Introduction to Real Analysis (5210), spring 2010

Final Exam:-The Final will take place on Thursday 5/6 from 1 to 3 pm in LCB 219. No books or notes allowed (nor calculators...)

-The Final will be comprehensive. Namely, it will cover (1) in Haaser-Sullivan: chapters 2, 4 (except 4.5 and 4.7), 5 (except 5.3), 7 (sections 1-5 and 8 + 8.3), and 11 (sections 1-4, 6,7). (2) in Royden: chapters 3 and 4 (except 4.5). (3) in Strichartz: p. 298-308 and 532-535 (handouts).

-The last office hours for this class will be Wednesday 5/5 from 2-4 pm in JWB 209.

Homework assignment for this week:

- Solutions for homework #12

-Week 14 (4/19-4/23): (due Wednesday 4/28).

-Read sections 11.1-11.4 and 11.6 of Haaser-Sullivan.

-Do problems #1-8 on p. 288 and 1-4 on p. 292.

- Solutions for homework #11

-Week 13 (4/12-4/16): (due Wednesday 4/21).

-Read p. 298-307 of Strichartz.

-Do problems #1,2,3,7,13,15 on p. 307-308.

- Solutions for homework #10

-Week 12 (4/5-4/9): (due Wednesday 4/14).

-Read sections 7.4, 7.5 and 8.3 of Haaser-Sullivan.

-Do problems #1-8 on p. 171.

- Solutions for Midterm #2

- Solutions for homework #9

-Week 11 (3/29-4/2): (due Tuesday 4/6).

-The second Midterm Exam will take place Wednesday 4/7. It will cover section 5.2 of Haaser-Sullivan (Banach fixed-point theorem) and chapters 3 and 4 of Royden, except 4.5 (Lebesgue measure and integral).

-Read sections 4.1-4.4 of Royden.

-Do problems #3,4,5,7,15,16 in ch. 4 of Royden. Optional problem: #2.

- Solutions for homework #8

-Weeks 9-10 (3/8-3/17): (due Wednesday 3/31).

-As announced in class, there will be no class on Friday 3/19.

-Read sections 3.6-4.2 of Royden.

-Do problems #20,21,22,24,25,28,29 in ch.3 and #1 in ch.4 of Royden. Optional problems: #30-31.

- Solutions for homework #7

-Week 8 (3/1-3/5): (due Friday 3/12).

-Read sections 3.1-3.5 of Royden.

-Do problems #1,2,3,4,6,7,10,11,14,17,18 in Ch.3 of Royden.

- Solutions for homework #6

-Week 7 (2/22-2/26): (due Wednesday 3/3).

-Read sections 5.1-5.5 (5.3 is for information only).

-Do problems #1-6 on p. 96.

- Solutions for homework #5

-Week 6 (2/15-2/19): (due Wednesday 2/24).

-Read sections 4.10-4.11.

-Do problems #4 on p. 88 and #1,2,3,4,6 on p. 91-92. Optional problems: #8,11 p. 92.

- Solutions for Midterm Exam #1

- Solutions for homework #4

-Week 5 (2/8-2/12): (due Tuesday 2/16).

-Read sections 4.8-4.9.

-Do problems #1,2,4,7,8 on p. 81 and # 1,2,3,7,8 on p. 84.

_The first Midterm Exam will take place Wednesday 2/17 and will cover all sections from which homework was assigned, namely 2.2-2.5, 4.2, 4.3, 4.4, 4.6, 4.8, 4.9, 7.2-7.4 and 11.2.

- Solutions for homework #3

-Week 4 (2/1-2/5): (due Wednesday 2/10).

-Read sections 4.3-4.7 (4.5 and 4.7 are for information only).

-Do problems #2,3,5,6,7,8 p.64, 7 p.68, 4 p. 75 and 14 p. 76 (and in the latter give a counter-example if f is only continuous).

- Solutions for homework #2

-Weeks 2-3 (1/19-1/29): (due Wednesday 2/3).

-Review sections 3.1-3.4, especially if you are not familiar with infinite dimensional vector spaces (you don't need to go through the proofs).

-Read sections 4.1, 4.2, 7.1-7.4, 11.1 and 11.2. Do problems #8 on p. 60, 4 p. 160, 2 p. 165, 4 p. 282, and these problems.

- Solutions for homework #1

-Week 1 (1/11-1/15): This first assignment will be due Friday 1/22. Read chapter 2, do as many problems as you can/want, and hand in #3-6 on p.25, 11 on p.26, and 1,4,7 on p.34. Optional problems: 5,6 p. 37 (sometimes known as Bolzano-Weierstrass theorem).

-Week 0: Review basics from Foundations of Analysis I-II and read chapter 1 of the textbook.

Lectures: Mondays, Tuesdays, Wednesdays and Fridays 2:00-2:50 pm in LCB 219.

Material: The textbook is Real Analysis by N.B. Haaser and J.A. Sullivan, Dover Publications. We will be roughly covering chapters 2--8 and 11, with possible additional topics depending on time and motivation. Note that for the Lebesgue integral we will use another reference to be specified later (the treatment of this topic in ch. 6 of the book is not standard and should only be used with caution).

Homework: Assignments will be given on-line each week, usually by Wednesday, and will be due in class the following Wednesday.

Exams: There will be two Midterm exams and a Final. The Midterm exams will take place during class time on Wednesday 2/17 and Wednesday 4/7. The Final will take place on Thursday 5/6 from 1 to 3 pm in LCB 219 (standard University calendar).

Grading: Homework, (the 2 Midterms) and the Final will each count for a third of the final grade.

Office hours: Tuesdays 3-4 pm in my office, JWB 209. If you can't make it, write me an email at paupert@math.utah.edu, or call 801-581-6846 to schedule an appointment.