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