MA-227 Reell analyse
- ECTS Credits:
- 10
- Responsible department:
- Faculty of Engineering and Science
- Course Leader:
- Trond Arnold Abrahamsen
- Lecture Semester:
- Spring
- 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
Rationals and real numbers. Completeness Axiom and its consequences.
Bijections, cardinality, countability, uncountability, and Cantor’s diagonal argument.
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.
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.
Examination requirements
Mandatory hand-ins must be approved. See Canvas for details.
Teaching methods
Lectures, group work, historical immersion project, and mandatory hand-ins. Estimated workload of the course is 267 hours.
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 |