Numerical Methods II is the second half of a two-course series meant to introduce graduate students to the fundamentals of numerical mathematics (but any Ph.D. student seriously interested in applied mathematics should take it). It will be a demanding course covering a broad range of topics. There will be extensive homework assignments involving a mix of theory and computational experiments, and a final. We will cover fundamental methods that are essential for the numerical solution of differential equations. It is intended for students familiar with ODE and PDE.

Topics covered include:

  • numerical quadrature
  • spectral methods
  • two-point boundary value problems
  • methods for ordinary differential equations
  • methods for elliptic partial differential equations
  • fast solvers, fast transforms, and multigrid methods
  • parabolic partial differential equations
  • hyperbolic partial differential equations
  • convergence analysis and mesh refinement strategies

Prerequisites

  • Numerical linear algebra, some ODE, PDE

Textbook

The course textbook is Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. Leveque. It is available for download in PDF format . Matlab and LaTex files are available on the author's website.

Recommended Texts

Assignments and grading

There will be regular (biweekly) assignments and a take-home final or project.

Announcements, etc.

Announcements, assignments, discussion etc. will be handled using NYU Classes.
Professor: Leslie Greengard
1117 Warren Weaver Hall
greengard@courant.nyu.edu
Phone: (212) 998-3306
Office hours: Tues (7-8 pm), Fri (9-10 am)