Differential Equations du/dt = Au and Exponential e^At of a matrix
In this lesson, we learn how to solve first order differential equations with matrices and how to work with an exponential with matrices. By finding the eigenvalues and eigenvectors of the matrix, we can get insight into the behavior of the solution, such as stability and steady states. The real part of the eigenvalues is important for determining stability and the trace of a 2 by 2 stable matrix will be negative.
Differential Equations du/dt = Au and Exponential e^At of a matrix -- Lecture 23. Learn how to solve first order differential equations with matrices and how to work with an exponential with matrices.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- Differential Equations Mini-Lecture - This is a mini-lecture demo lesson on Differential Equations.
- How do you solve a system of first order differential equations with matrices?
- How do you compute the exponential of a matrix?
- How do you compute e^At?
-
Staff Review
A very interesting video that brings Linear Algebra and matrices together with first order differential equations. This video explains how to solve these first order linear equations by using the exponential function. A good explanation of some complex ideas.
