3210 Foundations of Analysis I - Summer 2006

(Tentative) Course Schedule


WEEK OF JUNE 7
1.1 Ordered field axioms
1.2 Well-Ordering Principle
1.3 The Completeness Axiom

WEEK OF JUNE 12
1.3 The Completeness Axiom (continued)
1.4 Functions, countability, and the algebra of sets
2.1 Limits of sequences
2.2 Limit theorems

WEEK OF JUNE 19
2.3 Bolzano-Weierstrass Theorem
2.4 Cauchy sequences
2.5 Limits supremum and infimum
3.1 Two-sided limits
3.2 One-sided limits and limits at infinity

WEEK OF JUNE 26
REVIEW for Midterm # 1 - Tuesday, June 27
Midterm # 1 - Wednesday, June 28
3.3 Continuity
3.4 Uniform continuity

WEEK OF JULY 3
No class on Tuesday, July 4 (Independence Day holiday)

4.1 The derivative
4.2 Differentiability theorems

WEEK OF JULY 10
4.3 Mean Value Theorem
4.4 Monotone functions and the Inverse Function Theorem
5.1 Riemann Integral
REVIEW for Midterm # 2 - Friday, July 14

WEEK OF JULY 17
5.2 Riemann sums
Midterm # 2 - Tuesday, July 18
5.3 Fundamental Theorem of Calculus
5.4 Improper Riemann integration
6.1 Infinite series of real numbers: Introduction

WEEK OF JULY 24
No class on Monday, July 24 (Pioneer Day holiday)
6.2 Series with nonnegative terms
6.3 Absolute convergence
6.4 Alternating series
REVIEW for Final Exam - Friday, July 28

WEEK OF JULY 31
7.1 Uniform convergence of sequences
FINAL EXAM - Tuesday, August 1
Last day of classes is Wednesday, August 2