Waves á la Fourier

A senior/graduate elective course on Fourier transforms and the physics of vibrations and waves has now been taught for 6 years. The textbook by Ronald Bracewell is used in the first half of the semester to lay the mathematical foundations: piecewise functions, convolution, generalized functions, the transform and the series, theorems on transform pairs, and techniques for evaluating transforms. The second half of the semester is devoted to physical applications, with relatively little time spent on vibrations or waveforms; the major focus is on the use of spatial transforms to describe basic processes of radiation and imaging. Examples are drawn from acoustics, optics, solid‐state physics, and medical imaging. The emphasis throughout this course is on the unifying structure of this approach to linear physics. Computational techniques and applications involving statistics or noise are deliberately avoided. An optional laboratory allows the students to see the ideas of the lecture course illustrated in concrete examples. Several students have gone on to do master's theses in acoustics after taking this course, and others have commented on its usefulness to them in a variety of fields.