Math 4332, Section 08436 - Spring 2001

Introduction to Real Analysis (part II)

Classes: 4:00-5:30pm MW, PGH 315
Instructor: Andrew Török
Office: 672 PGH
Phone: (713) 743-3478
E-mail: torok@math.uh.edu
Office hours: see home-page

MIDTERM 3

Will be take-home. Most likely you will receive the problems on Monday, April 30, and will have to return the exam in 2-3 days.
Please let me know it this conflicts with another exam of yours.

As we advance, I am going to post the reading assignments and the homeworks.

HOMEWORKS:

More difficult problems are marked by a ^*.
You might also find an indication about what Theorems are needed for a given problem.
WARNING: please do not use arguments like "clearly", "obviously" etc. in your solutions! You might lose points if you do not motivate your steps and conclusions.

HOMEWORKS
Chapter HAND-IN (due date) Solve only, do not hand-in

6 3 (Jan. 24)
7, 8 (Jan. 31) 1, 2, 4
5, 9, 10, 11, 12, 17, 18, 19
7 1, 2 (Feb. 7)
4, 10 (Feb. 14; extended to Feb. 19)

18, 20 (Feb. 28; extended to March 5)

21, 24 (Mar. 7; extended to March 19) 3-7 (<= Thm. 7.10)
8-11, 12^*, 14, 24 (<= Thm. 7.16)
15 (<= Defn. 7.22)
13, 16, 17, 18, 19^* (<= Thm. 7.25)
20, 21, 22, 25^*, 26^* (<= Thm. 7.33)
23 (not related to any Thm.)
8.1-8.5, 8.15 1, 2, 3, 22(a) (Thm's 8.1-8.5)
19 (Thm. 8.15)
4, 5 (use power series for c, d), 6, 7, 8,
9 (compare to the Integral Test), 10, 11
9 4, 5, 6 (March 21)
17, 21 (April 11) 1-5 (<= Thm. 9.9)
8 (see 9.16-9.18)
7, 9-15 (<= Thm 9.21)
16-24 (Thm's 9.24, 9.28)
26-29 (see 9.39-9.42)
30,31: Taylor's polynomial
11 1, 2 (April 25; extended to April 30) 15, 3^*, 4-6, 8, 9, 10, 12, 14 (<= Thm. 11.33)
10, 18 (Thm. 11.35)
11 (similar to Thm. 11.42)
13, 16, 17 (>= 11.34)

HOMEWORKS
6	3 (Jan. 24) 7, 8 (Jan. 31)	1, 2, 4 5, 9, 10, 11, 12, 17, 18, 19
7	1, 2 (Feb. 7) 4, 10 (Feb. 14; extended to Feb. 19) 18, 20 (Feb. 28; extended to March 5) 21, 24 (Mar. 7; extended to March 19)	3-7 (<= Thm. 7.10) 8-11, 12^, 14, 24 (<= Thm. 7.16) 15 (<= Defn. 7.22) 13, 16, 17, 18, 19^ (<= Thm. 7.25) 20, 21, 22, 25^, 26^ (<= Thm. 7.33) 23 (not related to any Thm.)
8.1-8.5, 8.15		1, 2, 3, 22(a) (Thm's 8.1-8.5) 19 (Thm. 8.15) 4, 5 (use power series for c, d), 6, 7, 8, 9 (compare to the Integral Test), 10, 11
9	4, 5, 6 (March 21) 17, 21 (April 11)	1-5 (<= Thm. 9.9) 8 (see 9.16-9.18) 7, 9-15 (<= Thm 9.21) 16-24 (Thm's 9.24, 9.28) 26-29 (see 9.39-9.42) 30,31: Taylor's polynomial
11	1, 2 (April 25; extended to April 30)	15, 3^*, 4-6, 8, 9, 10, 12, 14 (<= Thm. 11.33) 10, 18 (Thm. 11.35) 11 (similar to Thm. 11.42) 13, 16, 17 (>= 11.34)

Last modified: August 2, 2001

Course description:

This is the second half of a two-semester course.
The prerequisite is Math 4331 (the first half, i.e. Chapters 1-5 of the textbook), or permission of the instructor.

The book we will be using this year is

Principles of Mathematical Analysis

In Fall 2000 we covered Chapters 1-5 (Real numbers, Topology, Sequences and series, Continuity, Differentiation).

In Spring 2001 we will discuss

Chapter 6 (The Riemann-Stieltjes integral),
Chapter 7 (Sequences and series of functions),
Chapter 9 (Functions of several variables) and
either
- Chapter 10 (Integration of differential forms)
- or Chapter 11 (Lebesgue integration)
(probably we will not have time for both).

Some of the topics are: integration on the real line, partial differentiation, the basic theorems of analysis (local inversion, implicit functions) and either integration on "surfaces" and Stokes' theorem, or Lebesgue integration.

The course will place a lot of emphasis on proofs. Most of the homework will be assigned from the textbook.

There will be weekly homeworks (the lowest two grades will be dropped), and the exams (open book; some might be "take home", or oral).

You can find here a very good set of web-notes for analysis on the real line (courtesy of Prof. John Orr, Univ. of Nebraska-Lincoln). Warning: it involves a lot of Java activity.

HOMEWORKS
Chapter	HAND-IN (due date)	Solve only, do not hand-in
6	3 (Jan. 24) 7, 8 (Jan. 31)	1, 2, 4 5, 9, 10, 11, 12, 17, 18, 19
7	1, 2 (Feb. 7) 4, 10 (Feb. 14; extended to Feb. 19) 18, 20 (Feb. 28; extended to March 5) 21, 24 (Mar. 7; extended to March 19)	3-7 (<= Thm. 7.10) 8-11, 12^, 14, 24 (<= Thm. 7.16) 15 (<= Defn. 7.22) 13, 16, 17, 18, 19^ (<= Thm. 7.25) 20, 21, 22, 25^, 26^ (<= Thm. 7.33) 23 (not related to any Thm.)
8.1-8.5, 8.15		1, 2, 3, 22(a) (Thm's 8.1-8.5) 19 (Thm. 8.15) 4, 5 (use power series for c, d), 6, 7, 8, 9 (compare to the Integral Test), 10, 11
9	4, 5, 6 (March 21) 17, 21 (April 11)	1-5 (<= Thm. 9.9) 8 (see 9.16-9.18) 7, 9-15 (<= Thm 9.21) 16-24 (Thm's 9.24, 9.28) 26-29 (see 9.39-9.42) 30,31: Taylor's polynomial
11	1, 2 (April 25; extended to April 30)	15, 3^*, 4-6, 8, 9, 10, 12, 14 (<= Thm. 11.33) 10, 18 (Thm. 11.35) 11 (similar to Thm. 11.42) 13, 16, 17 (>= 11.34)