Instruction

Name Cr Method of study Time Location Organiser
Spectral theory 10 Cr Lecture Course 13.1.2020 - 30.4.2020
Name Cr Method of study Time Location Organiser
Spectral theory 10 Cr Lecture Course 16.1.2018 - 20.3.2018

Target group

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Prerequisites

B.Sc.-level mathematics, Functional analysis

Learning outcomes

Knowledge of basic spectral theory for bounded and unbounded operators in Hilbert spaces and applications to partial differential equations

Timing

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

Contents

Unbounded operators in Hilbert spaces; closed, symmetric and self-adjoint operators; spectral theorem; perturbation theory; applications to elliptic PDE

Activities and teaching methods in support of learning

Lectures and exercise classes

Study materials

Required: lecture notes.

Recommended: Reed-Simon, Methods of modern mathematical physics; Davies: Spectral theory and differential operators

Assessment practices and criteria

Exam and excercises, Course will be graded with grades 1-5

Recommended optional studies

Sobolev space theory, Fourier analysis, theory of distributions

Completion methods

Exam, other methods will be described later