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%