Contents |
Course Code
IAM 567 (9700567)
Credit
(3-0) 3
Prerequisites
Consent of instructors
Content/Aims
This course gives an introduction to real motivations, their translation into mathematical language and, then, the choice and performance of computational means. Students will learn about the nature of mathematical modelling, starting with a physical or biological model, representing it mathematically, simplifying and solving the resulting model and interpreting the results. They will be suggested to work in teams, to communicate appropriately and to present their results. Models and cases studies from mechanics in form of ordinary and partial differential equations. Geometric and discrete models. Stochastic models in finance. Coursework and computer lab with MATLAB
Learning Outcomes
Suggested Textbooks
- N. Bellomo, L. Preziosi, “Modeling Mathematical Methods and Scientific Computing”, CRC Press 2000.
- A. Friedman, W. Litmann, “Industrial Mathematics, A Course in Solving Real-World Problems”, SIAM 1994.
- J. Gebert, M. Laetsch. S.W. Pickl. G.-W. Weber, R. Wünschiers, “Mathematical modeling and approximation in observing and predicting Of gene expression patterns”, to appear in the proceedings of CASYS, Liege, Belgium, 2003.
- A. Quarterioni, R. Sacco, F. Saleri, “Numerical Mathematics”, Springer, 2000.
- C.F. van Loan, “Introduction to Scientific Computing”, Prentice Hall, 1999.
There will be manuscript(s) provided.
- MATLAB 6.1
Outline
- 1. week Dynamical Systems short overview
- 2. week Inverse Prolems short overview
- 3. week Estimation problems short overview
- 4. week Student Presentations of the Case Studies
- 5. week Student Presentations of the Case Studies
- 6. week Student Presentations of the Case Studies
- 7. week Numerical Methods in Mathematical Modeling
- 8. week Student Presentations of the Simulations
- 9. week Student Presentations of the Simulations
- 10. week Student Presentations of the Simulations
- 11. week Basic Functional Analysis concepts short overview
- 12. week Optimization Problems short overview
- 13. week Introduction of some Computational Biology Problems