Session Overview
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We now begin an in depth study of constant coefficient linear equations. These are the most important DE's in 18.03, and we will be studying them up to the last few sessions. In this session we will learn algebraic techniques for solving these equations. Exponential functions will play a major role and we will see that higher order linear constant coefficient DE's are similar in many ways to the first order equation x' + kx = 0. |
Session Activities
Read the course notes:
Watch the lecture video clips:
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Constant Coefficient Second Order Homogeneous DE's (00:12:25)
Constant Coefficient Second Order Homogeneous DE's
> Download from iTunes U (MP4 - 95MB)
> Download from Internet Archive (MP4 - 95MB)
- Real Roots: Overdamping (00:14:59)
Read the course notes:
Check Yourself
Take the quiz:
Session Activities
Read the course notes:
Watch the lecture video clips:
- Complex Roots: Underdamping (00:15:10)
- Repeated Roots: Critical Damping (00:07:26)
Read the course notes:
Watch the lecture video clip:
- Real Solutions from Complex Roots (00:23:02)
Watch the problem solving videos:
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Homogeneous Constant Coefficient Equations: Real Roots (00:09:16)
Homogeneous Constant Coefficient Equations: Real Roots
> Download from iTunes U (MP4 - 20MB)
> Download from Internet Archive (MP4 - 20MB)
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Homogeneous Constant Coefficient Equations: Any Roots (00:11:28)
Homogeneous Constant Coefficient Equations: Any Roots
> Download from iTunes U (MP4 - 25MB)
> Download from Internet Archive (MP4 - 25MB)
Complete the practice problems:
Check Yourself
Complete the problem set: