NMAK17002U Complex Analysis 2

Volume 2018/2019
Education

MSc Programme in Mathematics

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

 

and related topics

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.

Introductory complex analysis (e.g. the course KomAn). We shall occationally use results from introductory measure theory, such as Lebesgue's dominated convergence theorem.
Five hours of lectures and three hours of exercise sessions per week for 7 weeks.
  • Category
  • Hours
  • Exam
  • 1
  • Exam Preparation
  • 39
  • Exercises
  • 21
  • Lectures
  • 35
  • Preparation
  • 110
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
There will be 30 minutes of preparation time before the oral examination.
Exam registration requirements

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

Aid
Only certain aids allowed

All aids allowed during the preparation time. No aids allowed during the examination.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners.
Re-exam

Oral examination, 30 minutes with 30 minutes preparation time. All aids allowed during the preparation time. No aids allowed during the exam.

To be allowed to take the re-exam, students who have not already had 2 out of the 3 mandatory assignments approved must re-submit all 3 assignments no later than two weeks before the beginning of the re-exam week. The assignment must be approved in order to take the re-exam.

Criteria for exam assesment

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