# Curvilinear Coordinates

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### Highlights of the activity

1. This small group activity is designed to introduce students to directed area elements in curvilinear coordinates.
2. Students work in small groups to determine directed area elements in polar, cylindrical and spherical coordinates.
3. The whole class wrap-up discussion emphasizes the use of infinitesimal reasoning and $d\rr$.

### Reasons to spend class time on the activity

• Essential building block if using $d\rr$ to evaluate integrals.
• Good geometric discussion of curvilinear coordinates.
• Opportunity to model the use of infinitesimal reasoning.
• Possible sequence with Curvilinear Volume, in either order.

(Similar to Vector Differential.)

### Instructor's Guide

Authors: Tevian Dray

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