Computational Physics In PowerPoint

  Course outline, supplemental information. Computer architecture
  Storing information digitally. Integer representations, floating point arithmetic
  Short discussion about projects. More on floating point arithmetic and problems you may encounter.
  Introduction to Unix shells and useful commands. 10,000 ft view of programming.
  Functions and roots. Roots for polynomials. Bracketing & Bisection, Newton-Raphson, hybrid NR-bisection, Secant Method.
  A global bracket finding strategy. Muller-Brent. Example of root finding from quantum mechanics.
  Introduction to interpolation. Difference between interpolation and fitting to data. Interpolation polynomials in Lagrange form. Hermite interpolation. Introduction to cubic splines.
  Finish cubic splines. Numerical approximations to derivatives. Richardson Extrapolation.
  LU decomposition for solving general matrices. General polynomial least squares fitting. Least squares function fitting and Hilbert matrices. Orthogonal polynomials and uses in fitting.
  Numerical integration. Simple Newton-Cotes formulas (trapezoid & Simpson's Rule). Romberg Integration. Gaussian quadrature.
  Problems that can be encountered in numerical integration. Change of variables, removal of singularities. Dealing with improper integrals. Multidimensional int egration.
  Introduction to ODE solvers. Euler method, including Modified and Improved variants. Classical Runge-Kutta with adaptive step size from Richardson Extrapolation.
  Issues with the adaptive step size procedure. Separating 2nd order ODEs into coupled first order system. Separating nth order ODEs into n coupled first order systems. Algorithm to integrate nth order systems.
  Introduction to Monte Carlo methods. Numerical integration techniques, rejection method, importance sampling.
  MC methods applied to molecular motion in gases - the random walk. Simulation method & how to choose points randomly on a sphere. Short overview of random number generators, advice for quick and dirty generators and what to use if you want really "good" random numbers.
  Introduction to parallel programming. Different types of parallel computers. When is parallel computing useful? Brief introduction to OpenMP.
  More details on parallel programming. Dealing with data dependencies and race conditions. Useful OpenMP commands reviewed.
  Introduction to visualization. Preattentive processing of information. How now to present information. Effectiveness of different colour maps. Getting started with Opendx.
  More on Opendx. Loading in data and using the default viewer. Visualization of 3d volumes, surface rendering versus volume rendering. How transfer functions highlight different parts of a data volume. Making movies.


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