Session Overview
 | This session will formally introduce the notion of operators and linearity. Our main example will be p(D), which we have already seen. We will see that linearity is equivalent to the superposition principles, which we have already seen with first-order equations. |
Session Activities
Read the course notes:
- Linear Operators, Time Invariance: Introduction (PDF)
- Operators (PDF)
- Linear Differential Operators With Constant Coefficients (PDF)
- Operator Rules (PDF)
- Example (PDF)
- Time Invariance (PDF)
- Proof of the Generalized Exponential Response Formula (PDF)
Watch the lecture video clip:
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Solving DE's with Exponential Input when p(a) = 0 (00:23:03)
Solving DE's with Exponential Input when p(a) = 0
> Download from iTunes U (MP4 - 91MB)
> Download from Internet Archive (MP4 - 91MB)
Check Yourself
Complete the problem set: