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Massachusetts Institute of Technology

Differential Equations: 2x2 Systems

Massachusetts Institute of Technology via edX

This course may be unavailable.


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.

The five modules in this seriesare being offered as an XSeries on edX. Please visit the Differential EquationsXSeries Program Page to learn more and to enroll in the modules.

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


Please note: edX Inc. has recently entered into an agreement to transfer the edX platform to 2U, Inc., which will continue to run the platform thereafter. The sale will not affect your course enrollment, course fees or change your course experience for this offering. It is possible that the closing of the sale and the transfer of the edX platform may be effectuated sometime in the Fall while this course is running. Please be aware that there could be changes to the edX platform Privacy Policy or Terms of Service after the closing of the sale. However, 2U has committed to preserving robust privacy of individual data for all learners who use the platform. For more information see the edX Help Center.


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

Taught by

David Jerison


5.0 rating, based on 5 Class Central reviews

Start your review of Differential Equations: 2x2 Systems

  • Anonymous
    Excellent course. Touched a little bit of linear algebra and convey the beauty between these subject. The notes are very easy to comprehend and explain every topic so well. The videos are also excellent. Hope to see more courses from the math department of MIT.
  • XYG
    The topic would have been much harder for me had I not been studying with the course. The lectures in combination of the mathlets are absolutely helpful.
  • Profile image for Jinqiang Zhang
    Jinqiang Zhang
    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
    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.
  • Interesting course. Lectures, homeworks and review exercises of any part are really well setup. One of the best MOOC on topic of differential equations.

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