Math 1B, Fall 2007
Math 1B, Fall 2007
Contents
This semester I was a GSI for two sections of Math 1B (instructor N.
Reshetikhin): Section #107 from 9:30 to 11:00 am on Tuesdays and
Thursdays, and Section #112 from 2:00 to 3:30 on Tuesdays and Thursdays.
The main course webpage is here; this
page will be used for things specific to my sections. In particular,
I will post quizzes and worksheets handed out in class. Quizzes,
worksheets, and answer keys are all PDFs. If you are on a Mac, these
should open automatically; Windows users may need to download Adobe Reader if it is
not already installed.
Worksheets
- 28 August 2007: Worksheet 1: Review
of 1A
- 30 August 2007: Worksheet 2: Integration
by Parts and Trigonometry
- 4 September 2007: Worksheet 3:
Trigonometric Integration
Typo: in 2(b), y=4√x should read y=4√2.
- 6 September 2007: Worksheet 4:
Integration by Parts
- 11 September 2007: Worksheet 5: Smorgasbord
of Integration, Worksheet 6: Approximate Integration
- 13 September 2007: Worksheet 7:
Approximate and Improper Integration
- 18 September 2007: Worksheet 8: Improper
Integration and Arc Length
- 20 September 2007: Worksheet 9: Surface Area
of a Surface of Revolution
- On 25 September 2007, we did not have a worksheet. Rather, we spent
most of the class reviewing the midterm from the previous day, and
finished by playing a sequence guessing game proposed by Julian Gilbey:
One player, let's call her Alice, thinks
of a sequence, and tells the rest of the players the first two terms.
Another player, Bob, say, thinks of a sequence that starts with those
two numbers, and announces the third term from his sequence. Alice
then tries to guess Bob's sequence. If she can, then players
continue guessing the third term of Alice's sequence. But, if Alice
cannot guess Bob's sequence, whereas Claire (another player) can,
then Alice must tell everyone the third term of her sequence, and the
game continues. If at any time Bob (or any other player) correctly
guesses
the next term of Alice's sequence, then Alice invites Bob to give the rule
for the original sequence. If Bob is right, he wins, and it's now his
turn to think of the main sequence (replacing Alice).
- 27 September 2007: Worksheet 10: Limits
of Sequences
- 2 October 2007: Worksheet 11: Infinite
Series
- 4 October 2007: Worksheet 12: (More)
Infinite Series
- 9 October 2007: Worksheet 13: Comparison
Tests, Alternating Series, etc.
- 11 October 2007: Worksheet 14: Ratio
Test
- 16 October 2007: Worksheet 15: Power
Series
- 18 October 2007: Worksheet 16: Manipulating
Power Series
- 23 October 2007: Worksheet 17: Taylor
Series
- 25 October 2007: Worksheet 18: More Taylor
Series
- 1 November 2007: Worksheet 19: Introducing
Differential Equations
- 6 November 2007: Worksheet 20: Separable
Differential Equations
- 8 November 2007: Worksheet 21:
Separable Word Problems
- 13 November 2007: Worksheet 22: Linear Word
Problems
- 15 November 2007: Worksheet 23: Linear
homogeneous second-order differential equations
- 20 November 2007: Worksheet 24: Some
Mathematics
- 27 November 2007: Worksheet 25:
Second-order linear nonhomogeneous differential equations
- 29 November 2007: Worksheet 26:
Applications of Second-Order Differential Equations
- 4 December 2007: Worksheet 27: A short
review of series and sequences Typo: In the first problem,
"n=2" and "n=3" shoud, of course, read "x=2" and "x=3".
- 6 December 2007: Worksheet 28: Convergence
of integrals, series, and sequences
Quizes
- 30 August 2007:
- 6 September 2007:
- Section #107 Quiz
2 and answers Errata: in the
answer to problem 3 I dropped a factor of 2.
- Section #112 Quiz 2 and answers Errata: in the answer to
problem 3 I dropped a factor of 2.
- 13 September 2007:
- Section #107 Quiz 3 and answers Errata: in the answer to
problem 3 I dropped a factor of 2.
- Section #112 Quiz 3 and answers Errata: in the answer to
problem 3 I dropped a factor of 2.
- 20 September 2007:
- 27 September 2007:
- 4 October 2007:
- Section #107 Quiz 6 and answers Errata: In the
statement of question 3, I mismultiplied 5*7=21. This has been
corrected in the answer key.
- Section #112 Quiz 6 and answers Errata: In the
statement of questions 3, there is a typo: the fraction should be
3/(3n-2)(3n+1). This has been corrected in the answer key.
- 11 October 2007:
- 18 October 2007:
- 25 October 2007:
- 8 November 2007: Quiz 10 and answers
- 15 November 2007: Quiz 11 and answers Errata: In
problem 3(d), I suggest that carbon-14 decays into carbon-12. In fact, it
decays into nitrogen-14 by beta-emmision.
- 29 November 2007: Quiz 12 and answers
- 4 December 2007: Quiz 13 and answers
(Note: My blog entries and the like
are often more advanced than is expected for the class, or otherwise
extend the material in some way. I link to them here just in case
you're curious about "why" questions, rather than the standard
calculus-class "how" questions.)
For posterity's sake, TeX sources for all files are available as a
tarball here.
Last updated 14 December 2007.
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