Kompleks Funktionsteori

KomAn (Complex Analysis) Blok 3A Spring 2007

Quick access to Homepage for studies in mathemtics
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 5.
Exercices: Monday 15.15-17.00. Thursday 10.15-12.00 in A 102. First exercise class on February 5. Teaching Assistant Kirsten Andersen < m03ka@math.ku.dk>
I will use a new English translation of a revised version of what was used in previous years:

Christian Berg: Complex Analysis, Matematisk Afdeling 2007.

The old Danish version cannot be used. The book is for sale in Naturfagsbogladen. The price is DKK 140.
  • Additional literature for the interested student
    Some important misprints in the new edition:
  • Page 3.3: line 3 form below: pair of triangles. I mention 6 triangles. They should have been paired in 3 pairs: the first two in one pair, etc.
  • Page 4.2, last line: =0 is missing at the end.
  • Page 4.13, first line: The bar over the disc K(a,r) shall be removed
  • Page 7.8. middle: \rho \le \varphi(z) shall be \rho\le |\varphi(z)|
    Obligatory work: During the course there will be assigned 3 obligatory sets of exercises which shall be handed to Kirsten 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 April 2, 2007.
    Exercise set for 15.2.2007: Exercises 1.8, 1.10.
    Exercise set for 1.3.2007: Exercises 4.15, 4.16.
    Exercises for 15.3.2007: problems
    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 April 2, 2007, as well as the reexam on August 13, 2007 guide The exam is from 10-13. Please remember to check the address of the exam.
    If you want to see the answers to the problems of the Exam on April 2, 2007: Solution and to the Exam on August 13, 2007: Solution
    Grades of the exam April 2,2007: Grades and grades of the exam August 13, 2007: 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: There will be a special meeting on Thursday March 29, 10.15-12.00 at A 102. CB will answer questions and go through the exams from 2006, where the text can be found below.
    Old exams

    Exams in Koman (Complex analysis)

  • Koman April 2006
  • Koman August 2006
  • Koman April 2007
  • Koman August 2007

    Exams (in Danish) for the previous course 2KF:

  • 2KF January 2002
  • 2KF June 2002
  • 2KF January 2003
  • 2KF June 2003
  • 2KF January 2004
  • 2KF June 2004
  • 2KF January 2005
  • 2KF June 2005
  • 2KF January2006

    berg@math.ku.dk/ August 16, 2007.