- 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.
SF1677 Foundations of Analysis 7.5 credits
Information per 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.
Information for Spring 2025 Start 14 Jan 2025 programme students
- Course location
KTH Campus
- Duration
- 14 Jan 2025 - 2 Jun 2025
- Periods
- P3 (3.7 hp), P4 (3.8 hp)
- Pace of study
25%
- Application code
61602
- Form of study
Normal Daytime
- Language of instruction
Swedish
- Course memo
- Course memo is not published
- Number of places
Places are not limited
- Target group
- No information inserted
- Planned modular schedule
- [object Object]
- Schedule
- Schedule is not published
- Part of programme
Degree Programme in Engineering Mathematics, åk 2, Conditionally Elective
Degree Programme in Engineering Mathematics, åk 3, Optional
Degree Programme in Engineering Physics, åk 3, Optional
Master of Science in Engineering and in Education, åk 4, MAFY, Conditionally Elective
Master of Science in Engineering and in Education, åk 4, MAKE, Conditionally Elective
Master of Science in Engineering and in Education, åk 4, TEDA, Conditionally Elective
Master of Science in Engineering and in Education, åk 5, MAFY, Conditionally Elective
Master of Science in Engineering and in Education, åk 5, MAKE, Conditionally Elective
Master of Science in Engineering and in Education, åk 5, TEDA, Conditionally Elective
Master's Programme, Applied and Computational Mathematics, åk 1, Optional
Contact
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus SF1677 (Autumn 2019–)Headings with content from the Course syllabus SF1677 (Autumn 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
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.
Grading scale
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
Examiner
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.
Offered by
Main field of study
Technology
Education cycle
First cycle
Add-on studies
No information inserted