Title of the course: Basic and Advanced topics in Complex Analysis
Instructor: Dr. Konstantinos Kalimeris
Institution: University of Cambridge
Dates: 31 August – 4 September 2020
Prerequisites: Nothing. We will derive all the results from first principles.
Level: Advanced undergraduate and graduate
Abstract: In this course we will study several topics from Complex Analysis, both from pure and applied point of view. Firstly we will give an introduction to complex variables and discuss the properties of analytic complex functions. Then, we will focus on complex integration where on the one hand we will present and prove some useful theorems, and on the other hand we will discuss techniques for computing explicitly complex and real integrals.
We will also discuss more advanced topics which involve asymptotic evaluation of integrals, the Riemann-Hilbert problem and Generalized Analytic functions. Finally, using these tools we will derive classical and novel transforms used for solving initial and boundary value problems associated with Partial Differential Equations.
The course is suitable for students interested in getting deeper in complex analysis, but also for those who would like to find out tools for treating a number of problems from Applied Mathematics.
The course aims an overview of complex analysis in two ways: firstly to discuss some essential basic topics, and secondly to introduce some not so well-known concepts which provide tools for treating a number of problems in Applied Mathematics.
Language: EN