PY 299, Computational Physics Instructors: John M Blondin, Michael P. Owen Projects are due the following week. ------------------------------------------------------------ Syllabus, Spring 1999 Week 1: Tuesday, January 5th Introduction to Computational Physics Overview of course, computing system, graphing Exercise: plot some functions with lines, points, etc. Simple programming in FORTRAN, C++, compiling, execution Exercise: simple program to output sin(x), and plot it Thursday, January 7th An Example Numerical Problem more programming highlights, arrays, variable declarations Start first numerical problem following Chapter 1 Taylor series expansion Exercise: Radioactive Decay testing programs: Are they telling you the right thing? Exercise: compare decay results with analytic solution Discuss HW format. intro to latex, equations, eps Project 1: Radioactive Decay with Style ------------------------------------------------------------ Week 2: Tuesday, January 12th Testing programs - truncation and round-off errors Exercise: radioactive decay for different h (done by different groups) plot log(error) vs. log h Reducing error, Higher-order algorithms Exercise: same as before, but new method to change error vs. h Exercise: program to compute function from a series such that round-off error hurts Discuss round-off error Thursday, January 14th developing a realistic model one step at a time The Euler Method Exercise: bicycle with constant power; compare with analytic soln Exercise: add drag and investigate v(t) Add a non-level terrain to the problem Project 2: Biking up a hill ---------------------------------------------------- Week 3: Tuesday January 19 - Holiday Thursday January 21 Extending to 2 dimensions: trajectory of a cannon shell Exercise: With prewritten program, find v(0) to hit a target. Compare this with analytic answer if no drag Basic approaches to root finding. Programming: subroutines Project 3 - use rootfinding to get theta to hit a target. ---------------------------------------------------- Week 4: Tuesday January 26 Making it more realistic: Throwing a Baseball Thursday January 28 Simple Harmonic motion Exercise: plot theta(t) for many cycles, E not conserved Exercise: change dt, E still not conserved Euler-Cromer method works - why? Exercise: EC on pendulum conserves Energy Project 4 - Energy conservation in Pendulum problem --------------------------------------------------- Week 5: Tuesday February 2 Chaos in the Driven Pendulum Add damping and driving to the pendulum Exercise: try different parameters Repeating, steady patterns vs chaos Exercise: theta(t) for slightly different starts Phase space plots Thursday February 4 Poincare sections, period doubling, frequency analysis Project 5 - Investigate some chaos model --------------------------------------------------- Week 6: Tuesday February 9 FFT, Power spectra of driven pendulum problem Thursday February 11 Keplerian Orbits angular momentum, energy conservation, Keplers laws. Project 6 - Something using Power spectra --------------------------------------------------- Week 7: Tuesday February 16 Keplerian Orbits review truncation term in EC method Exercise: test error dependence introduce RK method, Verlet Exercise: confirm better convergence Exercise: highly elliptical orbit wastes cpu time Variable timestepping Thursday February 18 Perihelion of Mercury Modified gravitational force, precession of perihelion Exercise: modify force, plot precessing orbit Exercise: extract perihelion(t) Least squares to find dtheta/dt --------------------------------------------------- Week 8: Tuesday February 23 3-body problem, give several examples in physics Thursday February 25 Electric potentials and fields Exercise: 2D square problem Convergence, efficiency Exercise: Test convergence Project 7 - 3-body problem of your choice --------------------------------------------------- Week 9: Tuesday March 2 Speeding up convergence, simultaneous over-relaxation Exercise: repeat square problem with SOR, testing convergence Poisson's equation Exercise: add a source to the square problem Thursday March 4 Currents and magnetic fields via numerical integration Exercise: simple numerical integration with analytic answer Exercise: simple integration that causes problems with round-off Project 8 - Plane parallel capacitor in a box --------------------------------------------------- Week 10: Tuesday March 9 - Holiday Thursday March 11 - Holiday --------------------------------------------------- Week 11: Tuesday March 16 Linear wave equation, analytic solution, numerical methods Thursday March 18 Waves in frequency domain Project 9 - Dispersion ----------------------------------------------------- Week 12: Tuesday March 23 6.3 Realistic Waves on a String Exercise Thursday March 25 6.4 Spectral Methods Exercise Project 10 - waves with spectral methods --------------------------------------------------- Week 13: Tuesday March 30 Random systems Random number generators distributions, chi squared statistics Exercise: compute chi-squared as a function of N different distributions (gaussian, boltzman, ...) random walks Exercise: 1D random walk Thursday April 1 Random Walks and Diffusion Project 11 - SN Neutrino pulse --------------------------------------------------- Week 14: Chapter 8 - Statistical Mechanics Tuesday April 6 8.1 The Ising Model & Stat Mech 8.2 Mean-Field Theory Exercise Thursday April 8 - Holiday --------------------------------------------------- Week 15: Tuesday April 13 Quantum Mechanics Time independent Schroedinger equation, aiming and shooting methods Thursday April 15 finding Eigenvalues and Eigenstates Project 13 - TDSE --------------------------------------------------- Week 16: Tuesday April 20 Time dependent Scroedinger equation direct solution Exercise Thursday April 22 Spectral methods Exercise --------------------------------------------------- Week 17: Tuesday April 27 Final Project Presentations Thursday April 29 Final Project Presentations ---------------------------------------------------