Applied Functional Analysis

The course treats problems where the variables are not numbers, as in more elementary calculus, but instead functions or more abstract objects. A linear structure, where objects can be added with each other or multiplied with scalars, is combined with a geometrical/topological structure that allows measures and limits. Functional analysis arose in the first decades of the 20th century, when mathematicians discovered that methods used to solve integral equations and partial differential equations also could be used in more abstract settings. During the course you will study normed spaces, Banach and Hilbert spaces, fixed-point theorems, compactness, spectral theory for compact self-adjoint maps, the Fredholm alternative, and applications to differential and integral equations.