The goal of the course is to develop experience working with Fourier series and Fourier transform, which can be (somewhat simplistically) described as a technique replacing a given function (or signal, as engineers would say) with a sum of simpler trigonometric functions. Along with the necessary mathematical background (orthogonality, integrable functions, distributions), we will cover quite a few applications culminating in the fast fourier transform algorithm ("the most important numerical algorithm of our lifetime" as some say).

• Classes: MWF 10:00am-10:50am, NDSU South Engineering, Rm 208
• Office hours: MWF 11:00am-12:00pm or by appointment (Minard 408E32)
• Syllabus: (pdf)
• Textbook (optional): Brad G. Osgood, Lectures on the Fourier Transform and Its Applications (Amazon). The lecture notes on which the book is based can be found (here).

• B. Riemann, On a representation of a function by a trigonometric series, 1854
• Historical introduction to Carslaw H.S., Introduction to the theory of Fourier's series and integrals, 1921

• Fourier Series.
• Fourier Transform.
• Distributions and Their Forier transform. Delta function.
• Sampling and Interpolation.
• Discrete Frourier Transform.