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

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.