- Your second assignment is returned today.
- 7/30 didn't hand it in; 3/30 have handed in neither assignment. You've got to do the homework: it's worth too much of your grade to ignore!
- Problems Graded:
- 4
- An easy one! A straight rectangle.... So why didn't everyone draw a rectangle?
- 14
- Linear functions (piece-wise, at any rate).
- One method: to figure out the exact form of g(t).
- Then to integrate
- A better method: use geometry! It's just triangles, afterall....
- Some of you seem to be missing the notion that there is both positive and negative area.
- 2 of the "short answers": What is a Riemann sum? What's a partition?
- A Riemann sum is an approximation to an integral, using crude rectangles.
- A partition is a collection of points, which subdivides the interval [a,b] into N subintervals.
- 4 of the "short answers": How are the sample
points determined for the three major rules (midpoint,
left endpoint, right endpoint)?
- The only difference between the three rules is the set of sample points (our author calls them intermediate points
).
- The sample points are the left endpoints of the partition for
; they're the right endpoints for
; and they're the average of each pair of endpoints for
.
- The only difference between the three rules is the set of sample points (our author calls them intermediate points
- 4
- In all cases: show work!
- You also got 2 points based on completeness.
- You have another homework due today: Section 5.3
- Please avoid the ragged paper -- it drives me crazy. Also please try to get your papers stapled in advance.
- Important Discussion: can we move the first test up a week or so, to Monday, 9/27?
- That's two weeks away.
- I'm going to be out of town, and that would avoid us having to have a substitute.
- The exam would then cover only chapter 5.
- 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.
- ???
You will undertake the following activity, concerning the rates of change and integrals thereof. I'll introduce a new example, that of a man drinking beer....
