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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