Complex Functions (2012, RU)
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Course Description
In this class we study the basic properties of holomorphic functions defined on a domain in the complex plane:
- Holomorphic functions and the Cauchy-Riemann equations
- Power Series
- Contour integrals
- Cauchy theorem
- Cauchy integral formula
- Laurent Series and isolated singular points
- Residue theorem
- Euler Gamma-Function
- Riemann zeta-function
Prerequisites
This is a course on elementary complex function theory for students in the second year of the bachelor.
The course is obligatory for students in mathematics and physics. We only assume familiarity with calculus.
Examination
Written exam: July 3, 2012, 8:30-11:30 h in LIN 4.
Second chance: August 16, 2012, 14-17 h in HG00.068.
The exam is not open book.
Grading
Exercises can be handed in one week after the mentioned week at Wednesday 11 h.
Your final grade will be the highest of the two marks 0.75E+0.25H and E,
where E is the exam grade and H the average of your homework.
Literature
We use the text book Princeton Lectures in Analaysis II: Complex Analysis, by Eli Stein and Rami Shakarchi.
There is an additional collection of exercises, slightly less theoretical than the ones in Stein and Shakarchi,
which can be found here.
Material covered during the lecture and in the exercise class
- Week 16: Lecture: Sections 1.1, 1.2.1, 1.2.2 Exercise class: 1.1 upto 1.5
- Week 17: Lecture: Sections 1.2.3, 1.3 Exercise class: 2.1, 2.3, 3.2, 3.3
- Week 19: Lecture: Sections 2.1, 2.2, 2.3, Exercise class: 3.4, 4.1, 4.2 in the next week on Wedensday
- Week 20: This week no lecture, but during lecture time there are exercise classes, due to Desda Symposium on Friday May 11.
Locations: Peter 't Hart HG01.058, Elise Hopman HG01.139, Robin Reuvers HG02.702, Roberta Iseppi HG03.632
- Week 21:
- Week 22:
- Week 23:
- Week 24:
- Week 25: