### Instruction

Name | Cr | Method of study | Time | Location | Organiser |
---|---|---|---|---|---|

Functional analysis | 10 Cr | General Examination | 5.2.2020 - 5.2.2020 | ||

Functional analysis | 10 Cr | Lecture Course | 2.9.2019 - 16.12.2019 | ||

Functional analysis | 10 Cr | General Examination | 12.6.2019 - 12.6.2019 | ||

Functional analysis | 10 Cr | General Examination | 6.2.2019 - 6.2.2019 | ||

Functional analysis | 10 Cr | General Examination | 19.9.2018 - 19.9.2018 | ||

Functional analysis | 10 Cr | Lecture Course | 3.9.2018 - 23.12.2018 | ||

Functional analysis | 10 Cr | General Examination | 23.5.2018 - 23.5.2018 | ||

Functional analysis | 10 Cr | General Examination | 10.1.2018 - 10.1.2018 | ||

Functional analysis | 10 Cr | Examinarium (electronic exam room) | 2.11.2017 - 2.11.2017 | ||

Functional analysis | 10 Cr | General Examination | 1.11.2017 - 1.11.2017 | ||

Functional analysis | 10 Cr | Lecture Course | 4.9.2017 - 13.12.2017 |

### Target group

Optional course.

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

Belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

### Prerequisites

Analysis I&II, Linear algebra I&II, Topology I

### Learning outcomes

Elements of linear functional analysis including Banach and Hilbert spaces and linear operators between them, three basic principles, and applications to differential equations.

### Timing

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

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

### Contents

Introduction to linear functional analysis including Banach and Hilbert spaces and linear operators between them; topology of normed spaces; examples of Banach spaces including sequence and function spaces; three basic principles; Fourier-series; Sobolev spaces; applications to differential equations.

### Activities and teaching methods in support of learning

Lectures and exercise classes

### Study materials

Required:

Funktionaalianalyysin peruskurssi, luentomoniste.

Recommended:

Rynne, B., Youngson, M., Linear Functional Analysis, Springer Undergraduate Mathematics Series, London, 2000. (Introduction to the topic)

Friedman, A., Foundations of Modern Analysis, Dover 1982. Conway, J. A Course in Functional Analysis. Springer, 1990. (Introduction to the topic) Werner, D., Funktionalanalysis, Springer Lehrbuch 1990. (In German)

### Assessment practices and criteria

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

### Recommended optional studies

Elements of measure theory and complex analysis

### Completion methods

Exam, other methods will be described later.