Analysis (Fall, 2009)

MATH 415


Contact:

Professor: Dr. Carl Toews
E-mail: toewsc * duq.edu
Office: College Hall 418
Hours: W 12:00-3:00 p.m., or by appointment


Course Information :

Syllabus

Homework

Note: problems in red will be payed particular attention when I grade.
Week Date Topics Sections Problems Due Date Solutions
Week 1 Aug 24 - Aug 28 Preliminaries
1.2 1, 2, 3, 5, 8, 10 Aug 31 1.2
Week 2 Aug 31 - Sep 4 Axiom of Completeness
Consequences of AoC
1.3
1.4
1, 2, 3, 4, 5, 6, 7, 9
1, 2, 3 , 4, 6, 7 , 8
Sep 9
Week 3 Sep 9 - Sep 11 Cantor's Theorem 1.5 1, 2, 3, 5, 6 , 7, 8, 9 Sep 14 Chapter 1 solutions
Week 4 Sep 21 - Sep 25 Rearrangements
Sequences
Limit Theorems
2.1
2.2
2.3
--
1, 2, 3, 7, 8
1, 4, 7, 8, 11
Sep 28 Chapter 2 solutions
Week 5 Sep 28 - Oct 2 Monotone convergence 2.4 1, 2, 4 , 5 Oct 5 -
Week 6 Oct 5 - Oct 9 Bolzano Weierstrass
Cauchy criterion
Infinite Series
2.5
2.6
2.7
1, 4, 6
1, 2, 4, 5, 6
1, 2, 4, 5 , 7, 8
Oct 12 -
Week 7 Oct 12 - Oct 16 Double summations 2.8 1, 2, 3 Oct 14
Week 9 Nov 2 - Nov 6 Cantor Set
Open and Closed Sets
Compact Sets
3.1
3.2
3.3
--
2, 3, 5, 11, 13
1, 3, 5, 7, 9
Nov. 9
Week 10 Nov 9 - Nov 13 Functional Limits
Continuous Functions
4.2
4.3
4.4
1a,c, 8, 9
3, 4, 7, 9, 12
2, 3, 4, 6
Nov. 16