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) |
|---|---|---|
| 1/22 | Course introduction | |
| 1/24 | The logical basis of mathematical statements | class notes |
| 1/27 | Sets | Section 1.1 |
| 1/29 | Functions | Section 1.2 |
| 1/31 | Algebraic and order properties of R -- PS 1 due, Quiz 1 | Section 1.3 |
| 2/3 | Mathematical induction | Section 1.4 |
| 2/5 | The least upper bound axiom | Section 1.5 |
| 2/7 | Countable and uncountable sets -- PS 2 due, Quiz 2 | class notes |
| 2/10 | Consequences of the least upper bound axiom | Section 1.5 |
| 2/12 | Sequences and limits | Section 2.1 |
| 2/14 | More on convergence of sequences -- PS 3 due, Quiz 3 | Section 2.1 |
| 2/17 | Limit theorems | Section 2.2 |
| 2/19 | Monotonic sequences | Section 2.3 |
| 2/21 | Exam I | Chapter 1, 2.1 |
| 2/24 | Sequences defined inductively | Section 2.4 |
| 2/26 | Subsequences | Section 2.5 |
| 2/28 | Bolzano-Weierstrass theorem -- PS 4 due, Quiz 4 | Sections 2.5 |
| 3/3,5,7 | Spring Break (no class) | |
| 3/10 | Limit of a function | Section 3.1 |
| 3/12 | Limit theorems for functions; other limits | Sections 3.2, 3.3 |
| 3/14 | Continuity -- PS 5 due, Quiz 5 | Section 3.4 |
| 3/17 | Intermediate value theorem | 3.5 |
| 3/19 | Extreme value theorem | Section 3.5 |
| 3/21 | Uniform continuity -- PS 6 due, Quiz 6 | Section 3.6 |
| 3/24 | The derivative | Section 4.1 |
| 3/26 | Derivative rules | Section 4.2 |
| 3/28 | Exam II | Rest of Chapter 2, Chapter 3. |
| 3/31 | Mean value theorem | Section 4.3 |
| 4/2 | Consequences of the MVT | Section 4.3 |
| 4/4 | The Cantor set and function -- PS 7 due, Quiz 7 | class notes |
| 4/7 | Definition of the definite integral | Section 5.1 |
| 4/9 | Properties of integrals | Section 5.2 |
| 4/11 | When is a function integrable? -- PS 8 due, Quiz 8 | Section 5.3 |
| 4/14 | The Fundamental Theorem of Calculus | Section 5.4 |
| 4/16 | Spare day | |
| 4/18,21 | Easter Break (no class) | |
| 4/23 | Infinite series | Section 6.1 |
| 4/25 | Convergence tests -- PS 9 due, Quiz 9 | Section 6.1 |
| 4/28 | Absolute convergence | Section 6.2 |
| 4/30 | Power series | Section 6.3 |
| 5/2 | Exam III | Chapters 4, 5, Section 6.1 |
| 5/5 | Course wrap-up | Section 6.3 |
Final Exam for this course will be given at 8:00am on Friday, May 9.
Last modified: April 8, 2014