Advanced Modelling in Science

Credits	6 credit points
Instructors	Peletier, M.A. (Technische Universiteit Eindhoven), Groesen, E.W.C. van (Universiteit Twente), Heemink, A.W. (Technische Universiteit Delft), Molenaar, J. (Wageningen Universiteit)
E-mail	m.a.peletier@tue.nl, e.w.c.vangroesen@ewi.utwente.nl, A.W.Heemink@its.tudelft.nl, jaap.molenaar@wur.nl
Aim	This course aims at teaching the principles and practice of mathematical modelling. An important part of the course is to recognize the essential mechanisms governing a phenomenon. These mechanisms have to be translated into mathematics and included into the model. This activity requires both a good understanding of the system under consideration and good mathematical skills. Although mathematical modelling may make use of all fields of mathematics, this course will concentrate on applications in physics and focus on models in terms of partial differential equations.
Description	The main topics are: * Basis Concepts of Mathematical Modeling; * Non-dimensionalization, Scaling; * Conservation Principles; * Constitutive Relations; * Stability and Robustness; * Variational Methods; Except from selfstudy and class-teaching, an important part of the course concerns working in a small group on a specific project. The topics for project work may differ from year to year.
Organization	The first part of the course consists of five lectures where the main topics are presented. Attendance of these lectures is obliged. After each lecture home-work assignments are given to the students. The final deadline for submitting the home-work is one week after the last lecture. For attending the "intensive course" the grade for the home-work should at least be a 5. The second part of the course is offered as a one week "intensive course", fully devoted to a project. Here the students work in groups of 3-5 students. In most cases a computer program for simulating a certain physical phenomenon has to be developed. A few weeks after the intensive week the written report of the project has to be handed in.
Examination	The grading will be based on performance in: hand-ins of home-work assignments (30% of the grade) a written report of group work on the project and an oral presentation about the project at the last day of the intensive week (70% of the grade).
Literature	Continuum Modeling in the Physical Sciences, E. van Groesen and J. Molenaar, Mathematical Modeling and Computation, Vol. 13, SIAM, 2007 (ISBN 978-0-898716-25-2).
Prerequisites	The participants will benefit from a solid knowledge of advanced calculus, basic knowledge of ordinary and partial differential equations and programming experience with Matlab (or an equivalent language).
Remarks	This is an intensive course and therefore only master students can participate. Intensive week: 23 until 27 March 2009 Additional classes: 2, 9, 16, 23 February and 2 March 2009 in Utrecht (Mathematics building, room 611ab)

Last changed: 08-09-2010 09:56