First, students are shown diagrams of cylindrical and spherical coordinates. Common notation systems are discussed, especially that physicists and mathematicians use opposite conventions for the angles \(\theta\) and \(\phi\). Then students are asked to check their understanding by sketching several coordinate equals constant surfaces on their small whiteboards.
For the cylindrical coordinate system shown below, draw three surfaces: one for constant \(s\), one for constant \(\phi\), and one for constant \(z\).
For the spherical coordinate system shown below, draw three surfaces: one for constant \(r\), one for constant \(\theta\), and one for constant \(\phi\).