Modelleren met ODE's en PDE's

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Cursusdoel

Zie onder vakinhoud.

Vakinhoudelijk

The course is an introduction to mathematical modeling, i.e. the process of translating real-world phenomena (arising for example in natural sciences, engineering or economics), into well-defined mathematical problems. A major challenge lies in finding a good compromise between accuracy of the model and accessibility of the resulting mathematical problem to analysis and computation.

‘Wiskundig Modelleren’ is one of the third year modelling courses. Student should at least choose one of this selection of courses. The course is recommended to students interested in partial differential equations and applied mathematics. Please find more information about the study advisory paths in the bachelor at thestudent website.

Leerdoelen:
We start by introducing basic concepts and modeling techniques, such as non-dimensionalization, scaling analysis and perturbation methods, in the context of applications. The rest of the course is organized according to the mathematical structures governing the models. After discussing how systems of linear equations can be used to describe electrical networks and space frames, we turn to models based on ordinary differential equations. This includes a first introduction to variational modeling, motivated by the historic brachistochrone problem, and to optimal control problems. At the example of population dynamics, we study questions in stability theory. The part on continuum mechanics covers amongst others kinematics, conservation laws, constitutive relations and is illustrated with models for (non)viscous fluids and elastic solids. Finally, we turn to the analysis of models involving partial differential equations, mainly elliptic and parabolic.

Onderwijsvormen:
Two times per week two hours of lectures and two times per week two hours of tutorials.

Toetsing:
The final grade is a weighted average of the scores on the final exam (80%) and the hand-in assignments (20%). Students are encouraged to discuss the hand-in problems in groups, but have to submit individual solutions. In case of a retake, the exam counts for 100% of the final course grade.

Herkansing en inspanningsverplichting:
Students with a final grade lower than 4 are eligible to do the retake exam only if they submitted at least 75% of the hand-in assignments and were present at the final exam.

Taal van het vak:
The language of instruction is English.

Werkvormen

Hoorcollege

Werkcollege

Toetsing

Eindresultaat

Verplicht | Weging 100% | ECTS 7,5

Ingangseisen en voorkennis

Ingangseisen

Er is geen informatie over verplichte ingangseisen bekend.

Voorkennis

Basics of linear algebra and analysis, ordinary differential equations (WISB231). Some experience with partial differential equations and numerical methods is useful, but not mandatory.

Voertalen

  • Engels

Cursusmomenten

Gerelateerde studies

Tentamens

Er is geen tentamenrooster beschikbaar voor deze cursus

Verplicht materiaal

Materiaal Omschrijving
BOEK \Introduction to the Foundations of Applied Mathematics” by Mark Holmes, Springer, 2019. Available as an e-book through WorldCat (UU Library).

Aanbevolen materiaal

Er is geen informatie over de aanbevolen literatuur bekend

Coördinator

prof. dr. ir. J.E. Frank j.e.frank@uu.nl

Docenten

prof. dr. ir. J.E. Frank j.e.frank@uu.nl

Inschrijving

Deze cursus is open voor bijvakkers. Controleer wel of er aanvullende ingangseisen gelden.

Inschrijving
Van maandag 30 mei 2022 tot en met vrijdag 24 juni 2022

Na-inschrijving
Van maandag 22 augustus 2022 tot en met dinsdag 23 augustus 2022

Inschrijving niet geopend
Permanente link naar de cursuspagina
Laat in de Cursus-Catalogus zien