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