MM109: Mathematical Anaysis 2

Entry requirements

You must be admitted to the Master's degree programme in mathematics in order to follow the course.

Academic preconditions

Have knowledge of the course ”Introduction to MathematicalAnalysis” or comparable.

Course introduction

This course belongs to the “Master I Matematik” study program.

The course aims at introducing a classical and widely used topic within the subject area of mathematical analysis, namely analytic functions of a complex variable. This topic generalizes and enhances essential subjects of high-school mathematics and puts them into perspective. In particular, this holds for integral and differential calculus.

The course builds on “Introduction to Mathematical Analysis

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

determine whether sequences and series of complex numbers are convergent or divergent
determine the convergence behaviour of given power series
define the notion of differentiability for functions of a complex variable and expose the rigidness of this notion in comparison with the real case
expose the connection between complex differentiability and curve integrals
calculate given integrals and curve integrals via the residue theorem
give a detailed explanation of selected subjects of the course syllabus including exact proofs

Content

The following main topics are contained in the course:

Repetition of complex number arithmetics
Sequences and series of complex numbers
Power series and their convergence behaviour
Diffferentiablity of a function of a complex variable
The class of holomorphic functions with special focus on power series expansions
Cauchy’s integral theorem and integral formula for curve integrals
Cauchy’s residue theorem and applications

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

January

Tests

Oral exam

EKA

N900017102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card

Language

Normally, the same as teaching language

Examination aids

Not specified, a closer description of the exam rules will be posted in itslearning

ECTS value

Indicative number of lessons

60 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.

Intro phase (lectures, class lessons) - 25 hours
Training phase: 35 hours, including 35 hours tutorials

Teaching is centered on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.

Study phase activities: Self-reliant work on the course contents, written response to course requirements, participation in online discussion forums, preparation of compilations

Teacher responsible

Name	E-mail	Department
Henrik Pedersen	Henrik@sdu.dk	Institut for Matematik og Datalogi

Timetable

Odense

Show full time table

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile	Education	Semester	Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study.

If a transitional arrangement has been made for a course, it will be stated in the list.

See transitional arrangements for all courses at the Faculty of Science.