The course is about problems where the variables are not numbers (as in calculus), but functions or more abstract objects. A linear structure where the objects can be added and multiplied with scalars is combined with a geometric/topological structure, where we can measure distances and take limits of the objects.

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.

**Syllabus**

The course is given

- in English - in the first half of autumn
- jointly with Chalmers TMA401

#### Course information 2020

- Course coordinator: Håkan Andreasson

#### Course information 2019

- Course coordinator: Håkan Andreasson

#### Course information 2018

Course coordinator: Peter Kumlin

- Schedule 2018

#### Course information 2017

- Course coordinator: Peter Kumlin

- Schedule 2017

#### Course information 2016

- Course coordinator: Peter Kumlin
- Schedule

#### Course information 2015

- Course coordinator: Peter Kumlin
- Schedule

- Course coordinator: Peter Kumlin
- Schedule

#### Course information 2012

- Course coordinator: Peter Kumlin
- Schedule

#### Course information 2011

- Course coordinator: Peter Kumlin
- Schedule

#### Course information 2010

- Course coordinator: Peter Kumlin
- Schedule

#### Course information 2009

- Course coordinator: Peter Kumlin
- Schedule

#### Course information 2008

- Course coordinator: Peter Kumlin
- Schedule

#### Course information 2007

- Course coordinator: Peter Kumlin
- Schedule