Comments on Lesson VC.03

• G.3 This is a nice easy problem to get people thinking about what a gradient does for you. I would assign it before problem G.2. However, note that most students seem not to understand what the NDSolve commands are doing without a refresher about differential equations.

• The difference between a plot of a function and it the level curves of the function confuses many students, especially for functions of two variables. They know that the gradient "points in the direction of greatest increase", so they think of it as pointing up hill, rather than just towards the top on the contour plot.