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.

- 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

- 30 August 2007:
- 6 September 2007:
- 13 September 2007:
- 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.

- Section #107 Quiz 6 and answers
- 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

- Common Errors in Undergraduate Mathematics
- If you would like to read more about approximate integration, you may want to check out the blog entry I wrote about it.
- I've also written a brief discussion about partial fraction decomposition.
- In Worksheet 15, checking the endpoints in one of the exercises
requires Stirling's Formula:
*n! ∼ (n/e)*. Here is a proof. The formula can be improved (although you don't need it to be any better for most applications):^{n}√(2πn)*n! ≈ ((n+1)/e)*. The "^{n+1}√(2π/(n+1)) (1 + 1/(12n) + O(1/n^{2}))*O(1/n*" means "something that's smaller than^{2})*C/n^2*for some constant*C*. Bender and Orszag give a complete "asymptotic expansion": a power series for*n!*in*x = 1/n*. The thing is that this power series doesn't converge for any*n*: the radius of convergence is 0. This is basically because the factorials of negative integers are infinite. - On my blog, I've posted a discussion of "the method of undetermined coefficients" in linear differential equations. It uses a fair amount of linear algebra, but nothing more.

(*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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