• Svenska

# SF1677 Foundations of Analysis 7.5 credits

### Choose semester and course offering

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

## Application

### For course offering

Spring 2025 Start 14 Jan 2025 programme students

### Application code

61602

Headings with content from the Course syllabus SF1677 (Autumn 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Real numbers. Metric spaces. Basic topological concepts. Heine-Borel's theorem. Bolzano-Weierstrass theorem. Convergence. Continuity. Derivative. Riemann-Stieltjes integral. Uniform convergence. Spaces of functions. Stone-Weierstrass theorem. Arzela-Ascoli theorem.
• Derivative of multivariable functions. Banach's fixed point theorem. Implicit and inverse mapping theorem. Something about the Lebesgue integral.

### Intended learning outcomes

After the course the student should be able to

• use concepts. theorems and methods to solve and present solutions to problems within the parts of foundations of analysis described by the course content,
• read and comprehend mathematical text, in order to learn to solve problems involving proofs of basic concepts in analysis.

## Literature and preparations

### Specific prerequisites

Completed basic course SF1626 Calculus in Several Variable or SF1674 Multivariable Calculus.

### Recommended prerequisites

SF1683 Differential Equations and Transforms, or corresponding courses.

### Equipment

No information inserted

### Literature

Announced no later than 4 weeks before the start of the course on the course web page.

## 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 - Exam, 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 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.

Technology

First cycle