## Mathematical Modelling

 Faculteit Science and Engineering Jaar 2021/22 Vakcode WBMA007-05 Vaknaam Mathematical Modelling Niveau(s) bachelor Voertaal Engels Periode semester I a ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Mathematical Modelling
Leerdoelen 1. The student is able to identify the fundamental dimensions of variables in a mathematical model, and is able to apply a dimensional analysis and scaling.
2. The student knows the basic concepts of continuum modeling: density, flux, conservation law, and is able to formulate simple continuum models, e.g. elastic deformation problems
3. The student is able to model waves mathematically, and can analyze wave equations using basic techniques.
4. The student is able to model diffusion, e.g. heat flow problems.
5. The student is able to apply the basic principles of mathematical network modeling to small-scale problems motivated by applications, and to analyze certain aspects of the obtained mathematical model.
6. The student is able to formulate simple identification problems in such a way as to apply basic parameter identification techniques.
7. The student is able to apply the basic principles of port-based network modeling to simple multi-physics system examples.
8. The student is able to formulate port-based network models as port-Hamiltonian systems, and to mathematically analyze the obtained models.
Omschrijving In the first two years of the bachelor program mathematical models of different kinds have been treated in various courses, sometimes in large detail and sometimes as examples of the theory. This course aims at providing a more systematic and fundamental treatment of classes of mathematical models as frequently arising in Applied Mathematics. The emphasis is on the common mathematical framework and the exploration of the mathematical aspects behind these models.

Below a list of topics to be treated:
- Dimensional analysis and scaling.
- The continuum description: densities, fluxes, conservation laws and constitutive relations.
- Waves, vibrations and light: wave reflection and refraction, acoustic waves, electromagnetic waves, linearization, perturbation, soliton, group velocity, wave front, shock waves.
- Elastic deformations, stretching, shear and torsion.
- Heat flow, natural and forced convection.
- Nonlinear models in science and technology.
- Introduction to network modeling of large-scale systems.
- Input-output partitioning of interconnection variables, and differential-algebraic systems.
- Black-box and grey-box modeling; introduction to system identification.
- Port-based modeling of complex systems by interconnection through power-variables.
- Port-Hamiltonian systems theory of complex multi-physics systems.
- Examples from various physical and engineering domains.
- Introduction to distributed-parameter port-Hamiltonian systems, and examples.
Uren per week
Onderwijsvorm Hoorcollege (LC), Opdracht (ASM)
Toetsvorm Opdracht (AST)
(Assessment takes place through five homework assignments. The final grade is the average of these five homework assignments. Students pass the course if the average grade of the homework assignments is higher than 5.5)
Vaksoort bachelor
Coördinator prof. dr. ir. R.W.C.P. Verstappen
Docent(en) Prof. Dr. J.G. Peypouquet ,prof. dr. ir. R.W.C.P. Verstappen
Verplichte literatuur
Titel Auteur ISBN Prijs
lecture notes
Entreevoorwaarden Basic knowledge of calculus, linear algebra, and differential equations.
Opmerkingen The course prepares for courses of the BSc and MSc programmes Applied Math that use mathematical models, e.g. Bachelor Project, Models for Fluid Flow, Modeling and Identification.

This course was registered last year with course code WIMOD-08
Opgenomen in
Opleiding Jaar Periode Type
BSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I a
BSc Mathematics: General Mathematics  (Electives and Minor General Mathematics) 3 semester I a keuze
BSc Mathematics: Probability and Statistics 3 semester I a keuze
BSc Technische Wiskunde 3 semester I a verplicht
MSc Industrial Engineering and Management: Production Technology and Logistics  (Optional technical PTL modules) - semester I a verplicht