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Complex Analysis 2
Provider: Faculty of Science

Activity no.: 5591-21-07-31 
Enrollment deadline: 22/11/2021
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time22.11.2021, at: 08:00 - 30.01.2022, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserHenrik Laurberg Pedersen    E-mail address: henrikp@math.ku.dk
Teaching languageEnglish partially in English
Semester/BlockBlock 2
Scheme groupC
Exam requirementsTo be allowed to take the oral exam the student should have at least 2 out of 3 homework assignments approved.
Exam formOral examination, 30 minutes
Exam detailsThere will be 30 minutes of preparation time before the oral examination.
Exam aidsOnly certain aids allowed
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Criteria for exam assessmentThe student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Exam re-examinationOral 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 categoryHours
Lectures35.00
Exercises14.00
Preparation117.00
Exam1.00
Eksamensforberedelse39.00
Sum206.00
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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