Complex Function Theory with Differential Equations

Complex functions, complex integration, Laurent series and residue calculus, Fourier series, ordinary differential equations in real and complex variables.

After completing the course, the student should be able recognize, understand and apply the basic theory of functions of one complex variable and compute integrals using residues. The student should also know basic results on existence and uniqueness for the solutions of ordinary differential equations in real and complex variables, and master some basic techniques for the treatment of singularities for such equations.

Lectures and exercises. Retake of examination may be given as an oral examination.