# Homework Solutions Real Analysis Solutions

## Math 4310. Introduction to Real Analysis. Fall 2015

### TuTh 2-3:15 pm, Dell 2 103

- Instructor: Mikhail Ershov
- Office: Kerchof 302
- e-mail: ershov
*at*virginia*dot*edu - Office hours: Tue 3:30-4:30 or 5-6 (changes from week to week; will be announced in class), Wed 2:30-3:15 and 4:45-5:30 and by APPOINTMENT

**Text:**

*Principles of Mathematical Analysis*, Walter Rudin, third edition

### SYLLABUS

### Final info

### Midterms

### Homework assignments:

- Homework #1 (due on Thursday, September 3rd)
- Homework #2 (due on Thursday, September 10th) Solutions
- Homework #3 (due on Thursday, September 17th) Solutions
- Homework #4 (due on Thursday, September 24th) Solutions
- Homework #5 (due on Thursday, October 1st) Solutions
- Homework #6 (due on Thursday, October 15th) Solutions
- Homework #7 (due on Thursday, October 22nd) Solutions
- Homework #8 (due on Thursday, October 29th) Solutions
- Homework #9 (due on Thursday, November 5th) Solutions
- Homework #10 (due on Thursday, November 12th) Solutions
- Homework #11 (due on Thursday, December 3rd) Solutions
- Homework #12 (not due) Solutions

## Solutions!

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## Apostol, Mathematical Analysis, 2/e (Shin-Yi Lee)

Ch1 - The Real and Complex Number SystemsCh2 - Some Basic Notions of Set Theory

Ch3 - Elements of Point Set Topology

Ch4 - Limits and Continuity

Ch5 - Derivatives

Ch6 - Functions of Bounded Variation and Rectifiable Curves

Ch7 - The Riemann-Stieltjes Integral

Ch8 - Infinite Series And Infinite Products

Ch9 - Sequences of Functions

Addon:

Something around the number e

Limit sup and limit inf

## Rudin, Principles of Mathematical Analysis, 3/e (Meng-Gen Tsai)

Total Solution(Supported by wwli; he is a good guy :)Ch1 - The Real and Complex Number Systems (not completed)

Ch2 - Basic Topology (Nov 22, 2003)

Ch3 - Numerical Sequences and Series (not completed)

Ch4 - Continuity (not completed)

Ch5 - Differentiation (not completed)

Ch6 - The Riemann-Stieltjes Integral (not completed)

## Bartle, The Elements of Real Analysis, 2/e (Meng-Gen Tsai)

8.beta## Solutions of Admission Exams

1. National Chung Cheng University Admission Exam for Advanced Calculus, 1998 (Meng-Gen Tsai)## Solutions of Mathematical Analysis of Algorithm

(Well, the following 9 homeworks are not completed.)Homework #1 (Problems) (Due to servon's comment, the solution of Problem 2 is wrong.)

Homework #2

Homework #3

Homework #4

Homework #5

Homework #6

Homework #7

Homework #8

Homework #9

Mirror: [http://plover.twbbs.org][http://www.csie.ntu.edu.tw/~b89089/]

Maintainer: Tsai

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