3rd
European Intensive Course on Complex Analysis
and applications to partial differential equations 

Departamento de Matemática,
Universidade de Coimbra, Portugal 3 to 21 March, 1997 

Goal of the Course  
This intensive course follows the ten held at the Universities of Coimbra and Aveiro from 1995 to 2004 (1995, 1996) and there are plans for intensive courses in the following years. The lecture notes of some of the courses have been published in Coimbra and others are in print. 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. 

First Week 





Title: Complex methods for boundary value problems  
Summary: 1. Function theory in the unit disk 2. Linear RiemannHilbert problems 3. Potential flow past a circular cylinder I 4. Explicit nonlinear RiemannHilbert Problems 5. Potential flow past a circular cylinder II 6. Implicit nonlinear RiemannHilbert Problems 7. Transmission problems 8. Identification of Memory Kernels and RiemannHilbert Problems 





Title: Computer aided calculations in Quaternionic Analysis and Geometric Algebra  
Summary:
1. Geometric Algebra  an algebra of abstract vector variables  axioms for Geometric Algebra  Geometric Algebra, Quaternions and Euclidean vector spaces  Analysis in Geometric Algebras 2. Application to selected topics in Physics  angular momentum and Kepler's laws  rotations of rigid bodies  electric and magnetic fields  boundary value problems for elasticity and electrodynamics 3. Introduction to MAPLE  program functions, exercises from real analysis, vector algebra and analytic geometry in R^2 and R^3  computations with complex numbers, quaternions, and Clifford numbers  first applications in geometry 4. Computer aided solution of physical problems 

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. 



With support from the Socrates programme 