We may earn an affiliate commission when you visit our partners.

Course image

Course image

Modelling with Differential Equations

Course image

Marleen Keijzer, Dennis den Ouden-van der Horst, Iris Smit, and Kees Vuik

Marleen Keijzer, Dennis den Ouden-van der Horst, Iris Smit, and Kees Vuik

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.

Read more

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.

What's inside

Learning objectives

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.
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
In the verified track, you will additionally:

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.
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
In the verified track, you will additionally:

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.

Read more

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Explores population dynamics and systems of ordinary differential equations, which are foundational concepts in many STEM fields

Involves hands-on exercises and problem sets to reinforce understanding of concepts

Teaches students how to implement Euler's method in Python, which is a valuable skill for solving differential equations

Suitable for a wide audience, including students from math, engineering, science, and even non- STEM fields with an interest in modeling real-world problems

May require some prior knowledge of differential equations and programming, as it builds on these concepts

Save this course

Create your own learning path. Save this course to your list so you can find it easily later.

Save

Reviews summary

Practical modeling with differential equations

According to students, this course offers a highly practical approach to mathematical modeling using differential equations, distinguished by its focus on real-world applications. Learners frequently praise the clear explanations and well-crafted hands-on exercises that consolidate understanding. The inclusion of Python simulations for Euler's method is highlighted as a valuable practical skill, particularly for those looking to apply concepts computationally. While providing a solid foundational understanding suitable for beginners, some advanced learners suggest it might not delve deeply enough into more complex topics. Overall, students view it as an excellent introduction to applying ODEs to real-life problems.

Graded problem sets in the verified track offer valuable additional practice.

"The extra problems in the Verified Track were invaluable for solidifying my skills with different applications."

"I highly recommend the Verified Track for the additional practice problems; they truly helped consolidate the new concepts."

"The graded problem sets challenged me to apply what I learned to new scenarios, which was very beneficial for deeper understanding."

Teaches Euler's method with practical, hands-on Python programming.

"Implementing Euler's method in Python was a huge plus for me; it brought the theoretical solutions to life in a practical way."

"The Python simulations are well-integrated and provide valuable experience for anyone looking to apply these methods computationally."

"Being able to code the solutions made the course much more engaging and showed me the immediate utility of what I was learning."

Complex topics are broken down and explained with exceptional clarity.

"The video lectures were very clear and easy to follow, even for someone who needed a refresher on some of the underlying math."

"The hands-on exercises are perfectly designed to reinforce the theory, making abstract concepts concrete and understandable."

"I found the explanations to be thorough yet concise, never overwhelming but always providing enough detail for me to grasp the concepts."

Strong emphasis on applying ODEs to practical, real-life problems.

"I particularly enjoyed how the course focused on applying differential equations to real-life problems like fish populations and flu epidemics. It made the concepts tangible."

"The course structure revolves around the mathematical modeling cycle, which is excellent for understanding how to tackle practical challenges."

"Finally, a course that shows me how to use these equations beyond abstract problems. The practical examples were incredibly helpful."

Provides a strong foundation but may lack depth for advanced learners.

"This course is an excellent starting point for learning about differential equations, very accessible for beginners."

"While the basics are covered well, I was hoping for more advanced techniques or complex problem-solving strategies in the later modules."

"If you're already familiar with the fundamentals, this might feel a bit too introductory and not provide enough new challenges."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Modelling with Differential Equations with these activities:

Review Calculus 1

Show steps

Calculus 1 concepts are widely used in this course, reviewing the basics can refresh your memory and reduce friction.

Browse courses on Differential Equations

Show steps

Review the concept of derivatives and integrals.
Practice solving differential equations using different methods.
Go through practice problems and review examples.

Euler's Method Practice

Show steps

Practicing Euler's method will strengthen your understanding and reinforce the concept.

Browse courses on Euler's Method

Show steps

Start with simple differential equations and gradually increase the complexity.
Solve the differential equations using Euler's method and compare the results with analytical solutions.
Analyze the errors and try to improve the accuracy of the numerical solutions.

