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
Abstracts  
Author: Lothar v. Wolfersdorf/Elias Wegert  - Univ. Freiberg, Germany

 
 Title: Complex methods for boundary value problems
Summary: 
  1. Function theory in the unit disk
  2. Linear Riemann-Hilbert problems
  3. Potential flow past a circular cylinder I
  4. Explicit nonlinear Riemann-Hilbert Problems
  5. Potential flow past a circular cylinder II
  6. Implicit nonlinear Riemann-Hilbert Problems
  7. Transmission problems
  8. Identification of Memory Kernels and Riemann-Hilbert Problems
 Author: Rudolf Heersink - Techn. Univ. Graz, Austria

 
 Title: Initial value problems in scales of Banach spaces
 Summary: 
  1. Banach-space-valued functions and initial value problems in Banach spaces
  2. Interior estimates and scales of Banach spaces
  3. Linear and non-linear abstract initial value problems, existence and uniqueness of solutions
  4. Applications to initial value problems in spaces of non-analytic functions
  5. Complex differential operators and generalizations of the classical Cauchy-Kowalewski problem
  6. Decomposition of the initial functions

Second Week
Author: Klaus Guerlebeck - Univ. Chemnitz/Weimar, Germany and H.R. Malonek - Univ. Aveiro, Portugal

 
 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.
Helmuth Malonek (Departamento de Matemática da Universidade de Aveiro)
Jaime Carvalho e Silva (Departamento de Matemática Universidade de Coimbra)
With support from the Socrates programme