A correct version of the solution for problem sheet 3 can be foundhere
Thanks to Ingvild for pointing out the error in problem 8.
For those interested, some solutions to old exam problems can be found here -SR
A proposed solution for problem set 3 can be found here
A short proposed solution (excluding problem 6, which I think everyone did well) can be found here . Beware of my mistakes. -SR
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.
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.
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.
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
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.
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.
Second submissions of the obligatory exercises have now been corrected, and results are updated in devilry. -SR
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.
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
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
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.
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.
A proposed solution to Oblig 1 can be found here .
There will be a replacement exercise session on Friday October 21st at the time and place usually used for lectures. -SR
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
Tomorrow's (October 18th) exercise session at 0815-1000 is cancelled due to illness.
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.
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.
MPORTANT: SECOND OBLIGATORY EXERCISE SET CAN BE DOWNLOADED FROM OBLIG2
DUE DATE FOR OBLIG 2: 27-10-2011
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
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)