Week 7: Applications of the derivative

We are almost at the midpoint of the course. Next week is Reading Week 😌, a well-deserved break and/or a chance to catch up, about which more below. But first we have this week to get through, and its question...

What can you do with a derivative?

So many things! 😎

But we only have one week, so I've chosen three things for us to look at:

1. More optimization. We've seen a bit of this, but we'll look at more of it this week. For example: How big a web should a spider weave? How large a territory should a bird strive for? And what is the best size for a moose to be?

   The mathematical manipulations required in these problems are almost an afterthought, it's formulating the problems, i.e. the translation from English, that is the challenge.

2. Modelling system dynamics in phase space 👽 🛸, aka drawing swirly pictures out of little arrows ⤳ ⤻ ↬ to visualize the development of a system over time.

3. Testing the solutions to differential equations. Differential equations are the standard modelling tool for dynamic systems, and the subject of an entire course (or often a 2-course sequence) in many science majors. They are complicated to solve because there are many techniques to master, but testing a solution is relatively easy. So that's what we'll look at. 😅

English ↔︎ Math

In some ways it's a light week. There are only 14 resources and 127 minutes of pencasts compared to Week 5's 32 resources and 230 minutes of pencasts, and we only look at a handful of problems. But it is conceptually rich, and the key skill we're working on this week is translating faithfully from English to mathematical concepts. And back again!

Next week is Reading Week 🎉

Ahhh reading week...

If things are going well 😇, and you're caught up, it gives you a chance to refresh and recharge. ... And then begin working on your cheatsheet for the final exam.

If you've fallen a bit behind 🙄, it's a chance to catch up, and lay the groundwork for a successful second half of the course. ... And then begin working on your cheatsheet for the final exam.

But if things are not going well 😔, then it's the time to assess how your courses are going, and determine if things are going to turn out the way you want, or need, them to, and to take action if not. To help you with this I'll be sending you a midterm grade summary showing how you are doing in the course so far. This will go out early in Reading Week, after I've marked Assignment 6 (which is due this Friday).

Exercise Set and Assignment extension

Reading week also means a break in our usual metronomic weekly schedule. Instead of having an Exercise set and Assignment due in Reading Week, they'll be due the week after, giving you two weeks to complete them.

That's all for now!

See you soon,
Tim

"Mathematical science is the language of the unseen relations between things." — Ada Lovelace