West Asia Mathematical Schools
WAMS – CIMPA
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Contact of local organizing institutions
Department of mathematics, College of Sciences, University of Diyala, Diyala, Iraq
Website: www.sciences.uodiyala.edu.iq
E-mail: mathematics@sciences.uodiyala.edu.iq
Department of mathematics, College of Sciences, University of Salahaddin, Erbil, Kurdistan-Iraq
Website: www.uni-sci.org
E-mail: herish_omer69@yahoo.com
Sponsors:
-CIMPA
-French Embassy
-University of Salahaddin
-University of Diyala-college of sciences
-IMU
Lecturers
Abdeljalil Nachaoui, Laboratoire de Mathématiques Jean Leray, Université de Nantes, France (Abdeljalil.Nachaoui@univ-nantes.fr).
Fatima M. Aboud, Department of mathematics, College of Sciences, University of Diyala, Iraq (fatimaaboud@yahoo.com).
Scientific committee
Abdeljalil Nachaoui, Laboratoire de Mathématiques Jean Leray, Université de Nantes, France (Abdeljalil.Nachaoui@univ-nantes.fr).
Abdelkrim Chakib, Department of Mathematics, University of Sultan Moulay Sliman Beni Mellal, Morocco (Abdelkrim.Chakib@univ-nantes.fr).
Oktay Veliev, Department of Mathematics, Dogus university, Istanbul, Turkey, (oveliev@dogus.edu.tr).
Date and place of the school
Date: The period from 18 to 29 October 2015
Place: Department of mathematics, College of Sciences, University of Salahaddin, Erbil, Kurdistan-Iraq.
Description of courses
1. Introduction.
Motivation : examples of boundary value problems. Green’s formula maximum principle
2. Sobolev spaces. • Motivation for Sobolev spaces • Definitions • Poincaré inequality
3. Embedding theorems
Sobolev embedding theorems
Weak convergence
General Sobolev inequalities
Rellich’s compactness theorem
4. Weak solutions to boundary value problems, • Definitions
Lax-Milgram Theorem
Existence and uniqueness of the solution
5. Approximation
Numerical methods
Implementation issues
Initiation into finite element software FreeFem++
The students need to have the following priori knowledge:
Measure theory and integration:
The monotone convergence theorem
Lebesgue’s dominated convergence theorem
Polynomial interpolation
Numerical integration
Definitions Properties of Hilbert space of Hilbert spaces
Notions of distributions
To cover this cours we will need 31 hours for theoretical part and 16 hours for practical part. In the end of the course there will be theoretical and practical evaluations. The students will have the possibility to speak about them interesting domain of research, so in the mid of course there will be 3 hours of communication.
Program of the school-First Weak
17 hours Theoretical courses – 8 hours Programming courses
3 hours of communications
Program of the school-Second Weak
14 hours Theoretical courses – 8 hours Programming courses
3 hours theoretical and programming evaluations