This course is a recent addition to our undergraduate offerings in applicable analysis and may be of particular interest to students of physics, astronomy, applied engineering physics and other scientific fields. It is a suitable alternative to Math 422. Both Fourier series and wavelets provide methods to represent or approximate general functions in terms of simple building blocks. Such representations have important consequences, both for pure mathematics and for applications. Fourier series use natural sinusoidal building blocks and may be used to help solve differential equations.
Wavelets use artificial building blocks that have the advantage of localization in space.
A full understanding of both topics requires a background involving Lebesgue integration theory and functional analysis. This course will present as much as possible on both topics without such formidable prerequisites. The emphasis will be on clear statements of results and key ideas of proofs, working out examples, and applications. This course is normally offered every fall semester, but will be offered in the spring only this year. Covers the basic existence, uniqueness, and stability theory together with methods of solution and methods of approximation.