Try to motivate why partial derivatives matter. Examples: Give evocative description of the heat equation flow. Cut a weird shape across the top of a trash can and cover it with saran wrap: what is the shape? Which way is up on a surface?
colliand
Rectangle
colliand
Line
colliand
Line
colliand
Rectangle
colliand
Line
colliand
Line
colliand
Line
colliand
Line
colliand
Rectangle
colliand
Line
colliand
Line
colliand
Line
colliand
Line
colliand
Rectangle
colliand
Rectangle
colliand
Line
colliand
Line
colliand
Line
colliand
Rectangle
colliand
Line
colliand
Line
colliand
Line
colliand
Sticky Note
Try to describe contour lines well! Which way is up on a surface? Across contour lines...
colliand
Rectangle
colliand
Line
colliand
Line
colliand
Line
colliand
Line
colliand
Line
colliand
Line
colliand
Line
colliand
Line
colliand
Line
colliand
Sticky Note
Try to get across the difference of limits in one dimension versus two dimensions. Contrast limits from left and right in one d versus the many ways to approach a point in 2d, including weird spirals or along parabolas or along x sin(x^{-1}), ...
