### General

**COMPLEX ANALYSIS , IT-distance - spring 2016**

Welcome to the distance course in Complex Functions! The course begins on the 18th of January, 2016. The course is scheduled to run during the full spring semester with a final exam on June 3. 2016 (re-examination on the 19th of August). If you can not attend the regular exam in Stockholm, it may be possible do it (simultaniously) in a different place, e g at another university. In this case you must yourself suggest an institution with which we can cooperate. Contact me as soon as possible if you have such ideas**.**

The course material is divided into 14 Sections, each of which approximately corresponds to one week's study. Each Section corresponds to a certain amount of text in the textbook. To each Section there are also Lecture Notes (pdf-format) and a Video Lecture. These are mainly to help you to get an idea about the main results in the Section. You can use the notes, the video or both (or none) to get acquainted with the material. But you should always be aware that the main part of your study consists in reading the textbook carefully and solving the problems.

Since this is a distance course, you can of course decide for yourself when and how to study each section. However, our experience says that the best results are usually obtained if you try to keep a more or less constant pace. To this end, there will be 4 WebWork problem sets with 5 problems in each, each of which will be open for approximately four weeks, see the course schedule below. These can give up to 3 bonus credits on the exam: at least 6 correctly solved problems gives 1 credit point, at least 12 correctly solved problems gives 2 credit points and at least 17 correctly solved problems gives 3 credit points, if you submit your answers before the corresponding dead-lines. The problems are corrected by our computer system WebWork. If you are not familiar with the use of WebWork, look here. Also note that there is a list of key concepts in each Section. Make it a habit to check that you can explain the meaning and use of each such key concept before you go on to the next Section.

So now it is time to get started with Section 1! Please let me know if you find errors. My main mission during this course will be to act as a tutor and try to help you out when you run into trouble. **You can always write to me when you get stuck and you can count on fairly rapid answers. This concerns both mathematical and practical questions.**** **In addition, I do incurrage you to make use of the discussion forum to discuss with your fellow students.

During the course I will also send letters to the whole group to keep you informed about changes and the general progress of the course. **Please make sure that you are activated on this coursepage.** If you don't receive any mail, please check the news forum below. If there are messages there which you haven't received, something is wrong with your profile settings.

Martin Tamm, Teacher

email: matamm@math.su.se

**Content**We discuss analytic functions, integration and expansions of analytic functions in power series, residues, conformal maps, harmonic functions, physical applications and some elementarty facts about analytic functions of several variables. This material can be applied to the modeling of processes within different areas of natural sciences, i.e. in physics.

**Textbook and other sources**

- Saff and Snider:
**Fundamentals of complex analysis**, Prentice-Hall. - Tamm:
**Elementary Properties of Analytic Functions of Several Variables**(pdf). - Earlier examinations with solutions.