# Mathematical Analysis (MAT310)

The course covers fundamentals of mathematical analysis with focus on complex analysis.

*Course description for study year 2023-2024*

Facts

## Course code

MAT310

## Version

1

## Credits (ECTS)

10

## Semester tution start

Autumn

## Number of semesters

1

## Exam semester

Autumn

## Language of instruction

English

**Time table**

## Content

Elements of mathematical logic, basic topological notions, analytic and harmonic functions of a complex variable, Cauchy-Riemann conditions, Cauchy's integral theorem and integral formulas, Taylor and Laurent series representations, classification of isolated singularities and residue theory.

## Learning outcome

Upon completing this course students should be able to:

- Clearly understand what is meant by a mathematical proof, and how to communicate mathematical arguments clearly in the form of a mathematical proof.
- Understand basic topological notions (closed, open, connected and compact sets, convergence, continuity).
- Get operational knowledge of analytic and harmonic functions, including maximum principle and integral representations.
- Determine Taylor and Laurent series of elementary analytic functions, find their zero points and singularities, and get knowledge of residue theory and its applications.

## Required prerequisite knowledge

MAT100 Mathematical Methods 1

## Recommended prerequisites

MAT200 Mathematical Methods 2, MAT210 Real and Complex Calculus, MAT300 Vector Analysis

## Exam

Form of assessment | Weight | Duration | Marks | Aid |
---|---|---|---|---|

Written exam | 1/1 | 4 Hours | Letter grades | No printed or written materials are allowed. Approved basic calculator allowed |

## Course teacher(s)

## Course coordinator:

Helge Paul Ruddat## Head of Department:

Bjørn Henrik Auestad## Method of work

6 hours lectures/problem solving per week.

## Overlapping courses

Course | Reduction (SP) |
---|---|

Mathematical Analysis (BMA100_1) | 5 |

Mathematics 5 - Complex analysis (ÅMA310_1) | 5 |

## Open for

Admission to Single Courses at the Faculty of Science and Technology

Mathematics and Physics - Five Year Integrated Master's Degree Programme
Exchange programme at Faculty of Science and Technology

## Course assessment

There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.