• To follow the process of the mathematical modelling cycle: formulate a real-life problem, construct an appropriate mathematical model, calculate solutions and validate the results.
• More about (systems of) ordinary differential equations.
• Solve the ordinary differential equations and implement Euler's method in a (Python) program.
• Write a scientific report (with LaTeX).

In the Verified Track, you will additionally:

• Consolidate your new skills by completing well-crafted problem sets on several interesting real-life applications.
• Learn the skill of mathematical modelling in the only way possible: by doing your own modelling project.

Module 1:

Introduction to the cycle of mathematical modelling. We will start describing a population of fish by a differential equation.

Verified Track: Two practice problems with other real-life applications to consolidate the theory learned. You start your personal modelling project. You can choose to work in a team of two.

Module 2:

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.

Verified Track: A new application to practice the theory. For your project you specify a real-life problem. You implement a 1-dimensional model.

Module 3:

Predator fish are added to the model. How do the populations interact? Systems of differential equations. 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.

Verified Track: One more practice problem to consolidate the theory learned about systems. You do more simulations with your own mathematical model and complete the modelling cycle several times. You apply your writing skills by writing a scientific report about your modelling project. You submit both a preliminary version of the report and the final version. Both are peer reviewed.

"Why do I need mathematics is no longer a question for me. So many phenomena and problems can be modelled using mathematics. I really enjoyed making a model to describe how the virus we studied spread. Every engineering or science student should take this course!"

"This course is excellent! I am an engineer, but have been working in another field for almost 2 decades, totally away from calculus, and this is exactly what I was looking for in order to brush up. I loved the videos and the questions as well. They are crafted in a very clever way to sediment concepts just learned."