F 8/24 -- We covered 12.2 and began 12.3. Most of the class
seems to have a passing familiarity with vectors.
HW2 -- 12.2: 4*, 5, 7, 8*, 19, 20*, 23, 24*.
No honors question for Monday 8/27.
M 8/27 -- We covered 12.3 and began 12.4.
HW3 -- 12.3: 19, 20*, 27, 28*, 47, 48*, 57, 58*
Extra Credit Honors Question: Prove that there is no equilateral triangle
*in the plane*, all of whose vertices have integer coordinates. That is,
if (0,0), (a,b) and (c,d) are the vertices of a triangle, with a,b,c,d
integers, then the triangle can't be equilateral.
Note: such a triangle exists in 3-space: (0,0,0), (-1,1,0), (-1,0,1), or
its more familiar-looking translate: (1,0,0), (0,1,0), (0,0,1).
The proof I have of this question involves knowing the behavior of
integers modulo 2 and modulo 4.
This problem is due on the Wednesday after Labor Day. No further hints!
W 8/29 -- We went over HW 3, especially #48 and #58, and finished
most of 12.4.
HW4: 12.4 -- 3, 4*, 9, 10*, 13, 14*, 25, 26*.
HQ4 Let a = <1,2,3> and b = <4,1,-2>. Determine all vectors u =
F 8/31 -- More discussion of the cross product, with an
indication of the right-hand rule, and a conceptual discussion of
the solution to HQ4. We began a quick once-over of 12.5.
HW5: 12.4 -- 29, 30*, 31, 32*, 42*, 45*
The answer to #45 is in the back. To receive credit, give an explanation
as well!
W 9/5 -- We discussed the Extra Credit Honors Question. I will
eventually link my handout to the page. Afterwards, we returned to
12.5 and did some examples.
HW6: 12.5 -- 8*,9,17,18*,24*,25,31,32*,37,38*.
F 9/7 -- More on lines and planes with some old exam questions.
A romp through conic sections in preparation for 12.6 on Monday.
Another extra-credit honors question: tricky but elementary.
HW7: 12.5 -- 51, 52*, 67, 68*; 12.6 -- 21 --> 28(*) (mix `n' match).
Get some sleep over the weekend.
M 9/10 -- We went through my patented natural history of
the quadric surfaces, adding a few to the ones in 12.6, including
the elliptical, parabolic and hyperbolic cylinders. We started 12.7
on cylindrical coordinates. No homework for Wednesday.
W 9/12 -- Following Chancellor Cantor's MASS-MAIL, we had a
discussion in class on the tragic events of 9/11. (I learned on
Wednesday afternoon that one of my college classmates was a passenger on one
of the hijacked planes.)
F 9/14 -- Back to class. Finish with Ch. 12 on cylindrical
and spherical coordinates, begin with Ch. 13 on vector functions.
The class sees what its instructor is like when he hasn't been
sleeping very well. HW8: 12.6 -- 31, 32*, 41, 42*; 12.7 -- 25,
26*. 29, 30*; 13.1 -- 7 --> 12 (*)(mix `n' match). Extra credit honors
trisection problem is due on 9/17.
M 9/17 -- Several people presented their solutions to the
trisection problem. We zoomed through 13.2 and began 13.3.
HW9: 13.1 -- 17, 18*, 31, 32*;
13.2 -- 5,6*,13,14*,19,20*.
W 9/19 -- Curvature, unit tangents and unit normals. One handout
on these topics, another old handout on distances.
HW10:13.2 -- 23, 24*, 32*, 39, 40*;13.3 -- 7, 8*, 13, 14.
The first fitful discussions about the timing of the first exam.
F 9/21 -- More discussion of curvature, etc., on a day nobody
seemed able to focus.
HW 11: 13.3 -- 16*, 17, 25, 26* (start by writing y = ax^2 + bx + c, and
solve for a, b, c)
13.4 -- 11, 12*
From Test 1, Math 242, Fall 97, one more (starred) homework question:
(Arrows omitted for clarity)
A curve r(t) has the property that v(0) = <1,1,2> and
a(0) = <1,-1,1>. Determine, the unit tangent vector at t = 0,
T(0), the unit normal vector at t = 0, N(0), and the curvature
at t = 0, K(0).
Coming up for the week:
M: any review of the course so far, plus Kepler's laws -- class decision
on the first exam. The earliest it could be is Monday 10/1 in class, but
it might be at night if we can all agree.
W: final finish-up and prospective look at the rest of the course
F: (Assuming the test is on 10/1, a review, and beginning of new
material.)
