Week 5: Nonlinear Models

It turns out the world isn't linear 😳 #uhoh

Linear models dominate most scientific analysis and modelling. But the reason they are so common is because they are easy to work with, not because all phenomena are actually linear. Lots of phenomena have more ... interesting ... behaviour, and for those we need non-linear models. This week we'll reacquaint ourselves with the big three, Quadratic, Exponential/Logarithmic, and Sinusoidal, and begin to use them to model nonlinear phenomena.

Towards Calculus

The next four-week section of the course will look at modelling non-linear systems and processes, and in particular at the calculus topics of:

1. Change: How, and how fast, quantities are changing,
2. Optima: Finding optimal values, and
3. Accumulation: The accumulation of quantities in systems.

A Superpower 💪

This week isn't built around a single big question about the behaviour of moose or corporations, it's a preparation week. A review-the-parts-we-need-from-Math-12/Pre-Calc/Math-060 week. But it does lead to a rare skill that may impress your future colleagues:

• The ability to look at an equation and effortlessly identify the family it's from and sketch it, and
• The ability to look at a plot (like the ones above), and quickly provide an equation to model it.

And we'll use another online tool to help us out called Desmos.

Blasts from the Past

You've seen most the material we'll cover this week before. It reawakens fairly well for most students. Even, to their surprise, for the topics they think they didn't learn at all the first time through (*cough* logarithms *cough*). But there are a ton of pencasts online (mostly brief!), because for some people Math 12 was a long time ago, or recent and yet not ... memorable. 😉

With so much material it's more important than ever to get an early start, and to use your time well. ⏳

Free tutoring available

YukonU has free tutoring services that can help you with Math 120. Check them out if you want another source of support!

Small tweaks

I'm not reminding you about the exercise set due Monday, because by now you know there'll always be one due on Mondays. [Ed. Isn't that a reminder? Uh...😏]

That's all for now!

See you soon,
Tim