Course Syllabus
Mathematical Modelling basics
Index
1. Introduction
1.1. Audit track / Verified track
1.2. Learning objectives
1.3. Course activities and resources
1.4. What we expect from you
1.5. What you can expect from us
2. Course structure, release dates & deadlines
3. Assessment
4. Resources & Tools
5. Certificate
1. Introduction
How do populations grow? How do viruses spread? What is the trajectory of a glider? Many real-world problems can be described and solved by mathematical models.
In this self-paced course, you will learn to use the modelling cycle: analyze problems, formulate them as mathematical models, solve the equations in the model, and validate the results. If the results are not solving the problem, one or more of the elements is refined or improved, and the cycle is followed again.
Restriction: There are many kinds of mathematical models: statistical models, discrete models, integer models, etc. Mathematical models are just as diverse as the field of mathematics is. In this introductory course, the proces of mathematical modelling is illustrated only with one type of mathematical model: a model consisting of ordinary differential equations. So in this course, while learning the process of mathematical modelling, you will also learn more about (systems of) ordinary differential equations, and how to simulate their solutions in a Python program with Euler's Method.
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 modelling can solve real-world problems.
Prerequisites: Calculus (1st-order ordinary differential equations); Experience with programming.
1.1. Audit Track / Verified Track
You can choose between two tracks: the Audit Track and the Verified Track. You can upgrade on your edX Dashboard to Verified before or during the course for $139. Do you need financial assistance? EdX offers up to a 90% discount on our verified certificates to learners who cannot afford to pay full price. Check the edX support page for financial assistance.
The free Audit Track includes the videos and texts on the mathematical contents of the course. You learn most of the new skills in mathematics and programming while completing sets of formative exercises. Those ungraded exercises are all included in the Audit Track.
The Verified Track is for you to
- consolidate your newly learned skills by doing many graded summative exercises,
- learn from many more applications of mathematical modelling
The Verified Track offers two elements additionally to the Audit track:
- seven practice problems,
- and when you complete the practice problems with enough points, you will receive a Course Certificate.
The practice problems are six problem sets about four real-world applications, so you can test and consolidate your new skills.
1.2. Learning objectives
In this course you'll learn how to follow the process of the mathematical modelling cycle. By the end of this course you will be able to:
- Formulate and specify a real-world 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
1.3. Course activities and resources
The Audit Track of the course offers the complete theoretical content of the course in videos, short texts and many formative exercises. One real-world application is used as an example.
Each topic combines Videos and guided Exercises, following the mathematical modelling cycle: Problem - Mathematical model - Calculation - Validation
The Verified Track has the additional practice problems.
The Verified Track is a 6 week course with an estimated workload of 4 to 8 hours per week. The course is organized in a consistent way so you know what to expect each week.
1.4. What we expect from you
As an online
This course is meant to be a place where you learn with and from others. In this sense, we'd like you to experience collaboration and
When communicating with your fellow learners and course team make sure you take into account the Discussion and Collaboration Guidelines.
1.5. What you can expect from us/the course team
The course team will release the modules, send announcements, monitor and answer questions on a regular basis. We'll try to have a daily presence, but as you might understand we cannot promise to quickly attend everyone, due to the thousands of learners participating in this course. But we'll do our best ;-)
2. Course structure, release dates & deadlines
This course is self-paced. That means that the whole content of the course releases when the course starts. Despite that, we recommend you to organize your learning path in the following diagram. You can see the main topics of each module organized by week. The grey boxes represent the Modelling theory (with exercises to practice) and the orange boxes indicate skills. In the Verified Track, the grey boxes indicate the practice problems.
Grapics: Y. Ruitenburg
A summary of each week is given below:
Module 1
Introduction to the cycle of mathematical modelling. We start describing a population of fish by a differential equation.
Verified Track: Two practice problems with other real-world applications to consolidate the theory learned.
Module 2
Complete more modelling cycles by improving the model and evaluating the consequences. Euler's Method is introduced for solving ordinary differential equations. You start simulating solutions in Python.
Verified Track: A new application to practice the theory.
Module 3
Predator fish are added to the model. How do the populations interact? Systems of differential equations.
Verified Track: One more practice problem to consolidate and test the theory learned about systems of differential equations.
For verified learners: there is only one deadline: the end of the course (November 16, 2023)
Course end date: November 16, 2023
Upgrade deadline: you can upgrade to verified until November 06, 2023
Certificate issue: when enough grade to pass the course is reached.
3. Assessment (Verified Track)
To complete the Verified Track you have to score at least 60% of the total mark of 100%. You will be able to score with the Practice problems in each of the modules.
4. Resources & Tools
All educational resources will be available in the course. They consist of short videos and lecture notes with additional details and examples to support you in the completion of the exercises and the project. You'll also find a Glossary with the most important concepts in the top menu.
Python
To simulate the results with a computer program, we recommend using Python. Python is a widely used high-level general programming language. You can download Python for free. Download and installation instructions are given in the Getting Started page. In the course you can download the necessary Python programs that are used for the simulations.
5. Certificate (Verified Track)
If you have succesfully, completed the Verified Track, you get an ID verified Certificate of Achievement. This certificate will indicate you have successfully completed the course, but will not include a specific grade. Certificates will be issued by edX under the name DelftX, designating the institution from which the course originated. Please note that this course doesn't lead to any type of formal credit at Delft University of Technology.
Generating an ID verified certificate
Verified certificates will be issued when completed enough of the course, and with a high enough grade (60%), to qualify for a certificate. This is automatically done and it can be downloaded from your dashboard or from the progress page.
Remember that in order to qualify for a certificate, you must achieve a total grade of 60% or higher. You can check your grade at any time under the course’s Progress page.
Once produced, a certificate cannot be reissued, hence it is very important that you verify the way in which your name appears. Check that, in your edx.org account, your name is spelled correctly, since it will appear on the final certificate. Please note that no Honor Code certificates will be given out by edX for this course.
6. Open Courseware
Most TU Delft MOOCs are published as Open Courseware a few weeks after the first run. You can find readings and videos on TU Delft's Open Courseware website.
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LICENSE
Unless otherwise specified the Course Materials of this course are Copyright of
