||6 credit points
||Groesen, E.W.C. van (Universiteit Twente), Heemink, A.W. (Technische Universiteit Delft), Molenaar, J. (Wageningen Universiteit), Tijsseling, A.S. (Technische Universiteit Eindhoven)
||firstname.lastname@example.org, A.W.Heemink@tudelft.nl, email@example.com, a.s.tijsseling@TUE.nl
||This course is introducing 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 mathematical equations and formulas, and included into a mathematical model.This activity requires both a good understanding of the system under consideration and good mathematical skills. Mathematical modelling is essential for understanding processes in the real life, complementing expensive experiments that sometimes cannot even be carried out at all. This course will concentrate on applications in physics and life sciences and focus on models in terms of ordinary and partial differential equations.
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.
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 phenomenon from physics or the life sciences has to be developed.
A few weeks after the intensive week the written report of the project has to be handed in.
||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 (70% of the grade)
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).
There is a possibility to buy the book for 50 Euro from the lecturer during the break of the first lecture in Utrecht. Please send an email before the start of the lectures to A.W. Heemink (firstname.lastname@example.org).
||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).