EP30.FSF1110 — Mathematical Modelling

This course provides a foundational and application-oriented introduction to mathematical modeling for undergraduate students in Applied Mathematics. The course equips students with essential concepts, techniques, and principles for constructing, analyzing, validating, and interpreting mathematical models arising in natural sciences, engineering, economics, and data-driven contexts. Topics include model classification, dimensional analysis, proportional reasoning, discrete and continuous models, optimization-based models, dynamic models, and ordinary differential equations. Emphasis is placed on model formulation, model analysis, solution interpretation, validation, and communication of modeling results. Students develop both technical and analytical skills through lectures, seminars, exercises, and two midterm assessments.

Requirements for Final Examination

Students are allowed to take the final/terminal exams (50%) if their attendance score (10%) is 5 or higher (on a 10-point scale).

See Appendix 2, Rubric 1 for attendance evaluation.

Requirements for Class Attendance

Students are responsible for attending all classes. In case of absence due to force majeure, students must provide sufficient and reasonable proof. For each absence, 1 point will be deducted from the attendance score. Students who miss more than 3 classes, with or without valid reasons, will be considered as failing to complete the course and must re-register.

Students will be awarded points for constructive comments. These points will be added to attendance and group assignment scores.

Groups that do not submit their group work will receive a score of 0. Late submissions will incur a deduction for each day they are late.

Requirements for In-class Behaviour

The course is conducted on the principle of mutual respect between learners and lecturers. Any behavior that disrupts the teaching and learning process is strictly prohibited.

Students must arrive on time for class. Those who are more than 10 minutes late will not be allowed to attend. Noise and other disturbances that affect the learning process are not permitted.

Laptops and tablets may only be used for taking notes and performing calculations related to lectures and exercises. Use for any other purpose is strictly prohibited.

Main topics:

• Fundamentals of mathematical modeling
• Model construction and modeling cycle
• Dimensional analysis & scaling
• Linear and nonlinear models
• Discrete and continuous models
• Optimization and applied model selection
• Dynamic models and ODE-based modeling
• Population models
• Model evaluation, verification, and validation
• Communication and interpretation of results