## 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. |