In 642:573, the topics are: the approximation of functions by polynomials and piecewise polynomials, numerical integration, and the numerical solution of initial value problems for ordinary differential equations.
Despite the many solution techniques presented in elementary calculus and differential equations courses, mathematical models used in applications often do not have the simple forms required for using these methods. Hence, a quantitative understanding of the models requires the use of numerical approximation schemes. This course provides the mathematical background for understanding how such schemes are derived and when they are likely to work.
To illustrate the theory, in addition to the usual pencil and paper problems, some short computer programs will be assigned. To minimize the effort involved, however, the use of Matlab will be encouraged. This program has many built in features which make programming easy, even for those with very little prior programming experience.
One of the following textbooks is recommended, but not required for the course:
Kendall Atkinson, An Introduction to Numerical Analysis,
John Wiley and Sons, second edition (1989),
(ISBN 0-471-62489-6).
A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics,
Springer Texts in Applied Mathematics 37 (2000),
(ISBN 0-387-98959-5).
Previous semesters:
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Last updated: May 10, 2007 by R. S. Falk