1.1 Ordered field axioms

1.2 Well-Ordering Principle

1.3 The Completeness Axiom

1.3 The Completeness Axiom (continued)

1.4 Functions, countability, and the algebra of sets

2.1 Limits of sequences

2.2 Limit theorems

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

3.4 Uniform continuity

No class on Tuesday, July 4 (Independence Day holiday)

4.1 The derivative

4.2 Differentiability theorems

4.3 Mean Value Theorem

4.4 Monotone functions and the Inverse Function Theorem

5.1 Riemann Integral

5.2 Riemann sums

5.3 Fundamental Theorem of Calculus

5.4 Improper Riemann integration

6.1 Infinite series of real numbers: Introduction

6.2 Series with nonnegative terms

6.3 Absolute convergence

6.4 Alternating series