Development of an Innovative Elementary Course in Fourier Analysis

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A text and related lecture materials for a lower division course in Fourier analysis for students in the mathematical, physical, and engineering sciences are being prepared and class tested at SIUC and a number of other colleges and universities. This course has become feasible due to the recent development of FOURIER, a software package that enables students to do calculations with a stack of `functions' in much the same way that they would do calculations with a stack of numbers on an RPN calculator. Students will use FOURIER to explore classic and contemporary phenomena commonly analyzed with Fourier series, Fourier transforms, or the discrete Fourier transform and thereby come to appreciate the essential roles of mathematical analysis and computer simulation in modern science and engineering.