As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.
| Date | Class Topic | Reading (from Bilodeau, Thie, Keough) |
|---|---|---|
| 1/26 | Course introduction | |
| 1/28 | Sets and functions | Sections 1.1, 1.2 |
| 1/31 | One-to-one and onto functions | Section 1.2 |
| 2/2 | Algebraic and order properties of R | Section 1.3 |
| 2/4 | The positive integers and mathematical induction | Section 1.4 |
| 2/7 | The least upper bound axiom | Section 1.5 |
| 2/9 | Consequences of the least upper bound axiom | Section 1.5 |
| 2/11 | Countable and uncountable sets | class notes |
| 2/14 | Sequences and limits | Section 2.1 |
| 2/16 | More on convergence of sequences | Section 2.1 |
| 2/18 | Limit theorems | Section 2.2 |
| 2/21 | Monotonic sequences | Section 2.3 |
| 2/23 | Sequences defined inductively | Section 2.4 |
| 2/25 | Exam I | Chapter 1, 2.1. |
| 2/28 | Subsequences | Section 2.5 |
| 3/2 | Bolzano-Weierstrass theorem | Sections 2.5 |
| 3/4 | Cauchy sequences; infinite limits | Sections 2.6, 2.7 |
| 3/7,9,11 | Spring Break (no class) | |
| 3/14 | Limit of a function | Section 3.1 |
| 3/16 | Limit theorems for functions; other limits | Sections 3.2, 3.3 |
| 3/18 | Continuity | Section 3.4 |
| 3/21 | Intermediate value theorem | 3.5 |
| 3/23 | Extreme value theorem | Section 3.5 |
| 3/25 | Uniform continuity | Section 3.6 |
| 3/28 | The derivative | Section 4.1 |
| 3/30 | Derivative rules | Section 4.2 |
| 4/1 | Exam II | Rest of Chapter 2, Chapter 3. |
| 4/4 | Mean value theorem | Section 4.3 |
| 4/6 | Consequences of the MVT | Section 4.3 |
| 4/8 | The Cantor set and function | class notes |
| 4/11 | Definition of the definite integral | Section 5.1 |
| 4/13 | Properties of integrals | Section 5.2 |
| 4/15 | When is a function integrable? | Section 5.3 |
| 4/18 | The Fundamental Theorem of Calculus | Section 5.4 |
| 4/20 | Spare day | |
| 4/22,25 | Easter Break (no class) | |
| 4/27 | Infinite series | Section 6.1 |
| 4/29 | Convergence tests | Section 6.1 |
| 5/2 | Absolute convergence | Section 6.2 |
| 5/4 | Power series | Section 6.3 |
| 5/6 | Exam III | Chapters 4, 5, Section 6.1 |
| 5/9 | Course wrap-up | Section 6.3 |
Final Exam for this course will be given: Tuesday, May 17, 2011, 3:00 - 5:30pm, in Swords 359.
Last modified: April 13, 2011