Day 07 in MAT227

Today:

• Announcements:
  • Your third assignment is returned today:
    • 9/30 didn't hand it in. You've got to do the homework: it's worth too much of your grade to ignore!
    • Problems Graded:
      • 22
        • Some of you are hanging on to the integral sign even after you've found the anti-derivative -- let it go!
      • 32
        • Have you forgotten your trig functions? Just checking!
        • Did you recognize the anti-derivative? If so, you could find it in the "table of integrals" in the back of the book! -- "Basic forms", #9.
      • 44
        • The easiest way to do 44 is by inspection! How so?
        • Don't forget to "square the negative" (or raise it to the fourth power).
    • In all cases: show work!
    • Although I graded this out of 6, it's worth the same as every other homework. I rescale them all to have equal weight in the end....
  • You have another homework due today: Section 5.4
  • So: as we discussed last time, we will move the first test up to Monday, 9/27.
    • That's less than two weeks away! Start preparing....
    • The exam will cover only chapter 5.
    • 50% will be thinly veiled homework problems.
    • You will be able to use your calculator, so be prepared.
    • It will be proctored by one of my favorite students, so be nice to Evan.

• First 30 minutes: answering your questions. Questions from sections 5.6 (or earlier)
  • Substitution
  • Net change as the integral of a rate
  • The Fundamental Theorem of Calculus, Part II
  • The last lab
  • The Fundamental Theorem of Calculus, Part I (it's really that easy!)
  • anti-derivatives
  • Definition of the Riemann sum (a function of three variables! See p. 262).
  • Definition of the definite integral.
  • Properties of the definite integral.
  • Summation formulas
  • Limits of summations (power sums)
  • Putting these formulas into your calculator.
  • ???

• Next 25 minutes:

  You will undertake the following activity (which you can do with a partner, rather than with a group of five).

• For the final 20 minutes, we'll switch to a class discussion of the proposed solution(s).