Mathematical Modelling
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WMIE03305 
Vaknaam  Mathematical Modelling 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester II b 
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 smallscale 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 portbased network modeling to simple multiphysics system examples. 8. The student is able to formulate portbased network models as portHamiltonian 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 largescale systems.  Inputoutput partitioning of interconnection variables, and differentialalgebraic systems.  Blackbox and greybox modeling; introduction to system identification.  Portbased modeling of complex systems by interconnection through powervariables.  PortHamiltonian systems theory of complex multiphysics systems.  Examples from various physical and engineering domains.  Introduction to distributedparameter portHamiltonian 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  master  
Coördinator  prof. dr. ir. R.W.C.P. Verstappen  
Docent(en)  Prof. Dr. S. Trenn ,prof. dr. ir. R.W.C.P. Verstappen  
Verplichte literatuur 


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 WIMOD08 

Opgenomen in 
