MA-227 Reell analyse
- ECTS Credits:
- 10
- Responsible department:
- Faculty of Engineering and Science
- Course Leader:
- Trond Arnold Abrahamsen
- 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-183 and MA-184
Course contents
Bijections, countability, uncontablity and the diagonal argument of Cantor. Rational numbers, algebraic numbers and real numbers. Limits and continuity in terms of epsilon-N and epsilon-delta arguments. Order- and metric completeness of the real numbers. Extension of the rational ordered field to a complete ordered field. The fundamentality of completeness in calkulus, the main theorems on continuity and differentiability. The Riemann integral. Sequences and series of continuous, differentable and integrable functions. Uniform convergens and its importance.
Learning outcomes
Upon successful completion of the course, the student will be able to
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Explain and apply central concepts connected to countability and uncontability.
-
Explain possibilities and limitations in using rational numbers and in a precise manner develop the term infinite decimal expression by the concept of limit.
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Demonstrate the main steps in the process of extending the rational numbers to a complete field and know how completeness is the key for making calculus work.
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Define and derive the most basic concepts and theorems of calculus concerning limits, continuity, differentiability and integrability.
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Analyze preservation of continuity, differentiability and integrability concerning limits of sequences and series of functions.
Examination requirements
Mandatory hand-ins must be approved. See Canvas for details.
Teaching methods
Lectures, group work, historical immersion project, and mandatory hand-ins. The module is estimated to require about 270 hours of effort.
Evaluation
The faculty member in charge of the module confers with the student rep which form of evaluation will be organized, and whether midterm or post hoc. Cfr the University regulations on quality assurance, chapter 4.1.
Admission for external candidates
No
Offered as Single Standing Module
Subject to capacity constraints
Assessment methods and criteria
Written, supervised, and graded exam, 5 hours.
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 |