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) |
|---|---|---|
| 1/23 | Course introduction | |
| 1/25 | Sets and functions | Sections 1.1, 1.2 |
| 1/28 | One-to-one and onto functions | Section 1.2 |
| 1/30 | Algebraic and order properties of R | Section 1.3 |
| 2/1 | Mathematical induction -- PS 1 due, Quiz 1 | Section 1.4 |
| 2/4 | The least upper bound axiom | Section 1.5 |
| 2/6 | Consequences of the least upper bound axiom | Section 1.5 |
| 2/8 | Countable and uncountable sets -- PS 2 due, Quiz 2 | class notes |
| 2/11 | Sequences and limits | Section 2.1 |
| 2/13 | More on convergence of sequences | Section 2.1 |
| 2/15 | Limit theorems -- PS 3 due, Quiz 3 | Section 2.2 |
| 2/18 | Monotonic sequences | Section 2.3 |
| 2/20 | Sequences defined inductively | Section 2.4 |
| 2/22 | Exam I | Chapter 1, 2.1. |
| 2/25 | Subsequences | Section 2.5 |
| 2/27 | Bolzano-Weierstrass theorem | Sections 2.5 |
| 3/1 | Cauchy sequences -- PS 4 due, Quiz 4 | Sections 2.6, 2.7 |
| 3/4,6,8 | Spring Break (no class) | |
| 3/11 | Limit of a function | Section 3.1 |
| 3/13 | Limit theorems for functions; other limits | Sections 3.2, 3.3 |
| 3/15 | Continuity -- PS 5 due, Quiz 5 | Section 3.4 |
| 3/18 | Intermediate value theorem | 3.5 |
| 3/20 | Extreme value theorem | Section 3.5 |
| 3/22 | Uniform continuity -- PS 6 due, Quiz 6 | Section 3.6 |
| 3/25 | The derivative | Section 4.1 |
| 3/27 | Derivative rules | Section 4.2 |
| 3/29,4/1 | Easter Break (no class) | |
| 4/3 | Mean value theorem | Section 4.3 |
| 4/5 | Exam II | Rest of Chapter 2, Chapter 3. |
| 4/8 | Consequences of the MVT | Section 4.3 |
| 4/10 | The Cantor set and function | class notes |
| 4/12 | Definition of the definite integral -- PS 7 due, Quiz 7 | Section 5.1 |
| 4/15 | Properties of integrals | Section 5.2 |
| 4/17 | When is a function integrable? | Section 5.3 |
| 4/19 | The Fundamental Theorem of Calculus -- PS 8 due, Quiz 8 | Section 5.4 |
| 4/22 | Spare day | |
| 4/24 | Infinite series | Section 6.1 |
| 4/26 | Convergence tests -- PS 9 due, Quiz 9 | Section 6.1 |
| 4/29 | Absolute convergence | Section 6.2 |
| 5/1 | Power series | Section 6.3 |
| 5/3 | Exam III | Chapters 4, 5, Section 6.1 |
| 5/6 | Course wrap-up | Section 6.3 |
Final Exam for this course will be given at 3:00pm on Wednesday, May 15.
Last modified: February 18, 2013