Systems of linear equations are the bread and butter of dynamical systems modeling. For one thing, we will go on to study systems of nonlinear equations, and to do stability analysis, we will have to analyze the linearization of the original system. But for another thing, linear equations themselves describe lots of phenomena... my favorite, of course, being biological macromolecules.
By the end of this lesson, you should be able to:
- Write down explicit solutions to systems of linear, constant coefficient, homogeneous differential equations.
Before class, please:
- Read Olver, Sec. 9.1.
- Read my notes, which may clarify.
- After you read the notes, watch this video to see another example.
In class, we will:
After class, please:
- Do these problems.