- Your quiz this week (our final quiz!) will be over Section 3.1.
- Your exam corrections are returned.
- Some of our classmates are presenting at the Celebration of Undergraduate
Research today, 12:30-2:30:
- Isabella Carr, et al. (two posters!): Locomotor activity in female and male rats after acute oxycodone; and Sex Does Not Influence Oxycodone-Conditioned Place Preference in Rats
- Idalia Martin (poster): Predictive Analysis of Computer Hardware Prices through Machine Learning
- Story problems!
- Introduced Section
3.3: Global Optimization via its Preview.
Discovered that algebra and a good understanding of functions would get
us a long way towards the solution.
- An important theorem: the
Extreme
Value Theorem. The basic idea is that, if the function is
continuous on a closed and bounded domain, then it
must have a global maximum and a global minimum.
- Then we looked at an example story problem, about the volume of a box.
- Let's continue on with some problems whose solutions truly involve calculus:
- Let's review our solution to Activity 3.3.4
- Example 3.3.4
- Let's look at #4 from your worksheet for 3.3.
By the way, on #2, \(f(0)\approx 2.40\), and \(f(5)\approx 2.31\).
(Why did we make it so close, without giving you the function??:)
- Then it's on to Section
3.4: Applied Optimization
- Applied optimization is exactly what you might expect: we're
looking at "real problems", and attempting 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!
- 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).
- Here's the latest worksheet.
- Applied optimization is exactly what you might expect: we're
looking at "real problems", and attempting 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