Differential Equations and exp(At)

« Previous | Next »

Session Overview

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

• Watch the video lecture Differential Equations and exp(At) (00:51:03)

  Flash and JavaScript are required for this feature.

  
  

  Differential Equations and exp(At)

  > Download from iTunes U (MP4)

  > Download from Internet Archive (MP4)

• Read the accompanying lecture summary (PDF)
• Lecture video transcript (PDF)

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)

  Flash and JavaScript are required for this feature.

  
  

  Differential Equations exp(At)

  > Download from iTunes U (MP4)

  > Download from Internet Archive (MP4)

• 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]

  Flash and JavaScript are required for this feature.

  
  

  微分方程指数矩阵(At)

  > Download from iTunes U (MP4 - 32MB)

  > Download from Internet Archive (MP4 - 32MB)

Check Yourself

Problems and Solutions

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

• Problems (PDF)
• Solutions (PDF)

« Previous | Next »