Arithmetic Applied Mathematics

Preface

Chapter 1 Gravity


1.1 Introduction


1.2 Gravity

Chapter 2 Long and Short Range Forces: Gravitation and Molecular Attraction and Repulsion


2.1 Introduction


2.2 Gravitation


2.3 Basic Planar Concepts


2.4 Discrete Gravitation and Planetary Motion


2.5 The Generalized Newton's Method


2.6 An Orbit Example


2.7 Gravity Revisited


2.8 Classical Molecular Forces


2.9 Remark

Chapter 3 The N-Body Problem


3.1 Introduction


3.2 The Three-Body Problem


3.3 Conservation of Energy


3.4 Solution of the Discrete Three-Body Problem


3.5 Center of Gravity


3.6 Conservation of Linear Momentum


3.7 Conservation of Angular Momentum


3.8 The N-Body Problem


3.9 Remark

Chapter 4 Conservative Models


4.1 Introduction


4.2 The Solid State Building Block


4.3 Flow of Heat in a Bar


4.4 Oscillation of an Elastic Bar


4.5 Laminar and Turbulent Fluid Flows

Chapter 5 Nonconservative Models


5.1 Introduction


5.2 Shock Waves


5.3 The Leap-Frog Formulas


5.4 The Stefan Problem


5.5 Evolution of Planetary Type Bodies


5.6 Free Surface Fluid Flow


5.7 Porous Flow

Chapter 6 Foundational Concepts of Special Relativiy


6.1 Introduction


6.2 Basic Concepts


6.3 Events and a Special Lorentz Transformation


6.4 A General Lorentz Transformation

Chapter 7 Arithmetic Special Relativistic Mechanisms in One Space Dimension


7.1 Introduction


7.2 Proper Time


7.3 Velocity and Acceleration


7.4 Rest Mass and Momentum


7.5 The Dynamical Difference Equation


7.6 Energy


7.7 The Momentum-Energy Vector


7.8 Remarks

Chapter 8 Arithmetic Special Relativistic Mechanics in Three Space Dimensions


8.1 Introduction


8.2 Velocity, Acceleration, and Proper Time


8.3 Minkowski Space


8.4 4-Velocity and 4-Acceleration


8.5 Momentum and Energy


8.6 The Momentum-Energy 4-Vector


8.7 Dynamics

Chapter 9 Lorentz Invariant Computations


9.1 Introduction


9.2 Invariant Computations


9.3 An Arithmetic, Newtonian Harmonic Oscillator


9.4 An Arithmetic, Relativistic Harmonic Oscillator


9.5 Motion of an Electric Charge in a Magnetic Field

Appendix 1 Fortran Program for General N-Body Interaction

Appendix 2 Fortran Program for Planetary-Type Evolution

References and Sources for Further Reading

Index