MA-227 Reell analyse (Spring 2027)
- ECTS Credits:
- 10
- Responsible department:
- Faculty of Engineering and Science
- Course Leader:
- Trond Arnold Abrahamsen
- Lecture Semester:
- Spring
- Teaching language:
- Norwegian or English
- Duration:
- ½ year
Table of contents
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
Recommended previous knowledge
Learning outcomes
Upon successful completion of the course, the student will be able to
- explain the axioms for real numbers.
- describe and apply key concepts related to cardinality such as countability and uncountability.
- explain and apply topological concepts like openness, closedness, and compactness on the real number line.
- define and derive the most fundamental results in calculus related to limits, continuity, differentiability, and integrability.
- determine the continuity, differentiability, and integrability of limits of sequences of functions.
Contents
Rationals and real numbers. Completeness Axiom and its consequences.
Bijections, cardinality, countability, and uncountability.
Sequences of numbers and limits of sequences by epsilon-N argumentation.
Functions, limits, and function continuity by epsilon-delta argumentation.
Open, closed, and compact sets of real numbers.
Importance of completeness for calculus, fundamental theorems on continuity and differentiability.
Sequences of continuous, differentiable, and integrable functions.
Pointwise and uniform convergence and their significance.
Riemann integral and fundamental theorems about the integral.
Teaching and learning methods
Examination requirements
Examinations
Student evaluation
Offered as a free-standing course
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-304 – Concepts in Analysis. | 7.5 |