A list of local and external learning resources relating to numerical analysis.  Please notify me of any broken link.
 
 

Course Related Materials


Outline of Numerical Analysis Topics:    This set of webpages provide information about numerical analysis topics that students are expected to learn in numerical analysis course.

Computer codes from textbook (usename/passwd required)

Comments/ outline of  Nonlinear System of equations and Eigenvalue problems (Math 411 related topics):
(PDF, Postscript)

Math 411 Topics Outline
 

 


 

General

The Definition of Numerical Analysis:

By L. N. Trefethen, November, 1992 issue of SIAM News (also  gzipped postscript version from author.)  Please note that the pages in the paper appear in reverse order in the file.

Predictions for Scientific Computing Fifty Years From Now:

By L. N. Trefethen, (also  gzipped postscript version from author)

Numerical Analysis FAQ

FAQ: Numerical Analysis & Associated Fields Resource Guide.  A text version in gzip format is also available.

Computational Science Education Project

CSEP is an electronic book for teaching Computational Science and Engineering. The intended
audience are students in science and engineering at the advanced undergraduate level and higher.
Tutorials for freely available networking and visualization software are included and have attracted
a range of users, including high-school students and people from the commercial sector.
Mathematical Optimization (Vanderbilt site)
Mathematical Optimization (ORNL site)
 

Unsolved Mathematics Problems:

For the curious minds.  From Mathsoft (maker of Mathcad).
 
 

References not on the web


[abstract: Nowhere is the old adage "a little knowledge is a dangerous thing" more apropos than in numerical computation. With minimal expertise and a powerful computer, the novice may now boldly attempt to simulate the physical world in which we are all embedded. However, this is essentially an invitation to 'shoot oneself in the foot' unless certain subtle pitfalls inherent in passing from continuum models of reality to the discrete domain of the digital computer are studiously avoided. We discuss seven of the most egregious such transgressions.]
 
Seven Deadly Sins of Numerical Computation, B. J. McCartin, American Math. Monthly, vol 105, num. 10, Dec 1988, pp 929--941.
Numerical Methods that Works, Forman Acton, reprinted by MAA, 1990, originally published in 1970.

Software Information and Sources


Netlib Repository

Netlib is a collection of mathematical software, papers, and databases
 

NIST Guide to Available Mathematical Software

A cross-index and virtual repository of mathematical and statistical software components of use in computational science and engineering. National Institute of Standards and Technology
 

Freely available linear algebra software:

This is a good place to start your search of high quality linear algebra software.  Maintained by Jack Dongarra.
 

Numerical Recipes

People have been arguing for a while about the routines in Numerical Recipes.  My view is that if you are performing preliminary studies or solving some toy problems and do not care much about carrying all the overhead that usually accompany quality software, by all means use the routines in the book.  Likewise, if you only want to have a very superficial understanding of the algorithms, the book does give an excellent overview of the basic ideas behind the numerical methods.  The content of the book is accessible  but the source code is a separate commercial product.

Numerical Recipes by Press, Teukolsky, Vetterling, and Flannery

For those people who think Numerical Recipes is the best there is, have a look at the following objections.  (Rebuttal of these objections may be found in the official Numerical Recipes website.

Why not Numerical Recipes?
Why not Numerical Recipes in C?
 
 

Papers

Google Scholar

NEC CiteSeer

An excellent scientific literature digital library.


Los Alamos e-Print archive

This is an archive of preprints or published papers in physics, mathematics and computer science: includes the   Computing Research Repository (CoRR).
 

Java

Javanumerics:

This is a good starting point for information on numerical computing in Java.
 
 
 

Mathematical Software Tutorials

Matlab

The Math department has only a limited number of licenses.  Accessible from computers on Labnet and in the Math Lab in 159 TMCB.
 
Kermit's Primer:  This popular tutorial has now been published by CRC.  Earlier postscript versions may still be found on the net. (Try searching on e.g. www.altavista using "matlab primer")
Second edition in PDF and Postscript forms
In DVI form
Getting Started With Matlab:  This is a nice tutorial for new matlab users, by D. Hart (Indiana University )
Indiana University Matlab Resource Page: an excellent starting point to find out more about matlab.
Matlab Tutorial Information:  University of New Hampshire
A Practical Introduction to Matlab: This is a fairly up-to-date tutorial by Mark S. Gockenbach.
Matlab tutorials and related m-files:  Southern Illinois University
Mathworks (maker of Matlab) site: FAQ
A MATLAB Primer: by Paul L. Fackler, North Carolina State University.

 
Practicum

Maple

This software is available campus wide.
Getting Started with Maple:  This is a nice tutorial for new maple users, by D. Hart (Indiana University )
Maple: An Introduction:  Useful summary of maple by Dominik Gruntz, et al (Institute for Scientific Computation, ETH Zurich)
Maple Lab Manual:    A useful guide to learning maple, by W. Farr (Worcester Polytechnic Institute )
Maple Tutorial:   Another nice tutorial from U. of Delaware
Basic Maple Tutorial:   A short tutorial from US Naval Academy
An Introductory Guide to Maple:   Short introduction by Mark Holmes (RPI) (pdf file, 15 pages)
Maple Tutorial:   Info on using worksheets, printing, etc. - from University of Texas at Austin. Some general material are useful.
A Maple Tutorial:   Informational tutorial from Los Alamos National Laboratory
The Maple Dictionary with Examples:   I have not looked at this and so I am not sure how good this is. By John V. Matthews (GZIPed PS file, 68 kBytes, 58 pages)
Maple in Action - An Introductory Handbook:    Covers calculus, Fourier series, Laplace and Fourier transforms, and vector fields - by Piroz Mohseni (GZIPed PS file, 135 kBytes, 62 pages)
"Online" tutorial system:   Consists of a group of Compressed Postscript files (U. of Dundee)

Mathematica

The Math department has only a limited number of licenses.  Accessible from computers in the Math Lab in TMCB.

 

Selected Topics in Numerical Analysis

Nonlinear Equations
Bisection method
Newton's method
Secant method
Floating Point Systems
Direct Methods for System of Linear Equations
Iterative Methods for System of Linear Equations
General Theory
Jacobi Iteration
Gauss Seidel Iteration
SOR Iteration
Least Squares Problems
Continuous Least Squares
Orthogonal Polynomials
Three-term recurrence relation
Polynomial Interpolation
Lagrange Interpolation
Divided difference form
Hermit Interpolation
Cubic Spline
Numerical Differentiation
Richardson's extrapolation
Numerical Integration
Newton-Cotes
Adaptive Quadrature
Romberg Integration
Gauss Quadrature
Nonlinear System of Equations
Eigenvalue Problems
Ordinary Differential Equations
Runge Kutta Methods
Multistep Methods
Stability
Boundary Value Problems
Approximation Theory
Trigonometric Polynomials
Fast Fourier Transform
Pade Approximation
Finite Difference Method
Derivation
Stability
Lax Equivalence Theorem

 
 
 
Finite Element Method
Finite Volume Method
Boundary Element Method
Krylov Subspace Methods
Steepest Descent
Conjugate gradient
GMRES

 
Multigrid Method
Grid Generation and Optimization

 
Computational Fluid Dynamics
Domain Decomposition

 
Singular Perturbation Problems
Homogenization

 
Bifurcation
Mathematical Programming
Mathematical Programming Glossary
Decision Tree for Optimization Software

 

Return to homepage