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Differential Equations: 2x2 Systems

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Overview

Differential equations are the language of the models we use to describe the world around us. Most phenomena require not a single differential equation, but a system of coupled differential equations. In this course, we will develop the mathematical toolset needed to understand 2x2 systems of first order linear and nonlinear differential equations. We will use 2x2 systems and matrices to model:

• predator-prey populations in an ecosystem,
• competition for tourism between two states,
• the temperature profile of a soft boiling egg,
• automobile suspensions for a smooth ride,
• pendulums, and
• RLC circuits that tune to specific frequencies.

* Wolf photo by Arne von Brill on Flickr (CC BY 2.0)
* Rabbit photo by Marit & Toomas Hinnosaar on Flickr (CC BY 2.0)

Syllabus

Unit 1: Linear 2x2 systems
1. Introduction to systems of differential equations
2. Solving 2x2 homogeneous linear systems of differential equations
3. Complex eigenvalues, phase portraits, and energy
4. The trace-determinant plane and stability

Unit 2: Nonlinear 2x2 systems
5. Linear approximation of autonomous systems
6. Stability of autonomous systems
7. Nonlinear pendulum

David Jerison

Reviews for edX's Differential Equations: 2x2 Systems 5.0 Based on 3 reviews

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• 4 star 0%
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Did you take this course? Share your experience with other students.

• 1
Jinqiang Z
5.0 8 months ago
by completed this course.
The course is a high standard and complete course. The applications used for showing different scenarios are rich: From Romeo & Juliet to typical Predator & Pray and more.

I feel I had a very good understanding in 2X2 system now.
Dna47a D
5.0 3 months ago
completed this course.
An excellent course. The video lectures, the exercise questions, the mathlets and the recitation problems together are great. The staff have done an outstanding job to bring this course on the edx platform. Thank you Jen French.
Gaetano P
5.0 9 months ago
by completed this course, spending 4 hours a week on it and found the course difficulty to be medium.
Interesting course. Lectures, homeworks and review exercises of any part are really well setup. One of the best MOOC on topic of differential equations.