Day 05 in MAT227

Today:

• Announcements:
  • Your first assignment is returned today.
    • Graded
      • 3 -- show work!
      • 22 -- watch for degrees, rather than radians.
      • 3 of the "short answers": convenience, for one thing. Some theoretical results are easy (using the power rules, for example) if we use regularly spaced subintervals.
      • 4 of the "short answers": it's good to talk about the under-estimation and over-estimation of the left and right rectangle rules (depending on the monotonicity of the function being evaluated). Midpoint is generally better than either of those.
    • In all cases: show work!
    • You also got 2 points based on completeness.
  • You have another homework due today: pp 270--: 1, 4, 8, 12, 14, 32, 44, 46, 48, 52, 70, plus questions.
  • Please avoid the ragged paper -- it drives me crazy. Also please try to get your papers stapled in advance.

• First 30 minutes: answering your questions. Questions from sections 5.4 (or earlier)
  • 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, concerning the distribution of cicadas in Florida. Why do we care? Because cicada killer wasps feed on them, of course! And the larger the cicada meal, the larger the wasps....

  

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

Links:

• A FTC Worksheet
  • Another one
  • Another
  • Another