Linear Algebra and NxN Systems
Learn how to use algebra and MATLAB to solve large systems of differential equations.
Course Information
Certificate Track
Learn for Free
About this Course
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,
- 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:
- 18.03.1x: Introduction to Differential Equations
- 18.03.2x: Differential Equations: 2x2 Systems
- 18.03.3x: Linear Algebra and NxN Systems
- 18.03.Fx: Differential Equations: Fourier Series and Heat Equation
- 18.03.Lx: Systems Functions and the Laplace Transform
*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
Meet your instructors
David Jerison
Professor of Mathematics
David Jerison received his Ph.D. from Princeton University in 1980, and joined the mathematics faculty at MIT in 1981. In 1985, he received an A.P. Sloan Foundation Fellowship and a Presidential Young Investigator Award. In 1999 he was elected to the American Academy of Arts and Sciences. In 2004, he was selected for a Margaret MacVicar Faculty Fellowship in recognition of his teaching. In 2012, the American Mathematical Society awarded him and his collaborator Jack Lee the Bergman Prize in Complex Analysis.
Professor Jerison's research focuses on PDEs and Fourier Analysis. He has taught single variable calculus, multivariable calculus, and differential equations at MIT several times each.
