This course serves as an introduction to numerical methods as they apply to
calculus and differential equations. It is, above all, a mathematics
course, not a programming course, so it will center around the mathematical
analysis of numerical algorithms, rather than on the development and
implementation of such algorithms. An understanding of the effects of
estimates and errors involved in the procedures (and in the very nature of
computational methods) and how these errors arise and can be minimized will form the
core of our studies. A secondary theme will be an analysis of the efficiency
of the methods we investigate.
We will develop and analyze methods in the following broad areas: