Math 471: Real Analysis (graduate-level)

Fall 2019

General Information

Instructor: Chris Staecker (Personal Homepage)

Email: cstaecker@fairfield.edu

Office: BNW 16

Office Hours: M 5-6:30, T 10-11, 2-3, F 10-11 or by appointment

Textbook: Introduction to Real Analysis by Bartle & Sherbert, 4^th edition

Class Meetings: Monday 6:30-9PM

Syllabus

• Syllabus

Calendar

9/23: Homework #1 due

Section 2.1: 18 (consider a-b, then use 2.1.9), 20 (use properties of < discussed in class)
Section 2.2: 6a, 8a, 10b, 16 (see Def 2.2.7)
Section 2.3: 3, 4 (don't prove it), 7
Section 2.4: 3, 17 (you may assume 2.1.13a holds for cubes)
Section 2.5: 2, 8, 9

10/7: Homework #2 due

Section 3.1: 5ac, 6a, 11, 12 (to start, use a trick like in Example 3.1.6d), 18
(In Section 3.1, prove directly using ε's, not using tricks from 3.2)
Section 3.2: 2, 3, 6acd (use Theorem 3.2.10 for c&d), 7
Section 3.3: 2, 3 (for these, use induction to show it's monotone)
Section 3.4: 1, 4, 14, 16
Section 3.5: 1, 2a, 7 (look up the definition of "ultimately constant")

10/28: Homework #3 due

Section 4.1: 9ad, 12ab, 15
(In Section 4.1, prove directly using ε's, not using tricks from 4.2)
Section 4.2: 1 (don't need to write all the details), 5, 6
Section 4.3: 5bg
Section 5.1: 5 (prove it will be continuous), 7, 8, 13 (prove it)
Section 5.2: 3, 8 (yes- prove it)), 11

11/11: Homework #4 due

Section 5.3: 1, 5 (just do the first part), 7 (consider x - cos(x), just get error less than 10^-2), 13
Section 5.4: 2, 4, 7 (just do the second part), 15
Section 5.6: 8, 9
Section 6.1: 2, 4, 9, 13

11/25: Homework #5 due

Section 6.2: 6, 7, 13, 15
Section 6.4: 2, 8, 9 (for 8 & 9, the "remainder term" is R_n on pg 190)
Section 7.1: 2b, 4a, 5, 10, 12, 15

12/9: Homework #6 due

Section 7.2: 2, 4, 6, 7, 8, 10 (use #8), 13
Section 7.3: 10, 14
Section 7.4: 2, 6 (use Corollary 7.4.9), 9, 10

12/16: Last day of class

12/23: Homework #7 due

Section 8.1: 1, 4, 11, 14 (for #14 just do the "not uniform" part), 17
Section 8.2: 3 (prove your convergence is uniform), 4, 7
Section 9.1: 7
Section 9.4: 2, 10 (use Thm 9.4.13)
No class on this day, email or bring your assignment to the professor sometime