MATH495M

An infinite series is the sum of the terms of an infinite sequence. In calculus we encounter infinite series of real numbers, for example, the geometric series. This course focuses on infinite series of functions, beginning with an introduction to function series and convergence. Students explore power series, Laurent series, and trigonometric series, culminating with an in-depth examination of Fourier series. Fourier series have numerous applications to areas such as partial differential equations, signal and image processing, acoustics and econometrics, to name only a few. Based on their interests, students investigate one or more of the aforementioned applications of Fourier series using current research papers and texts in mathematics and computer software. Prerequisite(s): MATH 301.