We can copy Taylor's series for ex to define eAt for a matrix A. If A is diagonalizable, we can use Λ to find the exact value of eAt. This allows us to solve systems of differential equations du / dt = Au the same way we solved equations like dy / dt = ky.
Lecture Video and Summary
- Watch the video lecture Differential Equations and exp(At) (00:51:03)
Lecture 23: Differential Equations and exp(At)
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 6.3 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on Differential Equations and exp(At) (00:10:19)
Problem Solving: Determinants and VolumeDifferential Equations and exp(At)
- Recitation video transcript (PDF)
- 观看视频: 习题讲解 -- 微分方程指数矩阵(At) (00:14:36)[watch this recitation in Mandarin]
Problems and Solutions
Work the problems on your own and check your answers when you're done.