Vector Calculus I 2022
This small group activity is designed to provide practice with the chain rule and to develop familiarity with polar coordinates.
Students work in small groups to relate partial derivatives in rectangular and polar coordinates.
The whole class wrapup discussion emphasizes the importance of specifying what quantities are being held constant.
What students learn
Uses the chain rule to relate partial derivatives in different coordinate systems.
Suppose that \(x=s\,\cos\phi\) and \(y=s\,\sin\phi\).

Let \(h(x,y)=xy\). Determine \(\frac{\partial h}{\partial s}\) (with \(\phi\) held constant)
and \(\frac{\partial h}{\partial\phi}\) (with \(s\) held constant).

Find at least one more way to compute these derivatives.
Make sure you get the same answer!

Determine \(\frac{\partial s}{\partial x}\) and \(\frac{\partial \phi}{\partial x}\) (with \(y\) held
constant).

Find at least one more way to compute these derivatives.
Make sure you get the same answer!
Copyright 2014 by The Raising Calculus Group
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 Learning Outcomes
