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Measurement and Calculus: Continuity and Derivatives through the Lens of Interval Arithmetic

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Tags: calculusderivativescontinuity

In this video, I motivate the study of interval arithmetic for reasoning about real-world measurements, and use that to motivate a precise definition of continuity and derivatives. This video is designed to be interesting and accessible to both students of Calc 1 who have and have not seen continuity and derivatives before. For educators who prefer a more active classroom, I have also added a visualizer for plugging in intervals of values to functions to my piecewise function grapher: https://trkern.github.io/pw_limit

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7 Overall score*

24 Rank

10 Votes

4 Comments

Comments

6.8

Actually pretty good! I think you can get to the point a bit faster and I think you should introduce how to calculate error in output due to error in input using the chain rule formula earlier - rather than relying on so much intuition.

8.2

Really nice explanation, the dart board example gives a ton of intuition about this and is very easy to understand just by imagining the physics.

Very thorough mathematical explanation of the precision concept.

5.5

It is okay overall, the explanation is clear and easy to follow. The topic is well motivated, but (subjective opinion, of course) does not feel as remarkable or memorable as other topics I’ve seen. But, the visualization is well made and makes the concepts very easy to grasp.