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 form a team with another student and work in a project to solve a real-life problem.
You will learn to analyze your chosen 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 program.
If needed, you can refine or improve your model, based on your first results. Finally, you will learn how to report your findings in a scientific way.
This course is mainly aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it will suit anyone who would like to learn how mathematical modeling can solve real-world problems.
What you'll learn:
- To follow the process of the mathematical modeling 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) program.
- Validate the results of the calculation.
- Write a scientific report in LaTeX about the mathematical model you construct.
Module 1 (week 1):
- Project: form a project team with another student.
- Mathematical modeling cycle: Model a growing population of fish.
- Introduction to the cycle of mathematical modeling. We will start describing a population of fish by a differential equation.
Module 2 (weeks 2 and 3):
- Project: you will choose an assignment and collect information about a real-life problem.
- Mathematical modeling cycle: Complete more modeling cycles by improving on the model and evaluating the consequences. Euler's method is introduced for solving ordinary differential equations.
Module 3 (week 4):
- Project: Specify your real-life problem and choose values.
- Mathematical modeling cycle: Predator fish are added to the model. How do the populations interact?
Module 4 (weeks 5 and 6):
- Project: You implement Euler's method for your problem and explore how you can extend your model. You write a short report on the first model.
- Mathematical modeling cycle: You learn how to write about your project in a scientific report. You will be introduced to scientific and mathematical writing. You will learn how to write a preliminary report about mathematical modeling in LaTeX.
Module 5 (weeks 7, 8 and 9):
- Project: You review the preliminary reports of your peers.
- Helped by the feedback of your peers, you complete the modeling 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.
- You write a final report on your model, implementing the feedback of your peers.
After submitting your final report, you'll review reports of your peers.
This is a Massive Open Online Course (MOOC) that runs on edX.
- Calculus (1st-order ordinary differential equations)
- Experience with programming