Real Analysis (MAT210)
Introduction to the theory of functions of one complex and several real variables, including convergence/divergence of series, both real and complex.
Course description for study year 2025-2026
Facts
Course code
MAT210
Version
1
Credits (ECTS)
10
Semester tution start
Spring
Number of semesters
1
Exam semester
Spring
Language of instruction
English, Norwegian
Time table
Admission requirements
Science and mathematics qualification (REALFA) / Higher engineering education (HING)
Content
Convergence, continuity, differentiability, completeness, and compactness in the real numbers. Differentiation and optimisation of functions of several variables. Taylor series, Fourier series.
Learning outcome
- Understand what is meant by a mathematical proof, and how to communicate mathematical arguments in the form of a mathematical proof.
- Understand basic topological notions (closed, open, connected and compact sets).
- Understand the concept of limit, and be able to define continuity and differentiability of functions of one and several real variables.
- Understand the concepts of convergence and divergence of series and power series of functions of one real variable, and be able to use different convergence tests, especially for finding the radius of convergence of a power series.
- Get operational knowledge of the basic concepts of multi-variable analysis. Be able to solve extremal value problems in several variables.
- Be able to find the Taylor and Fourier series of given simple functions.
Required prerequisite knowledge
None
Recommended prerequisites
MAT100 Mathematical Methods 1
Exam
| Form of assessment | Weight | Duration | Marks | Aid |
|---|---|---|---|---|
| Written exam | 1/1 | 4 Hours | Letter grades | Basic calculator, Compilation of mathematical formulae (Rottmann), |
Written exam is with pen and paper.
Coursework requirements
2 compulsory assignments
2 compulsory assignments must be approved to have access to the exam.
The assignments are handed in individual. All aids are allowed.
Course teacher(s)
Course coordinator:
Tyson RitterHead of Department:
Bjørn Henrik AuestadHead of Department:
Bjørn Henrik AuestadMethod of work
6 hours lectures and problem-solving classes per week.
Overlapping courses
| Course | Reduction (SP) |
|---|---|
| Mathematical Methods 2b (MAT220_1) | 1 |
| Mathematical Methods 2 (ÅMA260_1) | 5 |
| Mathematical methods 2b (ÅMA270_1) | 1 |
| Mathematical methods 2c (ÅMA330_1) | 5 |
| Mathematics 5 - Complex analysis (ÅMA310_2) | 5 |
| Mathematical Methods 2 (MAT200_1) | 5 |
| Mathematics 5 - Complex analysis (ÅMA310_1) | 6 |
Open for
Course assessment
The faculty decides whether early dialogue should be conducted in all or selected groups of courses offered by the faculty. The purpose is to gather feedback from students for making changes and adjustments to the course during the current semester. In addition, a digital evaluation, students’ course evaluation, must be conducted at least once every three years. Its purpose is to collect students` experiences with the course.
