Kompleks Analyse

KomAn (Complex Analysis) Blok 1C Fall 2010

Quick access to Homepage for studies in mathemtics

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 in Auditorium 5. Wednesday 9.15-10.00 in Auditorium 8 and 13.15-15.00 in Auditorium 5.
First lecture on September 6. Lecturer: Christian Berg

Exercices: First exercise class on September 6.
Monday 15.15-17.00 in Auditorium 9, Wednesday 10.15-12.00 in A109. Teaching Assistant: Andreas Næs Aaserud < andreas.naes.aaserud@gmail.com>

Teaching material

Christian Berg: Complex Analysis, Matematisk Afdeling 2010.

The book is for sale in Polyteknisk Boghandel, Science section at the Biocentre, and is a reprint of the edition used in block 3 2009-10.
Additional literature for the interested student

A translation to Danish of the principal terminology of the course

Maple
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 Wednesday at 12.00 in the weeks 37,39,41. Two of these have to be passed in order to be admitted for the written exam.
Exercise set for 15.9.2010: Exercises 1.7 and 1.10
Exercise set for 29.9.2010: Exercises 4.1 and 4.16
Exercise set for 13.10.2010: Problem set 3

Exam
The exam takes place Wednesday November 3, 2010. It is a 3-hour written exam with grades. The first 90 minutes are without access to books, notes and pocket calculators, the last 90 minutes with access to these things, but you are not allowed to bring personal computers. Reexam: Same conditions as the ordinary evaluation.

Grades November 2010

Guide to the coming exam on November 3, 2010 as well as the reexam on March 3, 2011 guide.

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.

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. Please ask me or the teaching assistents if there is something you do not understand. 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 36: § 1 - Details: Week 36

Week 37: § 2, 3.1, 3.2 - Details: Week 37 I will start on 3.2 next week. The proof of Goursats lemma given in the notes is due to Alfred Pringsheim (1850-1941), a mathematician from Munich. In litterary circles he is known as the father in law of the author Thomas Mann.

Week 38: § 3.2, 4 - Details: Week 38 On Wednesday I will start with Theorem 4.4

Week 39: § 5 - Details: Week 39 Misprints: On page 5.4, lines 12,13 from bottom: t_0 appears 3 times. It shall be delta_0. On page 5.18, middle of page: In the second sum we have used : The expression stated is wrong. It shall be
alpha_k(gamma(t_{k+1}))-alpha_k(gamma(t_k))=argvar(gamma|[t_k,t_{k+1}])=theta(t_{k+1})-theta(t_k)

Week 40: § 6 - Details: Week 40

Week 41: § 7 - Details: Week 41 Remember that your evaluation of the course shall be done this week-access via Absalon is open until October 19 at midnight. It is important that as many as possible answers the questionaire.

Week 42: § 8,9 - Details: Week 42

Week 43: The course is over, but the following help is offered:
Monday October 25, 15.15-17 (auditorium 9): Andreas will discuss problems from the exams april 2006-april 2008
Wednesday October 27, 10.15-12 (A109): Christian Berg will discuss problems from the exams August 2008-September 2010
Wednesday October 27, 13.15-15 (auditorium 5): Christian Berg will answer questions related to the theory and proofs in the lecture notes.

week 44: Remember the exam is on Wednesday November 3. It is from 9.00-12.00 and is at Mariendals-Hal A, Mariendalsvej 21 C. You have to be there 15 minutes before the exam starts, and you will not be allowed to enter if you arrive after the exam has started. Remember to bring you university ID or another photo-ID.

Old exams

Exams in Koman (Complex analysis)

Koman April 2006

Koman August 2006

Koman April 2007 Solution Solution

Koman August 2007 Solution Solution

Koman April 2008 Solution solution

Koman August 2008 Solution solution

Koman March 2009 Solution Solutions

Koman August 2009

Koman April 2010 Solution Solutions

Koman September 2010