Analytic Functions
Syllabus, Master's level, 1MA039
This course has been discontinued.
- Code
- 1MA039
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 15 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
BSc, Topology, Complex Analysis
Learning outcomes
In order to pass the course (grade 3) the student should be able to
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
Content
Infinite series and products. Partial fractions and factorisation. The gamma and the beta functions, Stirling's formula, the method of steepest descent. Riemann's zeta function. Normal families, the Riemann mapping theorem. Harmonic functions, Poisson's formula, Jensen's formula, the distribution of zeros of entire functions. Analytic continuation: continuation along arcs, the monodromy theorem, the modular function and Picard's theorem. Subharmonic functions. Dirichlet's problem.
Instruction
Lectures and problem solving sessions.
Assessment
Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.