About this course
- 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)
What you'll learn
- How to model real world problems by 2x2 systems of differential equations
- How to use matrix methods to solve homogeneous systems of 2 first order linear differential equations
- How to use graphical methods to understand the qualitative behavior of linear and nonlinear systems, and how to apply linear approximation to nonlinear (autonomous) 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
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Frequently asked questions
No. The only prerequisite is 18.031x. 18.03Lx treats the special topic of the Laplace transform, and is aimed at more advanced and experienced students.
Who can take this course?
Unfortunately, learners from one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. EdX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.