SF2745 Advanced Complex Analysis 7.5 credits

Generalizations of Cauchy’s integral formula, analytic continuation, normal families and the Riemann mapping theorem, special classes of conformal maps, complex differential equations.

Suggested applications:

• Hardy spaces
• Boundary behavior of analytic functions
• Riemann-Hilbert problems
• Harmonic functions and harmonic measure
• Infinite products of analytic functions

After the course the student should be able to:

• formulate and prove theorems concerning analytic functions such as, e.g., the generalized Cauchy integral formula and the Riemann mapping theorem;
• use and analyze conformal maps;
• discuss the theory of analytic continuation and properties of solutions to complex differential equations;
• be able to use this knowledge in the context of further applications

Completed courses SF1677 Foundations of mathematical analysis and SF1691 Complex analysis.

Announced no later than 4 weeks before the start of the course on the course web page.

If the course is discontinued, students may request to be examined during the following two academic years.

• TEN1 - Exam, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examiner decides about adapted examination for students with documented, severe disabilities in consultation with the contact person for disabilities at KTH (Funka). The examiner may allow a different form of examination for re-examination of individual students.

Jonatan Lenells

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.