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