Day 12 in MAT227

Today:

• Announcements:
  • The exams are graded (scored out of 78).
  • You can get back 40% of the points you missed by visiting me with your corrected exam. That turns a 50 into a 70 (a passing grade); a 90 can turn into a 94. I'll put a link to the exam here, in case you want to do the problems you missed on a fresh page....
  • Homework Section 6.1 due today.
  • For next time: visit Gil Strang's website, and see what he has to say about "the magic number e" (watch the video). I consider Gil one of the greatest living masters of mathematics. Tell me what do you think.

• Today we're looking at section 6.3: Volumes of Revolution. What questions do you have about this topic, or any of our previous topics?
  • Setting up Integrals by Disks and Washers
  • Setting up integrals:
  • The difference in area between two curves
  • The last lab
  • Substitution
  • Net change as the integral of a rate
  • The Fundamental Theorem of Calculus, Part II
  • 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.
  • ???

• I'd like to take a little time to work a couple of examples:
  1. A standard disk problem (#20, p. 326)
  2. A standard washer problem (#49, p. 326)

• Next 25 minutes:

  You will undertake the following activity: mass of the atmosphere

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