# Mathematical Analysis (MAT310)

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

*Course description for study year 2022-2023. Please note that changes may occur.*

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:**Alexander Rashkovskii

**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**

**Course assessment**

Questionary and/or discussion.

**Literature**