MM109: Mathematical Anaysis 2
Study Board of Science
Teaching language: Danish or English depending on the teacher
EKA: N900017112, N900017102
Assessment: Second examiner: None, Second examiner: External
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Professional Master
STADS ID (UVA): N900017101
ECTS value: 5
Date of Approval: 29-04-2019
Duration: 1 semester
Version: Archive
Comment
Entry requirements
Academic preconditions
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
Examination regulations
Prerequisites for participating in the exam a)
Timing
Autumn
Tests
Mandatory assignments
EKA
N900017112
Assessment
Second examiner: None
Grading
Pass/Fail
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
0
Additional information
See danish version for further information .
The prerequisite examination is a prerequisite for participation in exam element a).
The prerequisite examination is a prerequisite for participation in exam element a).
Exam element a)
Timing
January
Prerequisites
| Type | Prerequisite name | Prerequisite course |
|---|---|---|
| Examination part | Prerequisites for participating in the exam a) | N900017101, MM109: Mathematical Anaysis 2 |
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 under 'Course Information' on Blackboard.
ECTS value
5
Additional information
The examination form for re-examination may be different from the exam form at the regular exam.
Indicative number of lessons
Teaching Method
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