G22.2421-001/G63.2020

Graduate Division

Computer Science/Mathematics

Spring 2000

**Instructor.** Prof. Yu Chen, Warren Weaver Hall (Ciww), Room 1126.
Tel: 998-3285, yuchen@cims.nyu.edu

**Class mailing list:** g22_2421_001_sp00@cs.nyu.edu

To subscribe: send mail to majordom@cs.nyu.edu, and in the body
of the message type subscribe g22_2421_001_sp00 (no subject, nothing
else in the body)

**
Reference for method of deferred corrections
A function for timing in (most) Unix systems
**

**
Class Time.
Lecture: 5:10 p.m.-7:00 p.m., Thur., room 102, Warren Weaver Hall (Ciww)
First meeting: Thursday, January 20.
Last day of class: Thursday, April 27.
Spring break: March 13--17; no class on March 16.
Number of lectures: 14
**

**
Office hours: 3:00 p.m. - 5:00 p.m. Thursday, and by appointment.
**

**
Prerequisite: Numerical Method I, Elements of ODE and PDE.
**

**
Important Note: This is computer-programming intensive, but
not a programming, course. We assume that you have some experience
writing and debugging codes in MATLAB and/or Fortran/C/C++ for the
basic tasks discussed in Numerical Methods I. These include matrix
factorizations, linear systems solvers, interpolation, approximation,
least squares problems, and numerical quadrature. Our goal is to
understand the techniques of computational mathematics.
**

**
Syllabus:
This course will cover fundamental methods that are essential for
the numerical solution of differential equations. It is intended for
students familiar with ODE and PDE and interested in actually engaging
in scientific computing, rather than addressing theoretical questions
in numerical analysis. Computer programming assignments form an
essential part of the course homework. We will consider the following
topics:
**

- Nonlinear equations and Newton's method
- Ordinary differential equations, Runge-Kutta and multistep methods, convergence and stability
- Boundary value problems for elliptic equations: finite difference and finite element methods, iterative methods for large scale linear systems of equations as result of discretizing continuous equations
- Fast solvers, multigrid methods
- Parabolic and hyperbolic partial differential (time dependent) equations.

**Required Text.** A first course in the numerical analysis of
differential equations, by A. Iserles; available at the
university bookstore.

**Reference Text.**

- Analysis of numerial methods, E. Isaacson, H. Keller.
- An introduction to Numerical analysis, G. Strang, G. J. Fix.
- Numerical methods, G. Dahlquist, A. Bjorck.
- Introduction to Numerical Analysis, J. Stoer and R. Bulirsch

yuchen@cims.nyu.edu (Yu Chen)

Last modified: March 23, 2000