- Your quiz today (our final quiz!) is over Section 3.1.
- We reviewed the example story problem, about the volume of a box, that we'd done Monday.
- Then we went over another story problem, Example
3.3.4, using the UPCE method --
- Understand
- Plan
- Carry Out
- Evaluate
- We're into Section
3.4: Applied Optimization
- Applied optimization is exactly what you might expect: we
look at "real problems", and attempt to crack them using tools
from calculus.
- Our authors have their own
version of UPCE, which is a little more specific to these
types of optimization problems.
- We'll focus on one example in this section, Activity
3.4.3, only in a slightly different context. While the
problem is stated in the context of a hiker, we'll do what is
effectively the same problem, only to demonstrate that a dog
does calculus!
- This example includes both a theoretical model -- one that
we can derive using calculus, and data obtained from
experiment, to see how well the data corresponds to the
model.
- The theoretical model in general can be derived by using
calculus, informing a process called "least squares",
or linear regression.
This example is inspired in part by Idalia's poster, in which she used a linear regression in her work. The linear regression model is obtained using derivatives.
Because we're doing univariate calculus, our hands are tied a little; but we can give you the idea.
- Do
Dogs Know Calculus? Certainly they do; they just don't
know they do!
Nature is very particular about choosing optimal paths, and so Elvis, creature of nature, is pretty good about doing so (even if he can't state the Extreme Value Theorem, and constantly misapplies the quotient rule).
- Here's the latest worksheet.
- Applied optimization is exactly what you might expect: we
look at "real problems", and attempt to crack them using tools
from calculus.
- Do Dogs Know Calculus?
- Cherry
blossoming data (from the EPA). Some "Key Points" cited in that webpage:
- Based on the entire 102 years of data, the average peak bloom date for Washington's cherry blossoms is April 4.
- Peak bloom date for the cherry trees is occurring earlier than it did in the past. Since 1921, peak bloom dates have shifted earlier by approximately seven days. The peak bloom date has occurred before April 4 in 16 of the past 20 years.
- While the length of the National Cherry Blossom Festival has continued to expand, the Yoshino cherry trees have bloomed near the beginning of the festival in recent years. During some years, the festival missed early peak bloom dates entirely.
- More generally, Leaf and Bloom Dates (EPA)
- A Keeling Analysis in Mathematica