# Messages

Published Dec. 9, 2011 4:02 PM

A correct version of the solution for problem sheet 3 can be foundhere

Thanks to Ingvild for pointing out the error in problem 8.

Published Dec. 8, 2011 10:55 AM

For those interested, some solutions to old exam problems can be found here -SR

Published Dec. 6, 2011 1:29 PM

A proposed solution for problem set 3 can be found here

Published Dec. 2, 2011 11:09 AM

A short proposed solution (excluding problem 6, which I think everyone did well) can be found here . Beware of my mistakes. -SR

Published Dec. 1, 2011 8:13 PM

LECTURE TOMORROW IS CANCELLED DUE TO ILLNESS.

As there are exams next week, there is no time for a review lecture. A set of solutions for problem set 3 will be posted on this page on tuesday. If you need some clarifications or discussions, contact me by email to set up a meeting. All the best for the examination.

Published Nov. 28, 2011 8:37 PM

VIKTIG: The lecture tomorrow is postponed until friday. This is to give you time to look at the problem sheet 3 and ask for clarifications in class.

NEXT LECTURE will be on friday at the regular time.

Published Nov. 28, 2011 8:33 PM

VIKTIG: A practice problem sheet for chapters 5 and 6 can be downloaded from here

There is no need to submit answers for this problem set. It is only to help you prepare for the exam.

Published Nov. 25, 2011 4:05 PM

In today's lecture, i proved the argument principle, presented and illustrated Rouche's theorem with examples.

In the next lecture, i will summarize the course.

VIKTIG: PENSUM (SYLLABUS) for final exam: Chapters 1, 2.1 to 2.5, 3.1 to 3.3, 3.5, 4.1 to 4.6, 5.1 to 5.3, 5.5, 5.6, 6.1, 6.2 and 6.7

Published Nov. 22, 2011 3:38 PM

In today's lecture, I proved Cauchy Residue theorem and provided several examples illustrating it. I also computed some real integrals by converting them into contour integrals.

In the next lecture, i will cover argument principle and Rouche's theorem.

Published Nov. 18, 2011 4:11 PM

In today's lecture: i finished chapter 5 by illustrating essential singularities. I also started chapter 6 by defining residues and computing residues for some complex functions.

In the next lecture: i will prove cauchy residue theorem, use it to compute both contour integrals as well as real integrals.

Published Nov. 16, 2011 12:11 PM

Second submissions of the obligatory exercises have now been corrected, and results are updated in devilry. -SR

Published Nov. 15, 2011 2:59 PM

Today, i classified zeros and singularities of complex functions.

In the next lecture, i will complete chapter 5 by explaining essential singularities and will start chapter 6 on residues.

Published Nov. 4, 2011 3:27 PM

Today, i showed convergence of Taylor series and introduced power series.

In the next lecture, i will show the relationship between Taylor and Power series and introduce Laurent series

Published Nov. 3, 2011 12:59 PM

The 2nd Obligatory exercises have been corrected and can be found in the usual place. The results have not been punched into devilry yet, as that system tries to live up to its name. -SR

Published Nov. 1, 2011 3:33 PM

Today, i started chapter 5 by discussing series of complex numbers, uniform convergence for series of complex functions and presenting the taylor series for analytic functions.

In the next lecture, i will prove the convergence of Taylor expansion and introduce and study general power series expansions.

Published Oct. 25, 2011 2:26 PM

Today, I derived several consequences of the Cauchy integral formula including analyticity of all derivatives of an analytic function and Morera's theorem.

In the next lecture, i will present generalized Cauchy integral formula and use it to derive Liouville's theorem and the fundamental theorem of algebra.

Published Oct. 21, 2011 1:28 PM

A proposed solution to Oblig 1 can be found here .

Published Oct. 18, 2011 4:31 PM

There will be a replacement exercise session on Friday October 21st at the time and place usually used for lectures. -SR

Published Oct. 18, 2011 4:20 PM

In today's lecture, i illustrated the deformation invariance theorem through several examples and also proved the Cauchy's integral formula.

In the next lecture, i will illustrate Cauchy's integral formula and derive several consequences of this powerful result.

VIKTIG: NO LECTURE THIS FRIDAY. The next lecture will be on tuesday 25.10.2011

Published Oct. 17, 2011 4:31 PM

Tomorrow's (October 18th) exercise session at 0815-1000 is cancelled due to illness.

Published Oct. 14, 2011 7:14 PM

In today's lecture, i proved the deformation invariance theorem and the Cauchy integral theorem.

In the next lecture, i will present several examples where the above theorems are used and will prove the Cauchy integral formula.

Published Oct. 11, 2011 4:59 PM

In today's lecture: I finished chap 4.3.

In the next lecture: i will start the preparation for showing Cauchy's integral theorem and (if time permits) prove the theorem.

Published Oct. 10, 2011 5:35 PM

DUE DATE FOR OBLIG 2: 27-10-2011

Published Oct. 7, 2011 5:36 PM

In today's lecture -- i introduced contour integration and finished chap 4.2

In the next lecture -- i will cover chap 4.3 and start 4.4

Published Oct. 4, 2011 4:22 PM

In today's lecture: i defined and provided several examples of contours (chap 4.1).

In the next lecture: I will define contour integrals and calculate them (Chap 4.2 and 4.3)