The course will involve the analysis of numerical methods used in
scientific computing. The emphasis will be on the mathematical
properties of the algorithms, but examples of their use will also be
presented. The course will provide an introduction to some concepts
in functional analysis, in particular, operators and functionals
defined on linear spaces of functions. Many of the main developers
of the field (Lagrange, Laplace, etc.) were active in Paris, and
visits to relevant historical sites will be scheduled. As time
permits, we will touch on current open questions related to the
foundations of scientific computation, such as the computability
of the Mandelbrot set.
The text for the course is a Dover classic and is available at Amazon as well as other book sellers at a reasonable price. Most of the key mathematical results in this classic text remain relevant, and we will update the discussion as necessary in class and via notes.