Analysis II, Fall '11 (114)

"They that can give up essential liberty to obtain a little temporary safety
deserve neither liberty nor safety" — Benjamin Franklin. (1706-1790)

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Week 1

Week 2

Week 3

Monday, Sep 5
☀ No classes — Labor Day
Wednesday, Sep 7
§9.6: 19abcde, 21.
◊ Look up binormal vector and TNB frame.
Friday, Sep 9
§9.6: 28, 30.

Week 4

Week 5

Week 6

Monday, Sept 26 — Kennedy-Nixon debate: the first televised presidential debate.
Wednesday, Sept 28
§ 10.2: 6, 7, 10c, LA: 16, 17
¤ See Fun with Functions in the notes.
Friday, Sept 30
§ 10.2: 17
◊ Extra Fun for Snowy Days.
1. Show: \(f(x) = x^{1/3}\) is continuous on \([0,1]\), but does not satisfy a Lipschitz condition on \([0, 1]\).
2. For which of the following subsets of \(\mathbb{R}^2\) does the function \(F(x,y)=x\sqrt{y}\) satisfy a Lipschitz condition?
  1. \(D = \{\|(x,y)\| < 1\}\)
  2. \(S = \{1 < x,y < 4 \}\)
  3. \(A = \{1 < \|(x,y)\| < 4 \}\)
  4. \(V = \{1 < x < 4 \}\)
  5. \(H = \{1 < y < 4 \}\)

Week 7

Monday, Oct 3
§ 10.3: 1, 5, 10
Wednesday, Oct 5
§10.3: 11
◊ Solve the DE: \(\left(x+\dfrac{y}{x^2+y^2}\right)dx+\left(y-\dfrac{x}{x^2+y^2}\right)dy=0\) (Hint: It might be exact.)
Friday, Oct 7
§10.4: 1, 3, 5, LA 6

Week 8

Week 9

Monday, Oct 17
§10.6: 1, 3, 6
Wednesday, Oct 19
§10.6: 7, 9, 13a, 17
Friday, Oct 21
¤ Work day — catch up on homework you missed while studying for the Stat comp.

Week 10

Week 11

Week 12 ∇ Daylight Saving Time ends.

Week 13

Week 14

Week 15 ♘ (This Week)

Monday, Nov 28
◊ Exercises:
1. Prove: If \(\{E_n\}\) is a countable collection of sets with \(\mu(E_n)=0\), then \(\displaystyle \mu\left(\bigcup_{k=1}^\infty E_k\right) = 0. \)
2. Prove: If \(\{E_n\}\) is an increasing sequence of measurable sets \( (E_1\subset E_2 \subset E_3 \cdots )\), then \(\displaystyle \mu\left(\bigcup_{k=1}^\infty E_k\right) = \lim_{n\to\infty} \mu(E_n). \)
Wednesday, Nov 30
◊ General Lebesgue Measure
Friday, Dec 2
◊ General Lebesgue Measure

Week 16

Final Exam (Week 17) ♘ (This Week)

Last modified: Wednesday, 01-Feb-2023 08:32:12 EST

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