- What is Jazz, Mr. Armstrong?

 - My dear lady, as long as you have to ask that question, you will never know it.

Mathematical Analysis I

Fall 2007

 

 

Course: MATH 411
Time/Location of Lectures: MTh3  12:00 PM - 1:20  pm  ARC-105 (BUS)
Instructor: Eduardo V. Teixeira
Textbook: "Principles of Mathematical Analysis" by Rudin
Office Hours: Th 10:40am to 11:40am or By appointment
Final: TBA
Teaching Assistant: Jeremy Engel

 

Grading

Homework and Quizzes 100 points
Midterm Exam 1 100 points
Midterm Exam 2 100 points
Midterm Exam 3 100 points
Final Exam 300 points

 

General Syllabus

  • The real and Complex fields

  • Basic Topology - metric spaces

  • Sequence and series

  • Continuity

  • Differentiation

  • The Riemann-Stieltjes Integral

  • Sequence of functions

Midterm Exams:

 

Exam

Date Material Covered

Sample Problems
Exam I October 11th, 07

  1. Finite, Countable and Uncountable Sets

  2. Real and Complex Numbers

  3. Metric Spaces

  4. Compact Sets

  5. Sequences in Metric Spaces

 Carefully Selected Problems I

Posted, Sept 30th
Exam II November 5th, 07

  1. Series

  2. Continuity

  3. Space of Continuous functions

  4. Ascoli-Arzela Theorem

 Carefully Selected Problems II

Posted, Oct 17th 
Exam III December 6th, 07

  1. Derivative

  2. Integral

 Carefully Selected Problems III

Posted, Nov 12th  
Final December 20th, 07 *Accumulative* Previous Selection of Problems.

 

 

Homework Assignments

 

HOMEWORK I

Due date: 09/19
  1. Read Chapter 1
  2. Page 22: Problems 5, 6, 11, 13, 16, 17, 18.

HOMEWORK II

Due date: 09/21
  1. Read pages 24 to 40
  2. Page 43: Problems 2, 5, 6, 7, 9.

HOMEWORK III

Due date: 10/04
  1. Read Chapter 2
  2. Page 44: Problems 16, 17, 23, 24, 30.

HOMEWORK IV

Due date: 10/11
  1. Read pages 47 to 58
  2. Page 78: Problems 1, 3, 14, 21, 22, 24.

HOMEWORK V

Due date: 10/22
  1. Read pages 59 to 78.
  2. Page 78: Problems 6, 7, 9, 10, 11, 12.

HOMEWORK VI

Due date: 10/31
  1. Read Chapter 4 and 143 to 151.
  2. Page 99: Problems 6, 8, 20, 23, 24
  3. Page 166: Problems 9, 13.

HOMEWORK VII

Due date: 11/05
  1. Read pages 154 to 158.
  2. Page 168: Problems 15, 16, 18, 19.
  3. Sample Problems for Exam II: Problems 21, 22, 25.

HOMEWORK VIII

Due date: 11/15
  1. Read Chapter 5.
  2. Page 114: Problems 1, 3, 5, 6, 11, 13,15, 22.

HOMEWORK IX

Due date: 11/26
  1. Start reading Chapter 6.
  2. Page 119: Problems 26, 27.
  3. Sample Problems for Exam III: Problems 3, 4, 6, 7, 11,  14.

HOMEWORK X

Due date: 11/29
  1. Read (very carefully) Chapter 6.
  2. Page 138: Problems 3, 5, 7, 8, 10, 12, 15, 17.