PHY 256: Lecture topics and notebooks


Notebooks used in Lectures

Topics
from W Jan 13 Lecture Class introduction, intro to python
from M Jan 20 Lecture Not numbers, discrete dynamical systems
W Jan 25 local/global variables, Decimal package, floating point precision, round-off error, attracting points in orbits of discrete maps
from M Jan 27 Lecture FLOPS, cProfile package, Lyapunov exponents, mixing in discrete dynamical systems, fractals, box dimension, chaotic attractor
M Feb 1 What is renormalization? ODEs with Newton's method (and size of error), scaling for first order ODEs, N-body units
W Feb 3 Snapshots of Spash Craters, Craters as a geophysical/astrophysical process. Calling odeint, midpoint and Runge Kutta method for integrating ODEs
M Feb 8 Accuracy of integrators. Variable step size integrators. Potential force problems preserve energy and volume in phase space. For my notes on integrators see this: notes on integrators
from W Feb 10 Lecture Using odeint to integrate equations of motion for potential force problems, Separating out center of mass motion for 2 body problems, Intro to the Discrete Fourier transform. Audacity demonstration!
M Feb 15 More on Discrete Fourier transforms. For some notes on this see DFT.pdf
W Feb 17 The convolution theorem. Autocorrelation and power as a function of frequency. Solving systems of linear equations using matrices. Introduction to linalg. Normal modes of mass/spring systems.
from M Feb 22 Lecture What is a Monte Carlo simulation? Histograms and probability distributions. Generating samples from a probability distribution using the inverse transform method.
W Feb 24 Random walks and diffusion. The central limit theorem. Diffusion equation.
M Feb 29 On anomalous diffusion and Levy flights. More on integration of ODEs. Incompressibility and preservation of volume in phase space.
W Mar 2 Time reversal symmetric and symplectic integrators. Leapfrog (Stormer-Verlet) vs 2-nd order Runge Kutta integrator.
Mar 7,9 Spring Break!
M Mar 14 Lagrangian vs Eulerian techniques for solving PDEs. Hyperbolic vs elliptic PDEs. Finite difference techniques for integrating partial differential equations. 1D hydrodynamics in conservation law form.
W Mar 16 Finite difference schemes on a grid for hyperbolic PDEs. notes on finite difference schemes in hydrodynamics Approximating derivatives on a grid. Pulsed cylindrical open and closed pipes as models for wind musical instruments. Characteristics, steepening of a pulse.
M Mar 21 Numerical Stability, CFL condition.
W Mar 23 Numerically generated dispersion and dissipation.
M Mar 28 Symbolic computation with sympy.
W Mar 30 Differential operators, Infinitesimal transformations, Computation of Lie and Poisson brackets.
M Apr 4 Using differential operators to construct low order integrators. Operator splitting. Deconvolution techniques (CLEAN, Weiner filtering).
W Apr 6 Markov Chain Monte Carlo models (Metropolis algorithm) for magnetization and phase transition in the Ising model. Numerical Integration of area under a curve (Trapezoids and Simpson's rule) and the associated error.
M Apr 11 Numerical integration of areas using Monte Carlo methods (mean value and weighting/importance sampling). Root finding, Fermi-Ulam problem.
W Apr 13 Minimization, least squares fitting. Numerical methods in quantum mechanics
M Apr 18 Numerical methods in quantum mechanics
W Apr 20 Mass Spring models in Astrophysics
M Apr 25 Cancelled
W Apr 27 Guest lecture Jonathan by Carroll-Nellenback, Center for Research Computing.