MA-304 Concepts in Analysis
- ECTS Credits:
- 7.5
- Responsible department:
- Faculty of Engineering and Science
- Course Leader:
- Rolf Tomas Nossum
- Lecture Semester:
- Autumn
- Teaching language:
- Norwegian or English
- Duration:
- 1 term
The course is connected to the following study programs
- Industrial Mathematics, Bachelor's Programme
- Advanced Teacher Education level 8-13, 5-year Master's Programme
Teaching language
Norwegian or EnglishRecommended prerequisites
MA-163, MA-216 and MA-215
Course contents
Work on examples that lead to understanding of the real numbers and to the concept of limit on the real line and in metric spaces. Further work on real functions and sequences of functions in order to study connections between continuity, differentiability and integrability.
Learning outcomes
On successful completion of the course, the student should be able to
-
explain the significance of completeness of the reals and consequences thereof, like the Bolzano-Weierstrass property
-
apply definitions of limits and continuity of real sequences and functions and to some extent generalize the definitions to metric spaces
-
explain the difference between pointwise and uniform convergence and continuity, and know results where this difference is essential
-
explain and use the definition of differentiability
-
decide integrability in the sense of Riemann and compute Riemann integral of real functions
-
explain the intermediate value theorem, the mean value theorem and the fundamental theorem of analysis and show how these results are connected with continuity, differentiability and integrability
-
Explain how the rational numbers extends to a complete ordered field.
Examination requirements
Required assignments must be approved, see Canvas for more information.
Teaching methods
Lectures, work in small groups and compulsory assignements. The course has an expected workload of around 200 hours.
Evaluation
The person responsible for the course, in consultation with the student representative, decides the method of evaluation and whether the courses will have a midterm- or end of term evaluation, see also the Quality System, section 4.1. Information about evaluation method for the course will be posted on Canvas.
Offered as Single Standing Module
Yes
Assessment methods and criteria
5-hour written examination. Graded assessment.
Reduction of Credits
This course’s contents overlap with the following courses. A reduction of credits will occur if one of these courses is taken in addition:
| Course | Reduction of Credits |
|---|---|
| MA-214 – Concepts in Analysis 1 | 7.5 |
| MA-227 – Reell analyse | 7.5 |