chapter 6 Vectors
6.1 Introduction
6.2 Two-Dimensional Vectors
6.3 Three-Dimensional Vectors
6.4 Exercises
Chapter 7 Gravitation
7.1 Introduction
7.2 The 1/r2 Law
7.3 Gravitation
7.4 Basic Planar Concepts
7.5 Planetary Motion and Discrete Gravitation
7.6 Newton's Method of Iteration
7.7 An Orbit Example
7.8 Gravity Revisited
7.9 Attraction and Repulsion
7.10 Remarks
7.11 Exercises
Chapter 8 The Three-body Problem
8.1 Introduction
8.2 The Equations of Motion
8.3 Conservation of Energy
8.4 Solution of the Discrete Three-Body Problem
8.5 The Oscillatory Nature of Planetary Perihelion Motion
8.6 Center of Gravity
8.7 Conservation of Linear Momentum
8.8 Conservation of Angular Momentum
8.9 Exercises
Chapter 9 The n-Body Problem
9.1 Introduction
9.2 Discrete n-Body Interaction
9.3 The Solid State Building Block
9.4 Flow of Heat in a Bar
9.5 Oscillation of an Elastic Bar
9.6 Exercises
Chapter 10 Discrete Fluid Models
10.1 Introduction
10.2 Laminar and Turbulent Flows
10.3 Shock Waves
10.4 Exercises
Chapter 11 Spinning Tops and Skaters
11.1 Introduction
11.2 The Spinning Top
11.3 Angular Velocity
11.4 The Spinning Skater
11.5 Exercises
Chapter 12 The Galilean Principle of Relativity
12.1 Introduction
12.2 The Galilean Principle
12.3 Remarks
12.4 Exercises
Appendix A Fortran Program for the Harmonic Oscillator Example of Section 4.4
Appendix B Fortran Program for the Wave Interaction Example of Section 5.3
Appendix C Fortran Program for the Orbit Calculation of Section 7.7
Appendix D Fortran Program for Three-body Problem of Section 8.2
Appendix E Fortran Program for General N-body Interaction
Answers to Selected Exercises
References and Sources for Further Reading
Index
- Edition: 1
- Published: April 11, 2015
- Language: English
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