# 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.

### Student Handouts

Authors: Corinne Manogue, Tevian Dray, & Katherine Meyer

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