Periodic Functions and Fourier Series

Skill Type Description Source
23.1 Periodic Functions Workbook Recognise periodic functions + determine the frequency, the amplitude and the period of a sinusoid + represent common periodic functions by trigonometric Fourier series HELM
23.2 Representing Periodic Functions by Fourier Series Workbook Calculate Fourier coefficients of a function of period 2pi + calculate Fourier coefficients of a function of general period HELM
23.3 Even and Odd Functions Workbook Determine if a function is even or odd or neither + easily calculate Fourier coefficients of even or odd functions HELM
23.4 Convergence Workbook Determine what a Fourier series converges to at each point, including at a point of discontinuity + use the convergence property of Fourier Series to obtain series for the number pi HELM
23.5 Half-range Series Workbook Choose to expand a non-periodic function either as a series of sines or as a series of cosines HELM
23.6 The Complex Form Workbook Express a periodic function in terms of its Fourier series in complex form + understand Parseval's theorem HELM
23.7 An Application of Fourier Series Workbook Solve a linear differential equation with a periodic forcing function using Fourier series HELM

Enquiries, feedback and comments to: mash@sheffield.ac.uk