|
T 12/1/09
|
No additional HW due. You have already endured a
test on the first day back after a break.
|
|
|
W 12/2/09
|
HW due: Read §§6-2 and 6-4; write §6-3 #30-46 even.
|
|
|
Th 12/3/09
|
HW due: Read §6-5; write §6-4 #7 plus any two of #9,
10, and 11. Remember, you must use the HappyCal
definition of ln.
|
|
|
F 12/4/09
|
HW due: Read §6-6, write §6-5 #1-15 odd, 24.
|
|
|
M 12/7/09
|
HW due: Read §6-7; write §6-6 #5-12 all, 19, 20.
Follow-up note regarding §6-4 #12: If r(u) = uln u, then u is the independent variable. Ouch!
That means that this is not an exponential function, and I violated my own
advice when I solved (or tried to solve) the problem three different ways.
Two of the methods were valid: the logarithmic differentiation method and the
“qr method” that Hank
generalized for us at the end of the period. However, we cannot use the shortcut method (function times ln of base times
CR adjustment), since the function is not exponential. The base is not a
constant, and that’s that.
Therefore . . . you have only two choices.
Method 1: Logarithmic differentiation
Method 2: Rewriting expression using exp and ln
|
|
|
T 12/8/09
|
HW due: Read §6-8; write §6-7 #16, 48, 59, 60, §6-8
#9, 10, 12, 30.
|
|
|
W 12/9/09
|
HW due: Read §6-9 (all review); write §6-8 #22, 24,
28, §6-9 #as many as possible (cut yourself off when you hit a reasonable
time limit).
|
|
|
Th 12/10/09
|
HW due: Read §§7-2 and 7-3; write §7-2 #2, 9. For
#2, do all the work as illustrated by Examples 1 and 2 (pp. 310-312).
However, after today, we will always “cut to the chase” when given a
situation involving rate of change proportional to the quantity present,
since all such situations are exponential growth or decay. In other words, if
we know that y is changing at a
rate proportional to y, we will (in
the future) immediately write y = Cekt or y = Cekx as the general solution, without showing any
work, depending on whether the independent variable is t or x.
I strongly recommend that you start reviewing for your midterm exam. A practice exam is available, but you
should not work any of the problems until you have studied and are ready to
challenge yourself. The reason is that the practice exam is not
comprehensive, nor could it be. To cover ever single topic in depth would
require an exam much too long to be practical. Thus there is a danger that a
student who skips the midterm review and goes straight to the practice exam,
and who then revises and tinkers until he can answer the practice exam
flawlessly in well under 2 hours, will be fooling himself. Admittedly, he
probably knows all the material on the practice exam at that point, but the
real exam could cover additional topics, such as symbolic logic, names of
prominent mathematicians (Mandelbrot, Newton, Leibniz, Gödel, etc.), the CRI,
and others. In other words, you can use the practice exam as part of your review
effort, but it cannot constitute your entire review effort.
|
|
|
F 12/11/09
|
HW due: Read §§7-4 and 7-5; write §7-3 #3 and the
problem below.
Given: dy/dx = x2/y, and y = 4 when x = 2.5
Solve for y.
Loose end from yesterday’s class: Normally
I would not issue a correction notice for a slip of the tongue (factual
misstatement), but since most of you listen very carefully, I need to clear
up a mistake of mine. I believe I said that the number of initial conditions
you need to solve a diffeq. depends on the order of the diffeq. Well, that is
somewhat true, but the real issue is the number of arbitrary constants you
have. Many exponential growth/decay problems leave k unstated, which means that you need two initial conditions in order to resolve the values of C and k.
|
|
|
M 12/14/09
|
Sleep Week begins.
HW due: ZZZ
Note to kind anonymous e-mailer: I
understand that this is, in your opinion, perhaps not the ideal week to try the
Sleep Week experiment because of the large number of commitments you have in
your other classes. I have thought about your proposal regarding grading, and
I have decided that as long as we are all committed to the goal of getting more sleep than we otherwise would have
had, Sleep Week will be a success. We’re shooting for about 35-45 extra
minutes per night, or whatever you would normally have spent on HappyCal
homework. Perfection is not required; just do the best you can. Try to take
this seriously, and I have faith that things will work out well.
The sleep researchers say that high schoolers get approximately one full hour
of sleep less per night, on average, than they did 30 years ago when I was in
high school. Since the best quality, most restorative sleep tends to occur in
the last phase of sleep, adding an extra 45 minutes can make a huge difference. Say, for the sake of
argument, that your final sleep phase lasts 30 minutes before you wake up.
Extend that by 45 minutes, and your best quality sleep more than doubles.
Thus, going from, say, 7.5 hours to 8.25 hours of sleep (a 10% increase) can
translate into a 150% increase in your high-quality long-term memory sleep.
Wow! That’s some serious leverage!
Optional assignment over the weekend: Please read this topic summary. Funny but
true story: I was searching the web for something that would serve as a
suitable review of the first semester. One of the links looked fairly good,
and when I clicked on it, I discovered that it was something I had written!
At first, I did not even remember writing it. This is actually a full-year
review for an IntroCal section I taught at STA some years back, but of course
in HappyCal we move at roughly twice the pace. Anyway, I would be interested
in hearing if you find the summary useful or if you have any suggestions for
improvement.
We will have a test (approximately 30 minutes long) on an unannounced day
this week to see whether everyone is keeping up on Chapter 6 and Chapter 7.
|
|
|
T 12/15/09
|
HW due: ZZZ
|
|
|
W 12/16/09
|
HW due: ZZZ
If you would like to write up any or all of yesterday’s in-class exercises, I will be happy to check (not
grade) them and give you some helpful feedback.
|
|
|
Th 12/17/09
|
Sleep Week
Test (100 pts.). It is my fervent
hope that nobody spends much time studying the night before this test. Please
focus instead on maintaining the essential spirit of Sleep Week. I had hoped
to hold the test on a randomly chosen, unannounced day, but that is not
possible for scheduling reasons. Instead, we can do the next best thing: I
will announce all the proofs for which you will be held responsible
(change-of-base, CRI, nothing else) and problem categories.
Because of an apparent bug that Sunil reported in the SLOPEFLD program, any
slope field sketching that you are required to perform on the test will be
strictly of the type that can safely be accomplished without a calculator at
all.
Important
announcement: The test will be held in MH-311 in order to provide better
test seating.
Evening: Lessons & Carols at the Cathedral.
|
|
|
F 12/18/09
|
Sleep Week ends.
HW due: ZZZ
|
|
|
|
Christmas break.
|
|