- Your test revisions are not reviewed yet -- sorry for the delay.
- Your quiz this week will cover the chain rule, section 2.5.
- Chain rule notes (and earlier stuff) from
- I'll be zooming this meeting, and recording it, for a student who
has a legitimate issue requiring it.
- You're invited! 2024
Math/Art Pop-Up Conference We'd love to have you join us for
- Fun activities
- Free lunch! (Yes, there is!)
- We reviewed the chain rule: \[ F^\prime(x) = f^\prime(g(x))g^\prime(x) \]
- And then did a fair number of examples.
- $h(x) = \tan(2^x)$
- $m(x) = e^{\tan(x)}$
- $z(x) = \sqrt{\tan(x)}$
- $F(x)=\sqrt{1-2x}$
- $F(x)=6\cot(nx)$
(we talked about the parameter $n$ -- just a number...)
- I shared with you an important problem involving compositions:
model the seasonal variation in Keeling's CO2 data:
We discussed some of the issues as we try to model this data: the periodic oscillations of atmospheric carbon dioxide, and the long-term trend (in particular its concavity -- don't model a banana with a straight line)
- Remember that I like to think of the chain rule this way:
\[
F^\prime(x) = f^\prime(stuff)stuff^\prime
\]
It will be particularly useful for our second example today:
- Further examples:
- $F(x)=4 + 0.35 \sin(2 \pi t / 5.4)$
What's the period and amplitude of \(F\)'s oscillation? - Trickier: $F(x)=\sin(\sqrt{1 + x^2})$
- $F(x)=4 + 0.35 \sin(2 \pi t / 5.4)$
- So let's model the seasonal variation in Keeling's CO2 data:
Keeling data with models:
- A summary from another class: The Chain Rule
- A Keeling Analysis in Mathematica
- The latest Keeling data