M 9/24, W 9/26, F 9/28, M 10/1, W 10/3, F 10/5 -- Well, it's
been a while! In these two weeks, we finished Ch.13, skipping Kepler's
Laws, reviewed for the first test, on 10/3, had the test, returned the
test, and moved on to Chapter 14. The distribution of scores on Test 1
was 100 - 1, 90's - 12, 80's - 5, 70's - 2. Anybody who wants to redo
any of the problems and have me look at them is invited to do so.
HW 13 is due on Monday: 14.1 -- 35,36*; 14.2 -- 7,8*,11,14*; 14.3 -- 21, 26*
HQ:-- suppose T = <1,0,0> and N = <0,1,0> and
curvature = k0 and speed = v0. Determine all possible velocity
and acceleration vectors.
M 10/8, W 10/10, F 10/12 -- We've been zipping through Ch. 14
This week, we're up to the middle of 14.5, although there have been
forays into topics like directional derivative and gradient from
later in the chapter. Here are the homeworks for the week:
(#14) 14.3 -- 33, 34*, 41, 42*, 45, 50*, 66abcd; 14.4 -- 1, 2*;
(#15) 14.4 -- 11, 12*, 17, 18*(don't bother to graph), 30*, 31, 32*,
33; and, (#16), which is due on Wed. 10/17: 14.5 -- 1,2*,9,10*,19,20*,
29,30*,36*,37 . For Monday, you should have read Chapter 14 through
14.5. There were also a couple of handouts on strange examples
of continuity, or the lack thereof, at (0,0).
M 10/15, W 10/17, F 10/19, M 10/22, W 10/24, F 10/26,
M 10/29, W 10/31, F 11/2, M 11/5, W 11/7, F 11/9, M 11/12,
W 11/14, F 11/16 -- Well, I've been a terrible correspondent!
Five weeks passed without an update, and while it's all my fault,
I have to admit that nobody asked about it in class. We've had
lots of homework, which I'll list below, and a test and a big
Bonus Honors Question (due 11/26), to which there were TeX'd handouts
which are linked below. I also remark that, for the "jailhouse
lawyers" in the group, here's the
Class
Organization. The Bonus Handouts can be found at
Quadrature
Notes and Supplemental
Quadrature
Notes .
HW16: 14.5 -- 1,2*,9,10*,19,20*,29,30*,36*,37
HW17: 14.6 -- 7, 8*, 29, 30*, 39, 40*, 50*, 51,
HQ a. Find the maximum of x^2y^3 subject to x\ge 0, y \ge 0 and x + y = 1.
(Hints, write y = 1-x and notice that the function is 0 at the endpoints.)
b. Find the maximum of x^2y^3z^8 subject to x\ge 0, y \ge 0, z \ge 0 and x
+ y +z = 1. (Hints, write z = 1-x-y and notice that the function is 0 on
the boundary of the set where it's defined.)
HW18: 14.6 -- 52*, 53;
14.7 -- 5,6*,9,10*,27,30*,37,38*
HW19: 14.7 -- 43, 44*; 14.8 -- 3, 4*, 7, 8*, 18*
HW20: 14.8 -- 15, 16*, 25, 26*, 35, 36*, 38*, 39
HW21: 15.1 -- 3, 4*, 12*, 13;
15.2 -- 1, 2*, 3, 4*, 13, 14*
HW22: 15.2 -- 15, 16*, 25, 26*; 15.3 -- 7, 8*, 13, 14*, 21, 22*
HW23: 15.3 -- 25, 28*, 39, 40*; 15.4 -- 7, 8*, 19, 20*, 23, 24*
HW24: 15.4 -- 27, 28*, 31, 32*; 15.5 -- 5, 6*, 7, 8*
HW25: 15.5 -- 11, 12*, 24*; 15.6 -- 1, 4*, 7, 8*;
15.7 -- 3, 4*
M 11/26 -- HW 26: 15.7 -- 13, 14*, 25, 26*;
15.8 -- 1, 2*, 7, 8*, 17, 18*. Solutions
to Quadrature Questions was passed out.
W 11/28, F 11/30, M 12/3, W 12/5, F 12/7. HW 27:
15.8 -- 13, 14*. 24*, 25
15.9 -- 1, 4*, 7, 10*, 11, 12*. We had the review for the third hour
exam, the exam itself, and it was graded and returned.
Sat. 12/8 -- Open office hour on Reading Day -- 1:30 -> 4:00 in
my office, 243 Illini Hall. Come in through the South Entrance.
Fri. 12/14 -- Final Exam (8:00 -- 11:00 am)