See all results for
    1. In India, MOOCs Are Now Part of the Education System
    2. Coursera’s Monetization Journey: From 0 to $100+ Million in Revenue
    3. Udacity Doubles Prices, Relaunches 1-on-1 Mentorships & Career Coaching
    See more
    1. Sign in
    2. Register

    Get started with custom lists to organize and share courses.

    Sign up

    Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

    Differential Equations: 2x2 Systems

    Massachusetts Institute of Technology via edX

    3 Reviews 1292 students interested
    Found in Mathematics
    Go to class

    Taken this course? Share your experience with other students. Write review

    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.
    The five modules in this series are being offered as an XSeries on edX. Please visit the Differential Equations XSeries 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)

    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

    Taught by

    David Jerison

    Help Center

    Most commonly asked questions about EdX EdX

    Browse More EdX Articles

    Related Courses

    Browse More Mathematics courses

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

    • 5 stars 100%
    • 4 star 0%
    • 3 star 0%
    • 2 star 0%
    • 1 star 0%

    Did you take this course? Share your experience with other students.

    Write a review
    • 1
    JZ
    Jinqiang Z
    5.0 2 years ago
    by Jinqiang 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.
    Was this review helpful to you? Yes
    DD
    Dna47a D
    5.0 a year ago
    Dna47a 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.
    Was this review helpful to you? Yes
    GP
    Gaetano P
    5.0 2 years ago
    by Gaetano 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.
    Was this review helpful to you? Yes
    • 1

    Class Central

    Get personalized course recommendations, track subjects and courses with reminders, and more.

    Sign up for free

    Never stop learning Never Stop Learning!

    Get personalized course recommendations, track subjects and courses with reminders, and more.

    Sign up for free