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Online Course

Differential Equations: Linear Algebra and NxN Systems of Differential Equations

Massachusetts Institute of Technology via edX

Overview

Differential equations are the mathematical language we use to describe the world around us. Most phenomena can be modeled not by single differential equations, but by systems of interacting differential equations. These systems may consist of many equations. In this course, we will learn how to use linear algebra to solve systems of more than 2 differential equations. We will also learn to use MATLAB to assist us.

We will use systems of equations and matrices to explore:

  • The original page ranking systems used by Google,
  • Balancing chemical reaction equations,
  • Tuned mass dampers and other coupled oscillators,
  • Threeor more species competing for resources in an ecosystem,
  • The trajectory of a rider on a zipline.

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.

*Zipline photo by teanitiki on Flickr (CC BY-SA 2.0)

Syllabus

Unit 1: Linear Algebra

  1. Solving linear systems: elimination and RREF
  2. Nullspace, vector space
  3. Column space, determinants, and inverses
  4. eigenvalues, eigenvectors, and diagonalization

Unit 2: Systems of Differential Equations

  1. Solving homogeneous NxN systems of differential equations
  2. Matrix exponential and diagonalization
  3. Decoupling and solving inhomogeneous systems of equations
  4. Solving nonlinear systems with MATLAB

Taught by

David Jerison and Bjorn Poonen

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Reviews

5.0 rating, based on 2 reviews

Start your review of Differential Equations: Linear Algebra and NxN Systems of Differential Equations

  • Anonymous

    Anonymous completed this course.

    Excellent! Part 3 of the differential equations series and still keep the same superb quality. The first two units is linear algebra and it helped to refresh my knowledge about it. It has done its best to teach the necessary linear algebra to pass this course. The final unit is also challenging but fun. The course team is very helpful throughout this course. Hope to see more courses from the math department from MITX!
  • Dna47a

    Dna47a completed this course, spending 8 hours a week on it and found the course difficulty to be medium.

    Another excellent course from MIT. The lecture videos are excellent and so are the exercises. This course also has MATLAB based exercises which is wonderful. The problem sets are excellent and so are the staff and the community teaching assistants who are always there to help any time.

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