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)

## 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.

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

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

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 is a collection of mathematical software, papers, and databases

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

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.

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.

### Papers

NEC CiteSeer

An excellent scientific literature digital library.

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
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