Faculty of Science

Objectives

To introduce students to the fundamental tools of functional transforms and variational methods and their applications to the solution of differential equations.

Contents

Functional transformations and properties (Fourier series, The Mellin transform, The Hankel transform, discrete and fast Fourier transforms etc.); Applications of functional transformations to the solution of partial differential equations; Function spaces and properties (Sobolev spaces, Banach spaces, Hilbert spaces, etc.); Linear variational problems and regularity of solution (elliptic variational theory; the Lax-Milgram theorem, Sesquilinear forms associated to elliptic operators, regularity of solutions of variational problems).