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
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Differential Equations and exp(At) (00:51:03)
Lecture 23: Differential Equations and exp(At)
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- Lecture video transcript (PDF)
- Read Section 6.3 in the 4th or 5th edition.
Problem Solving Video
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Differential Equations and exp(At) (00:10:19)
Problem Solving: Differential Equations and exp(At)
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- 观看视频: 习题讲解 --
Problems and Solutions
Work the problems on your own and check your answers when you're done.