Collaborative Problem-Solving Group

Show steps

Working with peers can enhance your understanding and develop your problem-solving skills.

Browse courses on Problem-Solving

Show steps

Join or form a study group with other students in the course.
Regularly meet to discuss course topics, solve problems together, and share ideas.
Take turns presenting solutions and explaining concepts to the group.

Three other activities

Expand to see all activities and additional details

Show all six activities

Python Implementation of Euler's Method

Show steps

Implementing Euler's method in Python can enhance your understanding and provide hands-on experience.

Browse courses on Python

Show steps

Follow online tutorials or documentation to learn the basics of Python programming.
Find resources or libraries that provide implementations of Euler's method.
Write your own Python code to implement Euler's method and solve differential equations.
Test your code with different initial conditions and differential equations.

Differential Equations Poster Presentation

Show steps

Creating a poster presentation will help you synthesize your knowledge and communicate your understanding.

Browse courses on Differential Equations

Show steps

Choose a topic related to differential equations that you find interesting.
Research the topic and gather information from credible sources.
Design a poster that visually presents your findings, including equations, diagrams, and explanations.
Practice presenting your poster to an audience.

Workshop on Systems of Differential Equations

Show steps

Attending a workshop can provide advanced insights into a specific aspect of differential equations.

Browse courses on Systems of Differential Equations

Show steps

Identify workshops or conferences that focus on systems of differential equations.
Register for the workshop and actively participate in the sessions.
Take notes, ask questions, and engage with experts in the field.

Career center

Learners who complete Modelling with Differential Equations will develop knowledge and skills that may be useful to these careers:

Operations Research Analyst

Operations Research Analysts apply analytical methods to help organizations make better decisions. They use mathematical models to simulate and analyze complex systems, and then recommend solutions to improve efficiency and effectiveness. The course 'Modelling with Differential Equations' can help Operations Research Analysts build a foundation in the mathematical techniques used for modelling and analyzing systems.

See salaries and explore the career path for Operations Research Analyst

Data Scientist

Data Scientists use mathematical and statistical methods to extract knowledge and insights from data. They use this knowledge to help organizations make better decisions. The course 'Modelling with Differential Equations' can help Data Scientists build a foundation in the mathematical techniques used for modelling and analyzing data.

See salaries and explore the career path for Data Scientist

Management Consultant

Management Consultants help organizations improve their performance. They use analytical methods to identify and solve problems, and then recommend solutions to improve efficiency and effectiveness. The course 'Modelling with Differential Equations' can help Management Consultants build a foundation in the mathematical techniques used for modelling and analyzing systems.

See salaries and explore the career path for Management Consultant

Financial Analyst

Financial Analysts use mathematical and statistical methods to analyze financial data and make investment recommendations. They use this knowledge to help individuals and organizations make better financial decisions. The course 'Modelling with Differential Equations' can help Financial Analysts build a foundation in the mathematical techniques used for modelling and analyzing financial data.

See salaries and explore the career path for Financial Analyst

Actuary

Actuaries use mathematical and statistical methods to assess risk and uncertainty. They use this knowledge to help insurance companies and other organizations make informed decisions about risk management. The course 'Modelling with Differential Equations' can help Actuaries build a foundation in the mathematical techniques used for modelling and analyzing risk.

See salaries and explore the career path for Actuary

Biostatistician

Biostatisticians use mathematical and statistical methods to analyze biological and health data. They use this knowledge to help researchers understand the causes and treatments of diseases. The course 'Modelling with Differential Equations' can help Biostatisticians build a foundation in the mathematical techniques used for modelling and analyzing biological data.

See salaries and explore the career path for Biostatistician

Epidemiologist

Epidemiologists use mathematical and statistical methods to study the distribution and determinants of health-related states and events in populations. They use this knowledge to help prevent and control diseases. The course 'Modelling with Differential Equations' can help Epidemiologists build a foundation in the mathematical techniques used for modelling and analyzing disease outbreaks.

