Day 42, Mat128: Calculus A

• The "take-home" quiz from last week is due.
  • A key for the homework
  • A key for the 3.1 worksheet

• Here are the notes from the "Dogs do calculus" problem of last time.

• For next time please read Section 3.5: Related Rates. Your last assignment is to do problems 2-6 at the end of that section.

• I've been asked to promote The Norse Marketplace event, happening tomorrow starting at 11:30

• We started Section 3.4: Applied Optimization.

• Our authors have their version of my "UPCE", which is a little more specific to these types of optimization problems.

• Then we did a problem leading to linear regression, one of the most important problems that we resolve using derivatives.

We'll review the problem from last time (we need to spend a few more minutes evaluating the solution), and then try a few problems from the handouts for these two sections 3.3 and 3.4

• 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).
  • Mathematica
  • Mathematica Output (pdf)

• Your worksheet for 3.3. Let's do the last problem.
• Here's the 3.4 worksheet. Let's do problem AC3.4.9 (which was also assigned for homework).

  (solution)

• 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