PHYS 305: Computational Physics II

Topics

1. Review
   • General information
   • Review of basic C programming
     • see Kernighan & Ritchie
     • see the C Language Tutorial
   • Review of basic C++ programming
     C++ Language Tutorial
   • Plotting graphs: tools
   • Plotting Practice
   
   
2. Some ``warm-up'' programming exercises
   
   
   • Summing a series: sine.c, sine1.c
   • Practice with functions: sine2.c, sine2a.c, sine3.c
   • Sample logic encountered in functions: examples
   
   
3. Differentiation and integration (review)
   
   
   • Numerical differentiation -- Numerical Lattice & Finite Difference
   • Numerical integration -- Trapezoidal and Simpson rules
   
   
   
4. Logistic map -- Logistic Map -- logistic.c -- logistic.cpp
   
   
5. Initial-value problem
   
   
   • Newton's equation of motion: simple scheme
   • in class: solve newton equation for a mass on a spring
   • in_class_newton.c
   
   
6. Numerical integration of Ordinary Differential Equations (ODEs)
   
   
   • ordinary differential equations
   • Simple numerical integration schemes: Euler and Mid-Point
   • Simple differential equations
   • Population biology model
   • Modular programming
   • Radioactive Decay
   • 1D Simple Harmonic Oscillator
   • SIR model
   • Predictor-Corrector integration scheme: Improved Euler
   • A standard integration scheme: Fourth-order Runge-Kutta integrator
   • The Simple Harmonic Oscillator Revisited: Standard codes
   • Differential Equation Revisited: ODE with class
   
   
7. Applications - Non-linear Dynamics
   • Chaotic Scattering
   • Population Dynamics Models
   • Lorenz Model
   • Order to Chaos in 2-Dimensional Motion - Henon-Heiles,
   • Henon map
   • Duffing Oscillator
   • bachaos.avi Movie by Dr. Tim Jones:
   
   
8. Applications - Eigenvalue Problem
   • 1D Schrodinger Equation
   • schro_skel.c
   
   
   
9. Special Integration Schemes
   • Mass in a Gravitational Field
   • Leapfrog integrator
   • Time Reversal Symmetry
   • Verlet ODE integrators
   • Mass in a Gravitational Field - Verlet ODE Solver
   
   
   
10. Molecular Dynamics
    
    
11. Adaptive Stepsizes
    
    
12. Electron in di-atomic molecule -
    
    
13. Monte-Carlo techniques
    
    
14. N-Body Systems