I am teaching calculus III in the upcoming semester. The course is fairly standard, just a brief run-down:
- Test 1: covers vectors and coordinate systems as well as the calculus of space curves including the Frenet frame, curvature and torsion.
- Test 2: covers functions of several variables, multivariate limits, partial derivatives, chain-rules,min/max theorems, Lagrange multipliers
- Test 3: covers multivariate integration, double and triple Cartesian integrals, Jacobians and the change of variables theorem, possibly Greene's Theorem
- Test 4: vector calculus. Theorems about conservative vector fields, line and surface integrals, curl, divergence, Gauss and Stokes' Theorems
I'm using Salas and Hille's text. I've recently noticed that Maxima is fairly accessible and the Sage cloud is very user friendly in some sense, but, perhaps a bit slow. I'd like to do some animations and manipulations (sliders). My question is somewhat broad:
Question: how can I get students to investigate calculation and visualization via Sage ( or Maxima etc... open source software ) without overwhelming them with work? I don't intend to test on the software aspect, so these assignments are mainly intended to help them crack calculationally intense homework (think torsion) and to visualize geometric data. Ideally, I want to craft 4 computer projects which give them a template and task to modify the template to solve some problem. Perhaps such assignments exist already, I've seen nice work in the help documentation linked to Sage, but I'm trying to find something with a bit more structure. Perhaps a good tutorial.
Secondary question: should I use the cloud or is it better to go for local installation of Sage? Does anyone have experience with either option as it applies to Sage or Maxima.