Comments on: Help? Multivariable Calculus!

By: Aaron Kahn

Aaron Kahn — Sun, 13 Jul 2008 07:10:57 +0000

I taught a course as a graduate student called “calculus with technology” at Michigan Tech. We used Mathematica to do real world problems in calculus, and the course was mainly directed toward the mostly engineering students at the university. I’m not so sure that it was successful.

I actually wouldn’t bother with worrying too much about teaching 3d software or LaTeX, as I think those tools are useful, but might ultimately distract from the task at hand – teaching calculus.

As for the answer to your nowhere differentiable continuous function – the most common example is to take a bounded sum of progressively more dense and less tall sawtooth functions.

By the way, I arrived at your site via presurfer.com which linked to NxE’s fifty most influential female bloggers (congratulations) – and I’m from Denver, so I clicked you.

So sorry to hear about your dog. Please feel free to email me with any calculus questions.

By: It’s Alive! Multivariable Calculus or Bust « Continuous Everywhere but Differentiable Nowhere

Sat, 12 Jul 2008 06:04:14 +0000

[...] you might recall, I’m spending a chunk of this summer designing a multivariable calc course. The oft repeated [...]

By: samjshah

samjshah — Thu, 10 Jul 2008 00:32:01 +0000

Anne, I’d love to get any ideas, investigations, activities that you come up with — any branch!

Discrete math is the most obvious place to get investigation accessible for high schoolers, I think.

But it might be fun to teach them a unit on plain old “problem solving” where they get competition problems (from AMC, AIME, etc.) and talk about solving them — and methods to solve problems (e.g. trial and error, induction, etc.). It’s about intuition, dead ends, and trying various approaches. (If you are ever in need of these sorts of problems, I have a bunch of places I can recommend.)

If you do anything with chaos/complexity theory, can I suggest looking at Steven Strogatz’s “Nonlinear Dynamics and Chaos.” It’s in paperback, and is totally investigative (using MATLAB for some great investigations), and many parts are accessible for students who have learned some very basic multivariable calc. In fact, now that I think about it, our mathclub investigated the logistic map and bifurcation diagrams (from the book), and that didn’t need anything past Algebra II and learning how to plot sequences on their TI-83s.

I pushed for my school to allow me to teach a course based around this book instead of the multivariable calc course, but unfortunately it was a no-go.

By: Anne Truitt Zelenka » links for 2008-07-08

Anne Truitt Zelenka » links for 2008-07-08 — Tue, 08 Jul 2008 23:36:26 +0000

[...] Help? Multivariable Calculus! « Continuous Everywhere but Differentiable Nowhere I’m going to be teaching a similar class: AP Calculus BC, to kids who already took a year of calculus. (tags: teaching math calculus ap) [...]

By: Anne Z.

Anne Z. — Tue, 08 Jul 2008 18:24:49 +0000

I am going to teach a similar class — AP calculus BC, to kids who already had a year of calculus. I don’t have any suggestions though because this is my first year teaching.

I want to do what you said, show the students “That math can be investigative instead of regurgitative. That math can be collaborative.” I’m thinking of making it a sort of exploratory course where in addition to multivariable calculus we look at other areas of math they might encounter in college: discrete math, statistics, linear algebra, mathematical modeling, complexity theory, network science, etc.