Modelling with Differential Equations

Overview

How do populations grow? How do viruses spread? What is the trajectory of a glider? Introduce yourself to the modelling cycle which includes: analyzing a problem, formulating it as a mathematical model, calculating solutions and validating your results.

What you'll learn

To follow the process of the mathematical modelling cycle: formulate a real-life problem, construct an appropriate mathematical model, calculate solutions and…
Analyze and use (systems of) ordinary differential equations.
Solve the ordinary differential equations and implement Euler's method in a (Python) program.
Complete well-crafted problem sets on several interesting real-life applications to consolidate your new skills

Syllabus 9

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.

Skills you'll practise

Mathematical Modeling Python (Programming Language)LaTeX Differential Equations Mathematics

Advantages and disadvantages

Advantages

University courses you can audit for free, with lectures, readings and practice quizzes.
A verified certificate from the university if you pay for it.
From Delft University of Technology, a well-regarded name.
Self-paced: start any time.
A clear syllabus (9 parts) you can see before you start.

Disadvantages

Graded assignments and the certificate need the paid track.
Audit access can expire a few weeks after the course ends.
Learning is free, but the certificate costs money.
Some parts (graded work, certificate) are paid.

Some points apply to every course of this kind; see how we rank.

Free to audit

Free: Choose "Audit this course" when you enrol: lectures, readings and practice are free.
Paid: Graded assignments and the verified certificate (Certificate $150). Audit access may end after the course closes.

Before you start

Calculus (1st-order ordinary differential equations), some programming skills are helpful. This course is aimed at Bachelor students from Mathematics, Engineering and Science disciplines.

Taught by

Marleen KeijzerDr.
Dennis den Ouden-van der HorstLecturer, Mathematics
Iris SmitDr.
Kees VuikProfessor, Numerical Analysis

Delft University of Technology is in Tier 2: excellent universities and the companies that build the technology of our institution ranking (86/100).

Get the course link

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Go to the course

Opens edx.org

PlatformedX

UniversityDelft University of Technology

PriceFree to audit Certificate $150

CertificatePaid certificate

LanguageEnglish

PaceSelf-paced

LevelIntermediate

Learners26,818

Found in

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