| Class Number |
Date |
Sections in Abbott |
Brief Description |
| 1 |
Friday, 8/31 |
1.1 |
Introduction, Historical Context, What are the Real Numbers? |
| 2 |
Monday, 9/3 |
1.1 - 1.2 |
Finding "Holes" in the Real Numbers, Ordered Fields |
| 3 |
Wednesday, 9/5 |
1.3 |
The Completeness Axiom, Supremums and Infimums |
| 4 |
Friday, 9/7 |
1.4 |
Archimedean Property, Density of Q in R, Existence of Square Roots |
| 5 |
Monday, 9/10 |
1.4 - 1.5 |
Nested Interval Theorem, Countable Sets |
| 6 |
Wednesday, 9/12 |
1.5 |
Countable and Uncountable Sets |
| 7 |
Friday, 9/14 |
- |
The Absolute Value Function, The Triangle Inequality, Introduction to Sequences |
| 8 |
Monday, 9/17 |
2.2 |
Convergence of Sequences, Uniqueness of Limits |
| 9 |
Wednesday, 9/19 |
2.3 |
Algebraic Properties of Limits |
| 10 |
Friday, 9/21 |
2.3 - 2.4 |
Order Properties of Limits, Monotone Convergence Theorem |
| 11 |
Monday, 9/24 |
- |
Infinite Limits |
| 12 |
Wednesday, 9/26 |
2.5 |
Subsequences, Bolzano-Weierstrass |
| 13 |
Friday, 9/28 |
2.6 |
Cauchy Sequences |
| 14 |
Monday, 10/1 |
2.7 |
Infinite Series |
| 15 |
Wednesday, 10/3 |
2.7 |
Series Convergence Tests |
| 16 |
Friday, 10/5 |
2.7 |
Absolute Convergence, Rearrangements |
| 17 |
Monday, 10/8 |
- |
First Exam |
| 18 |
Wednesday, 10/10 |
3.1 - 3.2 |
Interior Points, Closure Points, Limit Points |
| 19 |
Friday, 10/12 |
3.2 |
Open and Closed Subsets of R |
| 20 |
Monday, 10/15 |
3.1, 3.3 |
The Cantor Set, Compact Sets |
| 21 |
Wednesday, 10/17 |
3.3 |
Compact Sets, Heine-Borel |
| 22 |
Friday, 10/19 |
4.1 - 4.2 |
Equivalents of Compactness, Functions and Limits |
| - |
- |
- |
Fall Break |
| 23 |
Monday, 10/29 |
4.2 |
Limits of Functions |
| 24 |
Wednesday, 10/31 |
4.3 |
Continuity |
| 25 |
Friday, 11/2 |
4.4 |
Extreme Value Theorem, Uniform Continuity |
| 26 |
Monday, 11/5 |
4.4 - 4.5 |
Uniform Continuity on Compact Sets, Intermediate Value Theorem |
| 27 |
Wednesday, 11/7 |
5.2 |
Differentiability |
| 28 |
Friday, 11/9 |
5.3 |
Mean Value Theorem and Consequences |
| 29 |
Monday, 11/12 |
7.1 - 7.2 |
The Riemann Integral |
| 30 |
Wednesday, 11/14 |
7.2 |
Riemann Integrable Functions |
| 31 |
Friday, 11/16 |
7.3 - 7.4 |
Riemann Integrable Functions, Properties of the Integral |
| 32 |
Monday, 11/19 |
- |
Second Exam |
| 33 |
Wednesday, 11/21 |
7.5 |
The Fundamental Theorem of Calculus |
| - |
- |
- |
Thanksgiving Break |
| 34 |
Monday, 11/26 |
6.1 - 6.2 |
Sequences of Functions, Pointwise Convergence |
| 35 |
Wednesday, 11/28 |
6.2 |
Uniform Convergence |
| 36 |
Friday, 11/30 |
6.2, 7.4 |
Properties of Uniform Convergence |
| 37 |
Monday, 12/3 |
6.3 - 6.4 |
Properties of Uniform Convergnece, Series of Functions |
| 38 |
Wednesday, 12/5 |
6.4 - 6.5 |
Weierstrass M-Test, Power Series |
| 39 |
Friday, 12/7 |
6.5- 6.6 |
Power Series, Taylor Series |
| 40 |
Monday, 12/10 |
6.6 |
Taylor Series, Lagrange Remainder Theorem |
| 41 |
Wednesday, 12/12 |
6.6 |
Functions and Taylor Series, The Complex Numbers |
| 42 |
Friday, 12/14 |
- |
Complex Numbers and Power Series |