Complex Analysis, 7.5 credits

Aims and objectives

General aims for first cycle education

First-cycle courses and study programmes shall develop:

• the ability of students to make independent and critical assessments
• the ability of students to identify, formulate and solve problems autonomously, and
• the preparedness of students to deal with changes in working life.

In addition to knowledge and skills in their field of study, students shall develop the ability to:

• gather and interpret information at a scholarly level
• stay abreast of the development of knowledge, and
• communicate their knowledge to others, including those who lack specialist knowledge in the field.

(Higher Education Act, Chapter 1, Section 8)

Course objectives

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 the most appropriate method for solving problems in complex analysis and be able to motivate the choice of method.

Main content of the course

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.

Teaching methods

Teaching is done in the form of lectures and seminars.
The teaching methods may be altered, should only a few students take the course.

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.

Examination methods

Theory, 4.5 credits (Code: A001)
Written exam
The re-exam will take place within eleven weeks after the regular exam.

Seminars, 3 credits (Code: A002)
Assignments and written and oral presentation of assignments.

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

For further information, see the university's local examination regulations (in Swedish).

Comments on examination methods

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

Grades

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 prescribe which grading system shall apply. The grade is to be determined by a teacher specifically appointed by the university (an examiner).

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

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

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

Seminars
Grades used are Fail (U) or Pass (G).

For further information, see the university's local examination regulations (in Swedish).

Specific entry requirements

Foundations of Analysis, 7.5 Credits.

For further information, see the university's admission regulations (in Swedish).

Transfer of credits for previous studies

Students who have previously completed higher education or other activities are, in accordance with the Higher Education Ordinance, entitled to have these credited towards the current programme, providing that the previous studies or activities meet certain criteria.

For further information, see the university's local credit transfer regulations (in Swedish).

Other provisions

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

Reading list and other teaching materials

Required Reading

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