MATH 4240

Wavelets and Fourier Series

Course Description

Course information provided by the Courses of Study 2014-2015.

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 presents as much as possible on both topics without such formidable prerequisites. The emphasis is on clear statements of results and key ideas of proofs, working out examples, and applications. Related topics that may be included in the course: Fourier transforms, Heisenberg uncertainty principle, Shannon sampling theorem, and Poisson summation formula.

When Offered Spring.

Prerequisites/Corequisites Prerequisite: MATH 2210-MATH 2220, MATH 2230-MATH 2240, MATH 1920 and MATH 2940, or permission of instructor.

Distribution Category (MQR)

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