Complex Analysis

Introduce the basic tools of complex analysis.

This lesson will cover the following topics:

- Analytic functions: definition, zeros of an analytic function, analytic extension, maximum principle

- Holomorphic functions: definition, examples (including the exponential and logarithms), Cauchy-Riemann equations, existence of antiderivatives.

- Cauchy’s formula and its implications: The loop index with respect to a point, Cauchy’s formula in a convex set, and the analyticity of holomorphic functions.

- Singularities and meromorphic functions: poles and essential singularities, meromorphic functions, Laurent series expansions, the residue theorem

The analysis courses in the first and second years of the bachelor’s program and the first semester of the third year, specifically:

- HAX403X Analysis 4: Function Sequences, Integral Series, Fourier Analysis

- HAX404X Topology of^{R^n} and Functions of Several Variables

- HAX502X Differential Calculus and Differential Equations

Recommended prerequisites: first semester of the third year of a bachelor's degree program

Hourly volumes:

            CM: 27

            TD: 27

            Practical Work: -

            Land: -