preparation

Mon Sep 4

• Start in on Stewart, come ready to talk about what you've read, especially what is unfamiliar or difficult.

Wed Sep 6

• Trig. Read through, and do some exercises from, the relevant appendix.
• Misc. info related to Wednesday's class:
  • See here for an intro to other trig functions.
  • For more on the history of \( \pi \) as both the circumference and area constant of a circle, see the article "Circular Reasoning" by David Richeson in The Best Writing on Mathematics available on my reserve shelf in the library. (Fun fact: also in that book is an article by Viktor Blasjo, former math fellow at Marlboro.)

Fri Sep 8

• Read 2.1: The Tangent and Velocity Problems and try Exercise 2.1.4 "The point \(P(0.5,2)\) lies on the curve \( y = 1/x \)...". Bonus: use the method of limits that we played with for \( y = x^2 \) to prove that your guess for part b is correct (or incorrect!).

Mon Sep 11

• There is an assignment due tomorrow. Make sure that you've had a good go at it so you can ask in class if you are stuck anywhere. If you're on top of it, there's Wednesday's prep to keep you entertained.

Wed Sep 13

• Read 2.2 and 2.3, attempting some exercises.
• Topical reading:
  • Hurricane Sandy Meets Mathematics
  • Forecasts have done a good job predicting Irma's shifting path

Fri Sep 15

• Read 2.4 on the epsilon-delta definition of a limit.
• (You might also want to start on Monday's prep, which covers two sections.)

Mon Sep 18

• Read 2.5 (Continuity) and 2.6 (Limits at Infinity and Asymptotes). We'll declare this the end of the chapter for homework purposes and split the material on differentiation from Chapter 2 and all of Chapter 3 into two.

Wed Sep 20

• Read 2.7 (Tangents, Velocities and other Rates of Change)
• (Q2.7.9a in my ed): If \( F(x) = x^3 - 5x + 1 \), find \( F'(1) \) [using the limit definition of a derivative] and use it to find and equation of the tangent line to the curve \( y = x^3 - 5x + 1 \) at the point \( (1, -3) \).

Fri Sep 22

• Make sure you have attempted the assignment that is due on Sunday and come to class with any questions you have.

Mon Sep 25

• Here are the two readings I mentioned on Friday:
  • A Mathematician's Lament by Paul Lockhart. Look at least the first few pages musing on what music or art would look like at school if it were taught like math and the "honest" course catalogue on the last couple of pages. How does it match (and not match) your own experiences? (I actually recommend the whole thing.)
  • A Mathematician's Apology by G.H. Hardy. No need to get into it unless you feel the urge (and please bear in mind the ambivalency I expressed in class), but Sections 10 - 13 are the ones relevant to the proof we saw in class (and 13 is the one that contains it).

Wed Sep 27

• Read 2.8 and 2.9 on derivatives.
• Questions 1-13 of 2.9 in my book are all geometric interpretations of derivatives. Work through these ready to discuss them in class (no need to write up answers, but have good enough notes to talk about them).

Fri Sep 29

• Read 3.1 to 3.3 (derivatives of polynomials, exponential functions, products and quotients, and some applications to science).

Mon Oct 2

• Have worked on the assignment due tomorrow and come with any questions. In particular, be ready to talk about what topic you've chosen for the last question, and why. (Also feel free to get started on Wednesday's prep.)

Wed Oct 4

• 3.4 and 3.5: Differentiating trig functions and the chain rule.

Fri Oct 6

• 3.6: Implicit Differentiation.
• Have started work on the assignment due on Sunday.

Mon Oct 9

• 3.7: Higher derivatives

Wed Oct 11

• 3.10: Related Rates.
• Browse the rest of Chapter 3 to get a sense of what we're skipping (for now).

Fri Oct 13

• Misc Day!
  • St. Andrews bios of Cardano and Galois. (These are the at the most restrained end of the stories, so you can probably bank on anything lurid here being true.)
  • Guns Plus Galois Equals the Real Good Will Hunting is, um, less concerned with scholarship.
  • Bell's Men of Mathematics, the source of many of the looser interpretations of fact, is in the library. The fictionalization of Evariste Galois gives a nice account of what Bell says and why it doesn't pass muster as a historical account.