Preface
About the Authors
1 A First Numerical Problem
1.1 Radioactive Decay
1.2 A Numerical Approach
1.3 Design and Construction of a Working Program:Codes and Pse docodes
1.4 Testing Your Program
1.5 Numerical Considerations
1.6 Programming Guidelines and Philosophy
2 Realistic Projectile Motion
2.1 Bicycle Racing:The Effect of Air Resistance
2.2 Projectile Motion:The Trajectory of a Cannon Shell
2.3 Baseball:Motion of a Batted Ball
2.4 Throwing a Baseball:The Effects of Spin
2.5 Golf
3 Oscillatory Motion and Chaos
3.1 Simple Harmonic Motion
3.2 Making the Pendulum More Interesting:Adding Dissipation, Nonlinearity, and a Driving Force
3.3 Chaos in the Driven Nonlinear Pendulum
3.4 Routes to Chaos:Period Doubling
3.5 The Logistic Map:Why the Period Doubles
3.6 The Lorenz Model
3.7 The Billiard Problem
3.8 Behavior in the Frequency Domain:Chaos and Noise
4 The Solar System
4.1 Kepler's Laws
4.2 The Inverse-Square Law and the Stability of Planetary Orbits
4.3 Precession of the Perihelion of Mercury
4.4 The Three-Body Problem and the Effect of Jupiter on Earth
4.5 Resonances in the Solar System:Kirkwood Gaps and Planetary Rings
4.6 Chaotic Tumbling of Hyperion
5 Potentials and Fields
5.1 Electric Potentials and Fields:Laplace's Equation
5.2 Potentials and Fields Near Electric Charges
5.3 Magnetic Field Produced by a Current
5.4 Magnetic Field of a Solenoid:Inside and Out
6 Waves
6.1 Waves:The Ideal Case
6.2 Frequency Spectrum of Waves on a String
6.3 Motion of a(Somewhat)Realistic String
6.4 Waves on a String(Again):Spectral Methods
7 Random Systems
7.1 Why Perform Simulations of Random Processes?
7.2 Random Walks
7.3 Self-Avoiding Walks
7.4 Random Walks and Diffusion
7.5 Diffusion, Entropy, and the Arrow of Time
7.6 Cluster Growth Models
7.7 Fractal Dimensionalities of Curves
7.8 Percolation
7.9 Diffusion on Fractals
8 Statistical Mechanics, Phase Transitions, and the Ising Model
8.1 The Ising Model and Statistical Mechanics
8.2 Mean Field Theory
8.3 The Monte Carlo Method
8.4 The Ising Model and Second-Order Phase Transitions
8.5 First-Order Phase Transitions
8.6 Scaling
9 Molecular Dynamics
9.1 Introduction to the Method:Properties of a Dilute Gas
9.2 The Melting Transition
9.3 Equipartition and the Fermi-Pasta-Ulam Problem
10 Quantum Mechanics
10.1 Time-Independent SchrSdinger Equation:Some Preliminaries
10.2 One Dimension:Shooting and Matching Methods
10.3 A Matrix Approach
10.4 A Variational Approach
10.5 Time-Dependent Schr6dinger Equation:Direct Solutions
10.6 Time-Dependent Schr6dinger Equation in Two Dimensions
10.7 Spectral Methods
11 Vibrations,Waves,and the Physics of Musical Instruments
12 Interdisciplinary Topics
APPENDICES
A Ordinary Differential Equations with Initial Values
B Root Finding and Optimization
C The Fourier Transform
D Fitting Data to a Function
E Numerical Integration
F Generation of Random Numbers
G Statistical Tests of Hypotheses
H Solving Linear Systems
Index
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