Lectures Time & Location : | Tue & Thur 12:30 - 1:45 p.m., SMLC 352 |
Office hours: | Tue and Thur 11:00 - 11:50 a.m., and also by appointment, SMLC 212 |
Professor Info: | Anna Skripka, skripka [at] math [dot] unm [dot] edu |
Week |
Important Dates |
Chapters |
Topics |
HW Assignments |
1 |
Aug 20 (Pretest), 22 |
Chapter 1 |
Review of Advanced Calculus. |
2 |
Aug 27, 29 (HW1) |
Chapters 2, 3 |
Cardinality. Cantor set. Monotone functions. Metric spaces. |
3 |
Sep 3, 5 (HW 2)
Drop with no grade: Sep 6 |
Chapter 3 |
Normed spaces. ℓp spaces. |
|
4 |
Sep 10, 12 (HW 3) |
Chapters 3, 4 |
Open and closed sets. Relative metric. |
|
5 |
Sep 17, 19 (HW 4) |
Chapters 5, 6 |
Continuous functions. Connectedness. |
|
6 |
Sep 24, 26 (HW5) |
Chapter 7 |
Completeness. Contraction mapping principle. |
|
7 |
Oct 1, 3 |
Chapter 8 |
Compactness. Uniform continuity. |
|
8 |
Oct 8 (HW6) |
Chapter 10 |
Pointwise and uniform convergence. |
|
9 |
Oct 15, 17 (Exam on Chapters 1-8) |
Chapters 1-8 |
Review exercises. |
HW on Chapters 1-8 for grade & practice |
10 |
Oct 22, 24 |
Chapter 10 |
Interchanging limits. Series of functions. Space B(X). The Weierstrass M-test. |
|
11 |
Oct 29, 31 (HW 7) |
Chapter 11 |
Power series. Nowhere differentiable function. Weierstrass approximation theorem. |
|
12 |
Nov 5, 7 (HW 8)
Withdrawal deadline: Nov 8 |
Chapter 11 |
Approximations in C(R). Equicontinuity. Compact subsets of C(X). |
|
13 |
Nov 12, 14 (HW 9) |
Chapter 13 |
Functions of bounded variation. |
|
14 |
Nov 19, 21 (HW 10) |
Chapter 14 |
Riemann-Stieltjes integral with an increasing integrator. |
|
15 |
Nov 26 |
Chapter 14 |
Properties of Riemann-Stieltjes integrable functions. |
|
16 |
Dec 3 (HW 11), 5 |
Chapter 14 |
Riemann-Stieltjes integral with a general integrator. Review. |
|
17 |
Final Exam: Dec 12 (Thursday), 10 a.m. - noon |
Office hour: Dec 10, 12:30 - 2 pm |