• Svenska

# SF2743 Advanced Real Analysis I 7.5 credits

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

Headings with content from the Course syllabus SF2743 (Spring 2022–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

Integration and measure theory: Basic measure theory, integration of measurable functions (Lebesgue integrals), convergence theorems, product measures, Fubini's theorem.

Functional Analysis: Introduction to functional analysis, metric spaces, Banach and Hilbert spaces, basic theorems about linear operators and functionals.

Applications which can be chosen among: topics from Fourier analysis, ergodic theory, probability theory, Sobolev spaces, differential equations.

### Intended learning outcomes

After the course the student should be able to

• explain basic concepts and theorems within the parts of analysis described by the course content,
• apply basic concepts, theorems and methods within the parts of analysis described by the course content in problem solving.

## Literature and preparations

### Specific prerequisites

English B / English 6
Completed course SF1677 Foundations of Analysis.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

No information inserted

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examination consists of a final exam and possible continuous examination in the form of written assignments or an oral exam.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Mathematics

Second cycle