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Differential Equations and exp(At)

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

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.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 6.3 in the textbook.

Problem Solving Video

  • Watch the recitation video on Differential Equations and exp(At) (00:10:19)
  • 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]

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you're done.

 

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