1st European Intensive Course on Complex Analysis 

and applications to partial differential equations

Departamento de Matemática, Universidade de Coimbra, Portugal

This intensive course will have a total of 48 hours of lectures and is at postgraduate level. Lecturers will have time available to discuss with the students. Successfully participating students will get a certificate. The course is mainly dedicated to students involved in the Galois network/Erasmus but open to all young mathematicians interested in Complex Analysis and its applications.

This intensive course will be followed by another two another covering other topics on the same subjects to take place in subsequent years.

There will be a Workshop "The teaching of mathematics for engineering and other sciences. Comparison of Complex Analysis curricula in several countries of the EC" at the Univ. of Aveiro in the 18 of March of 1995 after the first week of the intensive course.

First Week

1. Green's formula, fundamental solutions, integral representations.
2. Solutions in the distributional sense, solutions of inhomgeneous differential equations, Weyl's lemma.
3. Complex integral operators with weakly and with strongly singular integrands.
4. Generalized analytic functions.
5. The inhomogeneous Cauchy-Riemann system in several complex variables.

1. Dirac and Cauchy-Riemann operators in Euclidian spaces

2. Monogenic functions and hypercomplex differentiability

3. Stoke's theorem and its applications

4. Series development

5. Spingroups

1. Normality of families of meromorphic functions and Montel's theorem

2. Fatou and Julia sets

3. Local bahaviour. Periodic points

4. Sullivan's classification

5. Parameter dependent systems, bifurcation and the Mandelbrot set

Travel and living expenses can be partially covered by Erasmus. Students should apply to the Erasmus Coordinator of their home universities, and also to the University of Aveiro/ Dep. of Mathematics. Informations about the Mathematics Department or the University of Aveiro can be seen in  http://www.mat.ua.pt . Further informations about travelling, accommodation etc. can be obtained from the organizers.