Complex Analysis, 6 credits

Learning outcomes

Knowledge and comprehension
After completed studies, the student should be able to

• show understanding of basic definitions and concepts in complex analysis, and
• show basic knowledge about theorems in complex analysis.

Proficiency and ability
After completed studies, the student should be able to

• apply definitions, theorems and methods in complex analysis in order to solve problems in real and complex analysis, and
• present well-structured solutions both in oral and written form for problems in complex analysis.

Values and attitudes
After completed studies, the student should be able to

• choose an appropriate method for solving problems in complex analysis and motivate the choice of method.

Content

The main contents of the course are analytic and harmonic functions, complex integration, Cauchy integral theorems, Laurent series, residue calculus, comform mapping, and some applications of complex analysis.

Examinations and grades

Theory, 3 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Seminars, 3 credits (Code: A002)
Grades used are Fail (U) or Pass (G).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).

In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.

The grades used on this course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Comments on grades

The grade from the examination part A001 is given as a grade for the course as a whole.

Modes of assessment

• Theory (code A001): Written exam
• Seminarier (provkod A002): Written assignment and oral examination

For students with a documented disability, the university may approve applications for adapted or other modes of assessment.

For further information, see the university's local examination regulations.

Specific entry requirements

Foundations of Analysis, 7.5 Credits.

For further information, see the university's admission regulations.

Other provisions

All or part of the course can be given in English.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Reading list and other learning resources

Required reading

Saff, Edward B., and Snider, Arthur David (latest edition)
Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics
Pearson