Kompleks Funktionsteori

KomAn (Complex Analysis) Blok 3A Spring 2009

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Study Board for Mathenatical Sciences

The principal mathematician in the course

Augustin-Louis Cauchy (1789-1857)

If you want to know more about Cauchy or any other mathematician, then look at MacTutor History of Mathematics Archive

The responsible for the course is Christian Berg . < berg@math.ku.dk> Information concerning the course will be given from this homepage. The course and exam will be given in English.

Officiel description of the course

Schedule: Lectures: Monday 13.15-15.00. Thursday 9.15-10.00 and 13.15-15.00 in Auditorium 7 First lecture on February 2.
Exercices: Monday 15.15-17.00 in A109. Thursday 10.15-12.00 in N034. First exercise class on February 2. Teaching Assistant Kirsten Andersen < m03ka@math.ku.dk>

I will use the book:

Christian Berg: Complex Analysis, Matematisk Afdeling 2007.

The book is for sale in Akademisk Boghandel (At the Biocentre) and is a new issue of the edition of last year. A few misprints have been corrected but the issue of last year can be used. Additional literature for the interested student

If you want to do some experiments in Maple to illustrate parts of the theory, you can download the following Maple worksheet and run it using maple. koman1.mw (You shall rightclick on the icon with the mouse. Then choose: "Save target as" and you save it where you want and call it koman1.mw. It is important that it gets the extension mw. The name itself is unimportant.)

Obligatory work: During the course there will be assigned 3 obligatory sets of exercises which shall be handed to the teaching assistant by Thursday at 17.00 in the weeks 7,9,11. Two of these have to be passed in order to be admitted for the written exam, which takes place on Monday March 30, 2009.
Exercise set for 12.2.2009: Exercises 1.8 and 1.10
Exercise set for 26.2.2009: Exercises 4.17 and 4.19
Exercise set for 12.3.2009: Exercise set 3

Assessment: Internal exam with grades in a 3-hour written exam. The first 90 minutes are without access to books, notes and calculators, the last 90 minutes with access to these things. Reevaluation: Same as ordinary evaluation.

Guide to the coming exam on March 30, 2009 as well as the reexam on August 13, 2009 guide. On August 13, the exam takes place from 10 to 13 in Festsalen, Øster Voldgade 10.

The text of the exam on March 30, 2009: Exam, solutions: Solutions, Grades: Grades

The text of the exam on august 13, 2009: Exam, Grades: Grades

In the lectures I do not have time to cover all proofs in details. This does not mean that the proofs are not important: You are supposed to study them yourself. It is important to learn the main concepts and to understand how they are related. In the first 90 minutes of the exam you will be asked to prove simple statements from the course material.

About reading the book: Every section starts with a small introduction telling about the main results of the section. Therefore, it can happen that you do not understand every word in this introduction because you have to read the whole section to get the full understanding. On the other hand, as soon as you start reading the main text of a section, you are supposed to understand every statement, and if this is not the case, you may have to go back to previous sections or refresh what you have learned in previous courses. Mathematics is learning by doing. So when you think you understand something: Close the book and write it down for yourself on a piece of paper or explain it to another student.

Overall plan for the course:

Week 6: § 1 - Details: Week 6

Week 7: § 2, 3.1 - Details: Week 7

Week 8: § 3.2, 4 - Details: Week 8

Week 9: § 5 - Details: Week 9

Week 10: § 6 - Details: Week 10

Week 11: § 7 - Details: Week 11

Week 12: § 8,9 - Details: Week 12

Week 13: Extra problem session with Kirsten related to the exam: Monday March 23, 15.15 in A109

Question session with CB: Thursday March 26, 13.15 in Aud. 7.

Old exams

Exams in Koman (Complex analysis)