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Vector Differential

Keywords: Small Group Activity, Vector Calculus, Coordinate Systems, Curvilinear Coordinates


Highlights of the activity

  1. This small group activity is designed to help students derive a geometric expression for $d\vec r$ in different coordinate systems.
  2. Students use provided geometric figures to write $d\vec r$ in cylindrical, spherical, and Cartesian coordinates.
  3. The wrap-up discussion addresses why $d\vec r$ is different based on the different coordinate system and ensures that all student have a correct expression for the geometric factors.

Reasons to spend class time on the activity

We use the vector differential to create a unified view of calculus. Students have a lot of difficulty writing down exact differentials and writing down equations for vectors in curvilinear coordinates. This activities allows students to use geometric reasoning to practice both of these skills.


Instructor's Guide

Student Handouts



Authors: Corinne Manogue, Tevian Dray, & Katherine Meyer
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