Modelling with Differential Equations

Overview

All models are (systems of) ordinary differential equations. In this course you will learn more about those by watching video lectures and reading short texts, and more importantly, by completing well-crafted hands-on exercises in which you can practice modeling yourself!

You will also learn how to implement Euler's method in a (Python) program.

In the verified track of this course you will additionally consolidate the new skills with graded problem sets about four other real-life applications.

This course is aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it is for anyone who would want to use differential equations for solving real-world problems, including business owners, researchers and students.

Syllabus

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 (filtering with sunscreen, mixing fluids) with other real-life applications to consolidate the theory learned.

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: the spread of a flu epidemic.

Module 3:

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

Verified Track : One more practice problem (electrical clock) to consolidate the theory learned about systems.