Week 7: Applications of the derivative


How large a web to weave?

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 had a taste of this on Friday, but we'll look at more of it this week. For example: How big a web should a spider weave? What is the best size for a moose to be? Why is the deadliest disease for a person not the worst disease for a population?

    English ↔︎ Math: Sometimes the mathematical manipulations required in these problems are almost an afterthought, and 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 dynamic behaviour 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. 😅

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

Reminder 1: No class this Friday

This Friday is the Heritage Day holiday, perhaps better known as Rendezvous Friday. Have some fun! 🎉

Reminder 2: Your Exam Cheat Sheet

Between the simplex method, all those functions two weeks ago, and the differentiation rules last week, we're accumulating a lot of procedures and formulas to remember. You'll be allowed to bring a cheat sheet into the final exam with you with anything on it you like: one 8.5 x 11 sheet created by hand. I mention it now because this is a good time to begin creating yours. The formulas you find yourself looking up to do the exercises and assignments should probably go on your cheat sheet.

Reminder 3: Final Exam Date

We have a date. The exam is scheduled for 9 am—12 pm on April 22nd in our usual classroom, A2801.

That's all for now!

See you soon,
Tim