# Real and Complex Calculus (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 2023-2024. Please note that changes may occur.*

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**

## Content

Functions of several variables, complex numbers and functions, analytic functions; series, Taylor series, Fourier series; residues.

## Learning outcome

- Understand the concept of limit, and be able to define continuity and differentiability of functions of several real variables and of one complex variable.
- Understand the concepts of convergence and divergence of series and power series of functions of one real and one complex variable, and be able to use different convergence tests, especially for finding the radius of convergence and area 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 calculate with complex numbers in Cartesian, polar and exponential form, find powers and roots of complex numbers.
- Be able to define and know basic properties of the complex exponential and logarithmic functions and complex trigonometric functions, and to differentiate elementary analytical functions.
- Understand the concepts of analytic and harmonic functions, and be able to understand and use the necessary conditions of differentiability.
- Understand and use basic properties of analytic and harmonic functions. Be able to determine Taylor series of elementary analytical functions.
- Understand the notion of residue and use it for computing contour integrals.
- Be able to find the Fourier series of a given simple function.

## 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), |

## Coursework requirements

3 compulsory assignments must be approved to have access to the exam.

## Course teacher(s)

## Course coordinator:

Tyson Ritter## Head of Department:

Bjørn Henrik Auestad## Method 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

There must be an early dialogue between the course coordinator, the student 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 course evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.