Session Overview
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The purpose of this session is to introduce the operator notation p(D). This will simplify the writing of differential equations and point the way to a more complete discussion of operators and their uses in a few sessions. We will start with the important notion of stability which tells us that the system will respond in essentially the same way to a given input regardless of the initial conditions. After that, we will learn to express the formulas for exponential response, sinusoidal response, gain and phase lag in the p(D) notation. We will make heavy use of these formulas in the coming sessions. |
Session Activities
Read the course notes:
Watch the lecture video clips:
- Definition of Stability (00:13:17)
-
Stability of Constant Coefficient Second Order DE's (00:06:23)
Stability of Constant Coefficient Second Order DE's
> Download from iTunes U (MP4 - 88MB)
> Download from Internet Archive (MP4 - 88MB)
Read the course notes:
Check Yourself
Take the quizzes:
- Damping and Phase Lag (PDF)
- Choices (PDF)
- Answer (PDF)
- Damping and Amplitude (PDF)
- Choices (PDF)
- Answer (PDF)
Session Activities
Watch the problem solving video:
- Gain and Phase Lag (00:10:39)
Complete the practice problems:
Check Yourself