Continuation: Repeated Real Eigenvalues, Complex Eigenvalues
In this lecture, we learn about solving systems using matrix algebra. We are reminded to find the characteristic equation, calculate its eigenvalues and eigenvectors, and use them to form a general solution. The lecture then delves into the more complicated cases of repeated real eigenvalues and complex eigenvalues. The lecturer goes through an example of a circular fish tank to demonstrate how to set up the differential equations and find the characteristic equation. The characteristic equation in this case turns out to have a repeated real eigenvalue of -3 and a solution to this problem requires a different approach.
Continuation: Repeated Real Eigenvalues, Complex Eigenvalues -- Lecture 26. Learn more about solving systems using Matrix Algebra.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- Lecture Notes - Lecture Notes
- Muddy Card Responses - Muddy Card Responses are explanations of topics that were confusing to students
- Supplementary Notes - Chapter 20 Supplementary Notes written by Prof. Miller
- Problem Set 6 - Problem Set 6
- Problem Set 6 Solutions - Problem Set 6 Solutions
- What happens if you have repeated eigenvalues?
- What happens if you have complex eigenvalues?
- What is a characteristic polynomial?
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Staff Review
This lecture picks up right where the last one left off. More example problems of systems of differential equations are solved using Matrix Algebra techniques by finding eigenvalues and eigenvectors. These problem solutions do not go as smoothly as most; counterexamples to the ordinary are discussed, such as with repeated eigenvalues and complex eigenvalues.
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