This Fall, Northeastern University is switching to the semester system, so for the first time we have a chance to teach vector calculus in our multivariable calculus course for engineers. I'm curious about computer exercises out there to help students get some intuition about what the concepts mean, and how they are used. If you have links to some please forward them to me. (I know about the materials on the Duke server.)
I am curious about points in this material that are trouble spots for the students, so if you know of any please let me know. (For example, when I introduce the gradient to the students, they have a lot of trouble integrating the properties of the gradient into their thinking to the level that permits them to solve simple word problems like, given the elevation function of a hill at a given point on the hill, in which direction is the hill level.)
I am also teaching a linear algebra course in the Spring to high school math teachers who are still working to complete their math certifications. Is there a text out there that supports the method in which the students develop most of the material themselves through investigations?