SF2713 Foundations of Analysis 7.5 credits
This course has been discontinued.
Last planned examination: Autumn 2018
Decision to discontinue this course:
No information insertedContent and learning outcomes
Course contents
Real numbers. Metric spaces. Basic topological concepts. Convergence. Continuity.
Derivative. Integral. Uniform convergence. Spaces of functions.
Banach´s fixed point theorem. Implicit and inverse mapping theorem. (Something about Lebesgue integral, alternatively something about differential forms and Stokes theorem.)
Intended learning outcomes
The course is a fundamental course for studies in more advanced mathematics and for studies in closely related fields.
By the end of the course the student should be able to solve problems on the different topics of the course. In particular the student should be able to
- Understand and be able to apply basic topological concepts. Be able to state the theorems of Heine-Borel and Bolzano-Weierstrass.
- Understand and be able to apply the concepts of continuity, convergence and derivative for functions between metric spaces. Be able to state Arzelà-Ascoli´s theorem and Weierstrass´ approximation theorem.
Literature and preparations
Specific prerequisites
Analysis corresponding to SF1602 and SF1603 or SF1600 and SF1601 and preferably also complex analysis, differential equations and transforms corresponding to SF1628 and SF1629.
Recommended prerequisites
Equipment
Literature
* Rudin, Walter, "Principles of mathematical analysis".
or
* Pugh, Charles Chapman, "Real mathematical analysis".
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
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.
Other requirements for final grade
Written examination. Possibly partial examination (optional) during the course.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
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
Offered by
Main field of study
Education cycle
Add-on studies
Contact
Supplementary information
The course is replaced by SF1677.