How do populations grow? How do viruses spread? What is the trajectory of a glider? Many real-life problems can be described and solved by mathematical models. In this course you will work in a project on your own real-life problem. You will learn to analyse a problem, formulate it as a mathematical model (containing ordinary differential equations), solve the equations in the model and validate your results. You will learn how to implement Euler's method in a Python programme. If needed you can refine or improve your model, based on your first results. Finally, you will learn how to write about your findings in a scientific way.
This course is aimed at Bachelor students from Mathematics, Engineering and Science disciplines.
The course is for anyone who would to use mathematical modelling for solving real world problems. It suits business owners, researchers, students...
What you'll learn:
- To follow the process of the mathematical modelling cycle
- Formulate and specify a real-life problem
- Construct appropriate ordinary differential equations with relevant parameters and conditions
- Solve the ordinary differential equations and implement Euler's method in a (Python) programme
- Validate the results of the calculation
- Write a scientific report in LaTeX about the mathematical model you construct
Week 1: Introduction to the cycle of mathematical modelling.
Week 2: We will start describing a population of fish by a differential equation.
Week 3: Complete more modelling cycles by improving on the model and evaluating the consequences. Euler's method is introduced for solving ordinary differential equations. You will run Python simulations.
Week 4: You choose an assignment for your project and specify your real-life problem. You will implement a 1-dimensional model.
Week 5: Predator fish are added to the model. How do the populations interact? Systems of differential equations.
Week 6: You include interaction in the simulations for your project. You also learn how to write about your project in a scientific report. You get an introduction to scientific and mathematical writing. You will learn how to write a preliminary report about mathematical modelling in LaTeX.
Week 7: You explore how you can extend your project model. You write a short report on the first model.
Week 8: You review the first project reports of your peers. You complete the modelling cycle several times. You specify your problem further, improve and extend your mathematical model, refine the calculations, and validate the results until your problem is solved.
Week 9: Helped by the feedback of your peers, you write a final report on your model. After submitting your final report.
Week 10: You review reports of your peers, and finish the course exercises.
This is a Massive Open Online Course (MOOC) that runs on edX.
Calculus (1st-order ordinary differential equations), some programming skills are helpful. This course is aimed at Bachelor students from Mathematics, Engineering and Science disciplines.