Chap. 1 A FIRST NUMERICAL PROBLEM
Radioactive Decay
A Numerical Approach
Construction of a Working Program
Testing Your Program
Numerical Considerations
Programming Guidelines and Philosophy
Chap. 2 REALISTIC PROJECTILE MOTION
Bicycle Racing: The Effect of Air Resistance
Projectile Motion: The Trajectory of a Cannon Shell
Baseball: Motion of a Batted Ball
Throwing a Baseball: The Effects of Spin
Golf
Chap. 3 OSCILLATORY MOTION AND CHAOS
Simple Harmonic Motion
Chaos in the Driven, Damped, Nonlinear Pendulum
Routes to Chaos: Period Doubling
The Lorenz Model
The Billiard Problem
Bouncing Balls: a Chaotic Mechanical Systems
Behavior in the Frequency Domain: Chaos and Noise
Chap. 4 THE SOLAR SYSTEM
Kepler's Laws
The Inverse Square Law and the Stability of Planetary Orbits
The Precession of the Perihelion of Mercury
The 3-body Problem and the Effect of Jupiter on the Earth
Resonances in the Solar System: the Kirkwood Gaps and Planetary Rings
Chaotic Tumbling of Hyperion
Chap. 5 POTENTIALS AND FIELDS
Electric Potentials and Fields: Laplace's Equation
Potentials and Fields Near Electric Charges
Magnetic Field Produced by a Current
Magnetic Field of a Solenoid: Inside and Out
Chap. 6 WAVES
Waves: the Ideal Case
Frequency Spectrum of Waves on a String
Wave Motion of a (somewhat) Realistic String
Waves on a String (again): Spectral Methods
Chap. 7 RANDOM SYSTEMS
Why Perform Simulations of Random Processes?
Generation of Random Numbers
Introduction to Monte Carlo Methods: Integration
Random Walks
Self Avoiding Walks
Cluster Growth Models
Fractal Dimensionalities of Curves
Percolation
Random Walks and Diffusion
Diffusion, Entropy, and the Arrow of Time
Chap. 8 STATISTICAL MECHANICS, PHASE TRANSITIONS, AND THE ISING MODEL
The Ising Model and Statistical Mechanics
Mean Field Theory
The Monte Carlo Method
The Ising Model and Second Order Phase Transitions
First Order Phase Transitions
Chap. 9 MOLECULAR DYNAMICS
Molecular Dynamics: Introduction to the Method
The Melting Transition
Chap. 10 QUANTUM MECHANICS
The Time Independent Schroedinger Equation: Some Preliminaries
One Dimension: Shooting and Matching Methods
A Variational Approach
The Time Dependent Schroedinger Equation
Direct Solutions
Spectral Methods
Chap. 11 INTERDISCIPLINARY TOPICS
Protein Folding
Earthquakes and Self-Organized Criticality
Neural Networks and the Brain
APPENDICES
1: Ordinary Differential Equations
The Euler Method and Some Relatives
Runge-Kutta Methods
The Verlet Method
2: The Fourier Transform
Theoretical Background
The Fast Fourier Transform (FFT)
Estimation of the Power Spectrum
FFT Programs: Discussion and Listings
3: The Method of Least Squares
Linear Least Squares
More General Applications of Least Squares
Program Listing: Linear Least Squares
SELECTED PROGRAM LISTINGS