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Modelling with Differential Equations
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!
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!
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.
Register for this course and see more details by visiting:
OpenCourser.com/course/zdk0wv/modelling
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
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
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.
Good to know
Good to know
Know what's good ,
what to watch for , 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
Save Modelling with Differential Equations to your list so you can find it easily later:
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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.
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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 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.
Data Scientist
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.
Management Consultant
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.
Financial Analyst
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.
Actuary
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.
Biostatistician
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.
Epidemiologist
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.
Quantitative Analyst
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.
Software Engineer
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.
Systems 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.
Mechanical 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.
Electrical 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.
Civil 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.
Chemical 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.
Environmental 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.
For more career information including salaries, visit:
OpenCourser.com/course/zdk0wv/modelling
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.
Save
This textbook is written specifically for a course on modeling with differential equations.
Save
Covers mathematical modeling for biological processes. It's a good resource for differential equations and their application to biology.
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
This textbook can be used as a more detailed reference for differential equations.
Provides a foundation for understanding the mathematical models used in biology.
Covers a wide range of mathematical methods used in physics and engineering, including differential equations.
Save
Provides a general overview of mathematical modeling, including differential equations.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/zdk0wv/modelling
Share
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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
Session
January 16, 2024
- December 17, 2024
Language
English
Transcript
English
Good to know
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
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