SF1677 Foundations of Analysis 7.5 credits
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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.
Course disposition
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
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
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
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 web
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.
Course web SF1677