Linear Algebra and NxN Systems

Learn how to use algebra and MATLAB to solve large systems of differential equations.

Linear Algebra and NxN Systems

Learn how to use algebra and MATLAB to solve large 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.

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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,
  • Three or more species competing for resources in an ecosystem,
  • The trajectory of a rider on a zipline.

This is part of a 5-part series in Differential Equations:

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

What you'll learn

After this course, you will be able to

  • Model and solve different real world phenomena with systems of differential equations.
  • Find the dimension and a basis for a (finite dimensional) vector space.
  • Formulate and solve eigenvalue and eigenvector problems.
  • Use MATLAB to explore solutions to large systems of equations.

Prerequisites

  • 18.03.1x Introduction to Differential Equations
  • 18.03.2x Differential Equations: 2x2 Systems

Meet your instructors

  • Featured image for David Jerison
    Professor of Mathematics

Who can take this course?

Because of U.S. Office of Foreign Assets Control (OFAC) restrictions and other U.S. federal regulations, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba, Syria, North Korea and the Crimea, Donetsk People's Republic and Luhansk People's Republic regions of Ukraine.