ABSTRACT
This chapter sketches some connections of Fourier series, the Fourier transform, and the Laplace transform with the theory of complex variables. It discusses the identification of the interval with the circle, and provides a remark on intervals of arbitrary length. Fourier coefficients are calculated using complex analysis. The chapter reviews steady—state heat distribution using some ideas from Fourier series and from Laurent series. A mathematical model of the disk is calculated. The Fourier transform is the analogue on the real line of Fourier series coefficients for a specific function. The chapter provides a set of exercises for solving differential equations using the Fourier transform.
