Clarke B.M.N. Fourier Theory

Macquarie University (Department of Mathematics), 65 pages.Linear differential operators.
Separation of variables.
Fourier Series.
Bessel's inequality.
Convergence results for Fourier series.
Differentiation and Integration of Fourier Series.
Half-range Fourier series.
General Intervals.
Application to Laplace's equation.
Sturm-Liouville problems and orthogonal functions.
Bessel Functions.
Fourier Transforms.
Inverse Fourier Transforms.
Applications to Differential Equations.
Plancherel's and Parseval's Identities.
Band Limited Functions and Shannon's Sampling Theorem.
Heisenberg’s Inequality.