Math 572 - Other References
This is not an exhaustive list of resources, but just what is sitting
on my desk, or that I have found helpful.
Books on PDEs
- Introduction to Partial Differential Equations with Applications,
by Zachmanoglou and Thoe, Dover, 1976.
This has been used in Math 512 often and provides reasonable coverage of
the basic theory and solution methods.
- A First Course in Partial Differential Equations, by Weinberger, Wiley, 1965.
I used it in my first PDE course. It gives nice coverage to the physical
interpretation of PDEs and Fourier theory.
General Books on Numerical Analysis
- Analysis of Numerical Methods, by Isaacson and Keller,
This is an inexpensive ($20) book and it often cited in other texts as
the source for the proofs of basic numerical results. Not an easy read,
but a good reference for the analysis of methods.
- Numerical Analysis, Any Edition, by Burden and Faires.
This is an undergraduate book, but contains the topics we are covering,
pseudo-code for most algorithms, and some reasonable examples worked out.
This is the text I use when teaching 471/472 due to it comprehensive
- Elementary Numerical Analysis: An Algorithmic Approach, 3rd
Edition, by Conte and de Boor, 1980.
There may be a more modern version of this book, but it is still a classic.
It is supposedly a undergraduate text, but it has lots of detail which
makes in useful for more advanced study. It also contains FORTRAN code.
This is the text I used as an undergraduate and I still use it.
- Numerical Analysis by Kincaid and Cheney, 1991.
Another undergraduate/graduate text. Good coverage of Approximation
and Interpolation. This is not a good text for a course, but its
slightly different approach makes it a good reference.
- Afternotes Goes To Graduate School by Stewart, 1998.
This is a collection of lecture notes for a graduate level course given
by Stewart and the Univ. of Maryland. It has some decent notes on
Approximation and Splines. There is also a undergraduate version,
Afternotes on Numerical Analysis, 1996, which covers
some other topics.
Books on Numerical ODEs
- Numerical Methods fo Ordinary Differential Systems by
This is the standard reference for analysis of methods, especially
Runge-Kutta methods. The theory is based on trees and is
fascinating (but difficult) to work through.
It has been used in the (distant) past as the text for 572.
- Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, by Ascher and Petzold, SIAM, 1998.
Has also been used in the (more recent) past as the text for 572. Lighter
coverage than Lambert, but more discussion of practical issues (for ODEs).
It works pretty well as a companion to Lambert (or vice-versa).
- Numerical Initial Value Problems in Ordinary Differential Equations
by Gear, 1971.
Slightly out of date, but covers Multivalue methods. It comes from a
time when Runge-Kutta methods were not in favor.
- What Every Computer Scientist Should Know About Floatint-Point Arithmetic by David Goldberg, ACM Computing Surveys, Vol. 23, No. 1, March 1991. (Postscript Copy)
This (long) paper is a readable discussion of the IEEE standard (which almost
all computers use now) for floating-point arithmetic. If you really want
to know what your computer is doing, this is an excellent place to start.
Last Modified: January 25, 2008