Mathematical Modeling

Lecturer: Prof. Dr. P. Dondl
Lectures: Wednesday 14:15-15:45 Uhr, SR226 (Hermann-Herder-Str. 10).
Office Hour: Monday 14-16 Uhr, Zi. 217, Hermann-Herder-Str. 10. Please send an email before coming to the office hour.
Assistant: E. Trébuchon
Office Hour: Upon request

News

The Rooms and Dates for the Tutorials changed! Bring your laptop if possible and if needed to the programming tutorials which will not be in the CIP-Pool anymore.

Content

This course provides a comprehensive introduction to mathematical modeling. We will learn the systematic process of translating real-world problems into mathematical frameworks, analyzing them using appropriate mathematical tools, and interpreting the results in practical contexts. The course covers both discrete and continuous modeling approaches, with emphasis on differential equations, variational problems, and optimization techniques. Through case studies in physics, biology, engineering, and economics, students will develop skills in model formulation, validation, and refinement. Special attention is given to dimensional analysis, stability theory, and numerical methods necessary for implementing solutions with a focus on numerical methods for ordinary differential equations. The course combines theoretical foundations with hands-on experience in computational tools for model simulation and analysis.

Credit points

See course handbook ("Modulhanbuch") and its complementa ("Ergänzungen").

Tutorial groups

SubjectDateRoomTutor
Assistance programming sheet 3 Di 03.06. 14:00-16:00 SR 218, Ernst-Zermelo-Str. 1 Eric Trébuchon
Correction exercise sheet 3 Di 10.06. 14:00-16:00 SR 218, Ernst-Zermelo-Str. 1 Grzegorz Kozera

Exercises

We will alternate every week between "mathematical" exercises and programming sheets. The former one should be handed in at the letterbox 3.21 in the basement of Ernst-Zermelo-Str.1, and the latter one per email at eric.trebuchon@math.uni-freiburg.de at each Wednesday at 14:00.

SheetDistributedReturn
Exercise Sheet 130.04.2025 07.05.2025
Programming Sheet 130.04.2025 14.05.2025
Exercise Sheet 214.05.2025 21.05.2025
Programming Sheet 215.05.2025 28.05.2025
Exercise Sheet 328.05.2025 04.05.2025
Programming Sheet 328.05.2025 11.05.2025

Literature

This lecture will closely follow Mathematical Modeling by Ch. Eck, H. Garcke, and P. Knabner.