# MATA200 Complex Calculus (5 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2020-2021, 2021-2022, 2022-2023

## Description

Complex numbers, functions of one complex variable (polynomials, exponential function, trigonometric functions, logarithm), complex derivative and holomorphic functions, complex integration, Cauchy's integral formula, residue theorem, basics of conformal mapppings

## Learning outcomes

After completing the course, the student:

- is able to apply the basic arithmetic, algebraic and geometric properties of complex numbers
- knows elementary complex functions and their basic properties
- knows analytical functions and their basic properties
- can use complex integration and apply both Cauchy integral formula and the Residue theorem
- can solve simple conformal mapping problems

## Additional information

Opintojakso on laskennallisempi kuin syventävät kurssit Kompleksianalyysi 1-2.

## Description of prerequisites

Calculus 2 or equivalent knowledge

## Study materials

Zill & Shanahan: A First Course in Complex Analysis with Applications

## Completion methods

### Method 1

**Evaluation criteria:**

Grading is based on points from course exam and the weekly exercises

Select all marked parts

### Method 2

**Evaluation criteria:**

The grading is based on points from the final exam

Select all marked parts

**Parts of the completion methods**

x

### Teaching (5 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Evaluation criteria:**

Course exam and homework

**Language:**

Finnish

**Study methods:**

Lectures 30 h (in Finnish), 7 sets of homework

#### Teaching

##### 8/26–8/26/2020 Exam

##### 5/24–7/31/2021 Lectures

##### 7/28–7/28/2021 Exam

x

### Exam (5 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Evaluation criteria:**

Final exam

**Language:**

English, Finnish

**Study methods:**

Independent study and Final exam