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I am teaching calculus III in the upcoming semester. The course is fairly standard, just a brief run-down:

  1. Test 1: covers vectors and coordinate systems as well as the calculus of space curves including the Frenet frame, curvature and torsion.
  2. Test 2: covers functions of several variables, multivariate limits, partial derivatives, chain-rules,min/max theorems, Lagrange multipliers
  3. Test 3: covers multivariate integration, double and triple Cartesian integrals, Jacobians and the change of variables theorem, possibly Greene's Theorem
  4. 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.

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I have some experience teaching students to use Maxima for evaluating integrals. I did it in a classroom with almost as many computers as students. Maxima was installed on all the computers locally, so they didn't have to install Maxima themselves, which would have been somewhat of a barrier. It worked fine, and they seemed to enjoy it, but Maxima has various usability problems which they needed help with. Most college-age people today have no experience with a terminal-style user interface. Some specific things that they needed my help with:

  • Use log(x) for ln x, exp(x) for e^x.
  • Use integrate(...), not integral(...).
  • For integrals involving symbolic constants, Maxima may ask if the constant is positive, negative, or zero. They need to type a semicolon after their response.

I have only a little experience with Sage, but it was pretty negative. When I tried it, the web browser interface was much too slow to be usable. If you download Sage and install it locally, it's a huge download. Sage seems to be sort of a hairball of other math packages, and the interface to the other packages often doesn't seem to be very good. The tutorial shows you how to do lots of fancy things using examples from abstract algebra, but doesn't tell you ordinary, useful things, like how to integrate $x^a$.

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    $\begingroup$ Maxima is also available for Android (on a phone/tablet the lack of a decent keyboard is a serious hindrance, but...) $\endgroup$ – vonbrand May 16 '14 at 13:35
  • $\begingroup$ Thanks for the answer Ben, I have all the same formatting problems (and more) using Mathematica with students. I will not have a lab at my disposal so all my instruction will be remote and/or in office hours. $\endgroup$ – James S. Cook May 17 '14 at 2:05
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I indicate the site https://www.wolframalpha.com

In this site you can make several types of calculations, such as derivatives, integrals and use of numerical symbology

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