# Differential Equations: Linear Algebra and NxN Systems of Differential Equations

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

## There is one session available:

After a course session ends, it will be archived.
Estimated 9 weeks
5–8 hours per week
Instructor-paced
Instructor-led on a course schedule
Free

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)

### At a glance

• Institution: MITx
• Subject: Math
• Level: Intermediate
• Prerequisites:

18.031x Introduction to Differential Equations (Scalar equations), 18.032x Differential Equations: 2x2 Systems (2x2 first order differential equations)

# What you'll learn

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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.

# Syllabus

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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

# Frequently Asked Questions

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What are the prerequisites for this course?

We assume familiarity with both 18.031x Introduction to Differential Equations and 18.032x Differential Equations: 2x2 systems. Knowledge from 18.03Lx is not required to succeed in this course.

# Who can take this course?

Unfortunately, learners from one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.

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