See salaries and explore the career path for Epidemiologist

Quantitative Analyst

Quantitative Analysts use mathematical and statistical methods to analyze financial data and make investment recommendations. They use this knowledge to help hedge funds and other investment firms make better investment decisions. The course 'Modelling with Differential Equations' can help Quantitative Analysts build a foundation in the mathematical techniques used for modelling and analyzing financial data.

See salaries and explore the career path for Quantitative Analyst

Software Engineer

Software Engineers design, develop, and maintain software applications. They use mathematical and statistical methods to ensure that software applications are efficient and reliable. The course 'Modelling with Differential Equations' can help Software Engineers build a foundation in the mathematical techniques used for modelling and analyzing software applications.

See salaries and explore the career path for Software Engineer

Systems Engineer

Systems Engineers design, develop, and maintain complex systems. They use mathematical and statistical methods to ensure that systems are efficient and reliable. The course 'Modelling with Differential Equations' can help Systems Engineers build a foundation in the mathematical techniques used for modelling and analyzing systems.

See salaries and explore the career path for Systems Engineer

Mechanical Engineer

Mechanical Engineers design, develop, and maintain mechanical systems. They use mathematical and statistical methods to ensure that mechanical systems are efficient and reliable. The course 'Modelling with Differential Equations' can help Mechanical Engineers build a foundation in the mathematical techniques used for modelling and analyzing mechanical systems.

See salaries and explore the career path for Mechanical Engineer

Electrical Engineer

Electrical Engineers design, develop, and maintain electrical systems. They use mathematical and statistical methods to ensure that electrical systems are efficient and reliable. The course 'Modelling with Differential Equations' can help Electrical Engineers build a foundation in the mathematical techniques used for modelling and analyzing electrical systems.

See salaries and explore the career path for Electrical Engineer

Civil Engineer

Civil Engineers design, develop, and maintain civil infrastructure. They use mathematical and statistical methods to ensure that civil infrastructure is safe and reliable. The course 'Modelling with Differential Equations' can help Civil Engineers build a foundation in the mathematical techniques used for modelling and analyzing civil infrastructure.

See salaries and explore the career path for Civil Engineer

Chemical Engineer

Chemical Engineers design, develop, and maintain chemical processes. They use mathematical and statistical methods to ensure that chemical processes are efficient and reliable. The course 'Modelling with Differential Equations' can help Chemical Engineers build a foundation in the mathematical techniques used for modelling and analyzing chemical processes.

See salaries and explore the career path for Chemical Engineer

Environmental Engineer

Environmental Engineers design, develop, and maintain environmental systems. They use mathematical and statistical methods to ensure that environmental systems are efficient and reliable. The course 'Modelling with Differential Equations' can help Environmental Engineers build a foundation in the mathematical techniques used for modelling and analyzing environmental systems.

See salaries and explore the career path for Environmental Engineer

Reading list

We've selected seven books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Modelling with Differential Equations.

Cover image

Cover image

Save

This textbook is written specifically for a course on modeling with differential equations.

Cover image

Cover image

Aquatic Chemistry

Save

Covers mathematical modeling for biological processes. It's a good resource for differential equations and their application to biology.

Aquatic Chemistry: Chemical Equilibria and Rates in...

Aquatic Chemistry: Chemical Equilibria and Rates in...

Cover image

Cover image

Modeling the Dynamics of Life: Calculus and...

Save

Provides an introduction to the mathematical modeling of biological systems using differential equations. It covers a wide range of topics, including population growth, predator-prey interactions, and disease transmission. The text is well-written and accessible to students in a variety of disciplines

Modeling the Dynamics of Life: Calculus and...

Modeling the Dynamics of Life: Calculus and...

Modeling the Dynamics of Life: Calculus and...

Modeling the Dynamics of Life: Calculus and...

Cover image

Cover image

Differential Equations and Their Applications

Save

This textbook can be used as a more detailed reference for differential equations.

Differential Equations and Their Applications: An...

Differential Equations and Their Applications: An...

