ESE 325 - Fourier Analysis and Applications in Engineering,Mathematics,and the Sciences

Institution:

University of Pennsylvania

Subject:

Description:

Prerequisite(s): Math 240, Junior or Senior Standing. This course focuses on the mathematics behind Fourier theory and a wide variety of its applications in divers problems in mathematics, engineering, and the sciences. The course is very mathematical in content and students signing up for it should have junior or senior standing. The topics covered are chosen from: functions and signals; systems of differential equations; superpositions, memory, and non-linearity; resonance, eigenfunctions; the Fourier series and transform, spectra; convergence theorems; inner product spaces; mean-square approximation; interpolation and prediction, sampling; random processes, stationarity; wavelets, Brownian motion; stability and control, Laplace transforms. The applications of the mathematical theory that will be presented vary from year to year but a representative sample includes: polynomial approximation, Weierstrass's theorem; efficient computation via Monte Carlo; linear and non-linear oscillators; the isoperimetric problem; the heat equation, underwater communication; the wave equation, tides; testing for randomness, fraud; nowhere differentiable continuous functions; does Brownian motion exist ; error-correction; phase conjugate optics and four-wave mixing; cryptography and secure communications; how fast can we compute ; X-ray crystallography; cosmology; and what the diffusion equation has to say about mathematical finance and risk free investment.

Credits:

3.00

Credit Hours:

Prerequisites:

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.upenn.edu

Phone Number:

(215) 898-5000

Regional Accreditation:

Middle States Association of Colleges and Schools

Calendar System:

Semester

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