Differential Equations: Linear Algebra and NxN Systems of Differential Equations

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)

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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 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