Differential Equations and Their Applications: An...

Cover image

Cover image

A Primer in Mathematical Models in Biology

Save

Provides a foundation for understanding the mathematical models used in biology.

A Primer on Mathematical Models in Biology (Other...

Cover image

Cover image

Mathematical Methods for Physicists

Save

Covers a wide range of mathematical methods used in physics and engineering, including differential equations.

Mathematical Methods for Physicists

Mathematical Methods for Physicists

Cover image

Cover image

Engineering Design

Save

Provides a general overview of mathematical modeling, including differential equations.

Engineering Design: Representation and Reasoning

Share

Help others find this course page by sharing it with your friends and followers:

Copy Link

Similar courses

Here are nine courses similar to Modelling with Differential Equations.

Personal Desktop Notifier in Python: Covid-19 notifications

Personal Desktop Notifier in Python: Covid-19...

Fake Instagram Profile Detector

Fake Instagram Profile Detector

Introduction to Big Data with Spark and Hadoop

Introduction to Big Data with Spark and Hadoop

Where, Why, and How of List Comprehension in Python

Where, Why, and How of List Comprehension in Python

Wrangling Data for Data Analysts with Python

Wrangling Data for Data Analysts with Python

Introduction to Search Techniques in Python: Binary Search

Introduction to Search Techniques in Python: Binary Search

Mastering Data Analysis with Pandas

Mastering Data Analysis with Pandas

Hierarchical relational data analysis using python

Hierarchical relational data analysis using python

Scripting with Python and SQL for Data Engineering

Scripting with Python and SQL for Data Engineering

edX Buyer Protection & Guarantee

Verified partner policies & purchase protections

World-Class University Partner

Free Trial & Audit

Free Audit Track Available

Free audit track available for most courses, giving open access to video lectures, course readings, and assignments at no charge.

Return & Refund Policy

14-Day Full Refund Window

14-day full refund available up to 14 days after course start or 14 days after payment (whichever comes second, up to 6 months max), provided verified certificate has not yet been earned.

Buyer Protections

Verified Academic & Industry Partner

University-backed credentials authored by elite institutions like Harvard, MIT, and Oxford, with tamper-proof certificate verification.

Key Purchase Protections

Free audit track for open learning access

14-day money-back guarantee on verified certificates

Prestigious university credentials (Harvard, MIT)

Automatic unenrollment refund process via dashboard

OpenCourser Verified Partner Policy details last reviewed: 2026-10-22

Course image

Effort

4 to 5 hours per week for 6 weeks

Level

Intermediate

Via

edX

Institution

Delft University of Technology

Instructors

Marleen Keijzer

Dennis den Ouden-van der Horst

Iris Smit

Kees Vuik

Language

English

Transcript

English

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Explores population dynamics and systems of ordinary differential equations, which are foundational concepts in many STEM fields

Involves hands-on exercises and problem sets to reinforce understanding of concepts

Teaches students how to implement Euler's method in Python, which is a valuable skill for solving differential equations

Suitable for a wide audience, including students from math, engineering, science, and even non- STEM fields with an interest in modeling real-world problems

May require some prior knowledge of differential equations and programming, as it builds on these concepts

Share this

Share to help others discover this course.

Link

Begin learning today

Enroll now to gain full access to Modelling with Differential Equations.

Enroll now Enroll in this course

Save for later

Add this course to your list. Find it anytime.

Save

Our mission

OpenCourser helps millions of learners each year. People visit us to learn workspace skills, ace their exams, and nurture their curiosity.

Our extensive catalog contains over 50,000 courses and twice as many books. Browse by search, by topic, or even by career interests. We'll match you to the right resources quickly.

Find this site helpful? Tell a friend about us.

Affiliate disclosure

We're supported by our community of learners. When you purchase or subscribe to courses and programs or purchase books, we may earn a commission from our partners.

Your purchases help us maintain our catalog and keep our servers humming without ads.

Thank you for supporting OpenCourser.

© 2016 - 2025 OpenCourser