PHYX 5350

Title: Methods of Theoretical Physics
Professor: Eric Held
Time: 2:30 - 3:20 MWF
Semester: Spring 2004

Course Objectives

  • Understand mathematical and physical issues of some important numerical methods used in computational physics.
  • Gain confidence solving problems numerically using Fortran 90.

    Syllabus
    I. Introduction
    Integration and Interpolation

  • Local interpolation and cubic splines
  • Definite integrals : trapezoidal rule, Romberg integration and Gaussian quadrature
  • Fortran 90 basics : syntax, modules, dynamic memory allocation, pointers, etc...

    II. Ordinary Differential Equations (ODE's)
    Linear and Nonlinear ODE's

  • Initial value problems: Runga-Kutta and adaptive methods
  • Boundary value problems: shooting methods

    III. Partial Differential Equations (PDE's)
    Parabolic (diffusion), elliptic (Poisson), hyperbolic (wave/advection)

  • Finite-difference and finite-element spatial discretization
  • Explicit, semi-implicit and implicit time-stepping schemes
  • Stability analysis

    Official Text: none

    Reference Texts:
    Undergraduate texts:

  • Introduction to Numerical Methods (Stark)
  • Applied Numerical Analysis (Gerald & Wheatley)
  • Numerical Methods for Physics (Garcia)
    Graduate texts:
  • Introduction to Numerical Analysis (Stoer & Bulirsch)
  • Numerical Recipes in Fortran 77 (Press, Teukolsky, Vetterling & Flannery)
  • Computational Methods for Fluid Dynamics (Ferziger & Peric)
    Fortran 90 references:
  • Upgrading to Fortran 90 (Redwine) best Fortran 90 reference
  • Fortran 90 Explained (Metcalf & Reid) acceptable Fortran 90 reference
  • Numerical Recipes in Fortran 90 (Press, Teukolsky, Vetterling & Flannery) do not buy as Fortran 90 reference

    Grading:
    Homeworks (7) 60%
    Midterm 20%
    Final Project 20%