Numerical Methods Qualifying Examination
Department of Computer Science and Engineering
University of Notre Dame

Jesús A. Izaguirre

Date: March 28, 2001

This exam is designed to test whether a student is qualified to begin Ph. D. thesis research. Beyond this, the Qual is used to enforce breadth requirement at deeper level. Included is a list of material that the student should know. In italics is essential material.

It is suggested that you prepare by getting several intermediate-level books in numerical methods and use them to flesh out the attached outline. You may work through the sample questions, and the review questions and exercises in Dr. Heath's textbook.

An important concept that underlies a lot of the material is that of a linear space (vector and function spaces), and a through knowledge of this is assumed. Following are some good reference books:

1. M. Heath, Scientific Computing: An Introductory Survey, McGraw-Hill, 1997.
2. G. Dahlquist and Å Björck, Numerical Methods, Prentice Hall, 1974.
3. H. R. Schwarz, Numerical Analysis, a comprehensive introduction, Wiley, 1989.
4. G. Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press, 1986.
5. G. W. Stewart, Afternotes on Numerical Analysis, SIAM, 1996.
6. W. Gautschi, Numerical Analysis: An Introduction, Birkhauser, 1997.

The material in the Qual goes beyond CSE 513 in breadth, but it is at about the same depth. The book by R. Skeel and J. Keiper, Elementary Numerical Computing with Mathematica, McGraw-Hill, 1993, treats certain elementary topics like errors and adaptive quadrature in greater detail.