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Total Differentials on a Surface: Instructor's Guide
Main Ideas
Students' Task
Estimated Time: 10 min
Prerequisite Knowledge
Props/Equipment
- Tabletop Whiteboard with markers
Activity: Introduction
Students should be introduced to the ideas of differentials using a one-dimensional graph and the corresponding symbolic relationship. Then, give each group a plastic surface representing a function $f(x,y)$ and ask them to sketch $df$, $dx$, and $dy$ on the surface and to relate these differentials geometrically and then symbolically.
