MATH 411 Outline and Homework

Math 411: Advanced Calculus II
Outline, Spring 2007

Reading assignments should be completed before the class after they are assigned. Problems assigned on Monday are due Friday of the same week; problems assigned Wednesday and Friday are due the Friday of the following week.

This site will be updated more or less weekly throughout the semester. In general, I will try to post assignments for the upcoming week by the previous Friday.

Class Date	Written Assignment Due Date	Topics and Assignment
8 January	12 January	Motivating questions Read: 4.1, 4.2 Do: exercise 1
10 January	19 January	4.2 Do: 4.2.1, 4.2.2, 4.2.4
12 January	19 January	4.2 Limits of functions Read 4.3 Do: 4.2.7, 4.2.8
15 January		MLK, Jr. Day --no class
17 January	26 January	4.3 Continuity Read: 4.4 Do: 4.3.9, 4.3.11
19 January	26 January	4.4 Uniform continuity Read: 4.5 Do: 4.4.6, 4.4.3
22 January		SNOW DAY
24 January	2 February	4.4 Do: 4.4.11, 4.4.13 Read: 4.5
26 January	2 February	4.5 IVT Do: 4.5.1, 4.5.3, 4.5.7 Read: 4.6
29 January	*	4.6 no new problems--we will work through the 4.6 set in class on Wednesday.
31 January	9 February	4.6, review of chapter 4 Do: All problems from 4.6 (most of this will be writing up results from class) To hand in do: 4.6.6-4.6.10 Read: 5.1, 5.2
2 February	9 February	5.1 questions about derivatives 5.2 rudimentary facts about derivatives Do: 5.2.1, 5.2.3
5 February	9 February	5.2 derivative rules re-proved Do: 5.2.6, 5.2.8
7 February		SNOW DAY
9 February	exam 1 in class	Read 5.3
12 February		No class, in honor of COMAP
14 February		SNOW DAY
16 February	23 February	5.2 Darboux's theorem 5.3 Rolle's theorem Do: 5.2.6, 5.2.8, 5.3.1, 5.3.2, 5.3.3
19 February	23 February	5.3 MVT, general MVT Ponder: 5.3.4, 5.3.11 Do: 5.3.5
21 February		sick day
23 February		5.3 L'Hopital's rules 5.4: a favourite function (continuous but nowhere differentiable) meditation on themes to date
26 February	exam 2 distributed	6.1 why sequences (and series) of functions are interesting and useful 6.2 uniform convergence of sequences of functions take-home midterm distributed by e-mail (chapters 4 and 5)
28 February		6.2 Cauchy Criterion for uniform convergence
2 March		6.2 more about uniform convergence
5- 9 March		Spring break; no class
12 March	March 30	6.2 an analog of Bolzano-Weierstrauss for sequences of functions Do: 6.2.8 Ponder: 6.2.13, 6.2.14, 6.2.15, 6.2.16
14 March		6.3 relevance of uniform convergence for differentiation
16 March		no class
19 March		6.4 series of functions CC for uniform convergence of series
21 March		6.4 Weierstauss M-Test 6.5 Power series Do: 6.5.1, 6.5.2, 6.5.3
23 March	exam 2 due	6.5 Abel's Theorem
26 March		6.6 Taylor series intro to integration
28 March		sick day
30 March		Generalizing Bolzano-Weierstauss: bounded sequences of functions The Arzela-Acsoli theorem
2 April		6.6 Lagrange Remainder Theorem (work through 6.6.1-6.6.12)
4 April		7.2 definition of the Riemann integral, criteria for RI
6 April		7.3 discontinuity and the RI Practice exam
9 April	exam 3 in class	third mid-term in class (covering chapter 6 and supporting topics)
11 April		7.4 properties of the RI
13 April		7.4 uniform convergence and the RI
16 April		7.5 FTOC
18 April		7.5 FTOC
20 April		7.6 Lebesgue's criterion for Riemann integrability
23 April		catch up/selected extension topics final exams distributed in class
25 April		selected extension topics
27 April		course summary, evaluations
1 May		final exams due by 6 pm in Roop 122. Analysis banquet in Roop 103, starting 6:15