Faculty of Science

Complex Analysis 2
Provider: Faculty of Science

Activity no.: 5591-21-07-31
	Enrollment deadline: 22/11/2021

Place

Department of Mathematical Sciences

Date and time

22.11.2021, at: 08:00 - 30.01.2022, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Henrik Laurberg Pedersen E-mail address: henrikp@math.ku.dk

Teaching language

English partially in English

Semester/Block

Block 2

Scheme group

Exam requirements

To be allowed to take the oral exam the student should have at least 2 out of 3 homework assignments approved.

Exam form

Oral examination, 30 minutes

Exam details

There will be 30 minutes of preparation time before the oral examination.

Exam aids

Only certain aids allowed

Grading scale

7 point grading scale. For PhD students: Passed / Not Passed

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Exam re-examination

Oral examination, 45 minutes with 45 minutes preparation time. All aids allowed during the preparation time. No aids allowed during the exam. To be eligible to take the re-exam, students who have not already had 2 out of three mandatory assignments approved must re-submit all three assignments no later than 2 weeks before the beginning of the re-exam week. The mandatory assignment must be approved in order to take the re-exam.

Course workload

Course workload category	Hours
Lectures	35.00
Exercises	14.00
Preparation	117.00
Exam	1.00
Eksamensforberedelse	39.00

Sum	206.00

Content

The course covers

- Holomorphic and harmonic functions and Poisson integrals
- Normal families, conformal mapping and Riemann's mapping theorem
- Infinite products and Weierstrass factorization
- Growth of entire functions
- Picard's theorems
- Eulers Gamma function

Learning outcome

Knowledge: After completing the course the student is expected to have a thorough knowledge of definitions, theorems and examples related to the topics mentioned in the description of the course content and to have a deeper knowledge of complex analysis, both from an analytic and a geometric/topological point of view.

Skills: At the end of the course the student is expected to have the ability to use the acquired knowledge to follow arguments and proofs of advanced level as well as to solve relevant problems using complex methods.

Competences: At the end of the course the student is expected to be able to:
1. reproduce key results presented in the course together with detailed proofs thereof,
2. construct proofs of results in complex analysis at the level of this course,
3. use the course content to study relevant examples and to solve concrete problems.

Literature

W. Rudin, Real and complex analysis. Supplementary notes might also be used.

Teaching and learning methods

Five hours of lectures and two hours of exercise sessions per week for 7 weeks.

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