This syllabus is valid: 2010-01-18
and until further notice
Course code: 5MA041
Credit points: 7.5
Education level: Second cycle
Main Field of Study and progress level:
Mathematics: Second cycle, has only first-cycle course/s as entry requirements
Grading scale: Pass with distinction, Pass, Fail
Responsible department: Department of Mathematics and Mathematical Statistics
Contents
The goal of the course is to give deeper knowledge of the theory of holomorphic and harmonic functions of one complex variable. The course covers elementary theory of holomorphic functions, harmonic and subharmonic functions. Furthermore Mittag-Lefflers theorem, the residue theorem, inhomogeneous Cacuhy Riemann equations, Cauchys general integral formula, Runges and Mergelyans theorems, the Riemann mapping theorem and the monodromy theorem are treated.
Expected learning outcomes
After the course the students are expected to be able to:
define and understand basic concepts in one variable complex analysis, such as holomorphic and (sub)harmonic functions, normal families, Blaschke products, analytic capacity and Riemann surfaces.
describe holomorphic functions as geometric mappings and be able to apply and prove the Riemann mapping theorem
apply and prove Weierstrass factorization theorem and Mittag Lefflers theorem
describe and apply Perrons method for solving Dirichlets problem
describe and apply Jensens formula and the notion of finite order of entire funcitons
apply and describe analytic continuation and the monodromy theorem
apply and prove Runges and Mergelyans theorems
Required Knowledge
Required knowledge to be able to take the course is the courses Introduction to Real Analysis (5MA086) and Complex Analysis (5MA077) or corresponding knowledge.
Form of instruction
Teaching is mainly given by lectures and supervision.
Examination modes
The examination is performed by written exam(s) and/or oral presentations. Possible grades for the course are: failed, passed or passed with distinction.The student has to pass all examinations and compulsory parts of the course in order to have passed the complete course. Those who have received the grade passed at the course cannot be reexaminated in order to achieve a higher grade.
For students that did not pass the first exam, a new opportunity for examination will be arranged. Students that failed exam twice, are entitled to reqest another teacher to grade the course. This request should be posed to the Head of the Department of Mathematics and Mathematical Statistics.
Examination based on this course syllabus is guaranteed at least two years after the student was first registered on the course.
Literature
The literature list is not available through the web.
Please contact the faculty.
