Unit 5 · Eigenvalues and Dynamics

Chapter 5.3

Differential Equations and the Matrix Exponential

du/dt = Au is the continuous twin of matrix powers: eigenvalues decide growth, decay, or oscillation, and e^{At} packages every solution at once.

11–15 min · in preparation · lesson 15 of 21

By the end

  1. 01Solve linear systems du/dt = Au by eigenvector expansion
  2. 02Read stability from the signs of eigenvalues
  3. 03Define and use the matrix exponential

In unit 5

  1. 5.1Eigenvalues and Diagonalization13–16
  2. 5.2Markov Matrices and Difference Equations11–15
  3. 5.3Differential Equations and the Matrix Exponential11–15
RELUE© MMXXVI

AP® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this content.