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MATH/CS 375 \qquad \qquad
Introduction to Numerical Computing 
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{\bf Catalog Data:}\\ 
(Please enter from Catalog)

{bf Text:} Shampine, Allen and Pruess, {\em Fundamentals of Numerical Computing} 

{\bf Goals:}\\ 
The purpose of this course is two-fold; to learn to intelligently
use computational methods to solve the basic problems of applied mathematics,
and to learn something about the design and analysis of these methods.

{\bf Prerequisites by Topic:}\\
(list prerequisites from catalog)\\
(Math. 162, Math. 163 (what else; please list from catalog).\\
The following courses can be quite helpful, although not required:\\
Math. 314, especially for (2), also for (3).\\ 
Math. 264 for (4).\\
Math. 316 for (6).

{\bf Topics:}
\begin{enumerate}
\item  Basic Ideas of Real Number Computation - Errors and 
Conditioning.  
\item Matrix Algebra and Analysis, Gaussian Elimination,
LU Factorization, Banded Systems. 
\item Polynomial Interpolation , Error Analysis, Divided
Difference Algorithm, Piecewise Polynomial Interpolation.
\item Solution of Nonlinear Equations, Newton's Method, Secant Method.
\item Integration, Adaptive Methods.
\item Ordinary Differential Equations - Initial Value Problems. 
\end{enumerate}

{\bf Computer Usage:}\\
Programs from the text are available in Fortran, C, C++ and Matlab.
You may write your programs in these languages or in Maple or Mathematica.
The computing assignments will generally have some theoretical components,
but the main goal will be to familiarize the students with the performance 
and uses of existing algorithms.

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