Wk | Date | Topics and activities | Assignments |
1 | 08/28 | Rational numbers | A construction of $\mathbf{Z}$ Note on fields |
08/30 | Ordered fields | Homework 1 and a solution | |
2 | 09/02 | The least upper bound property | |
09/04 | The field of real numbers | ||
09/06 | No Class (Dorian) | ||
3 | 09/09 | Cardinality, Euclidean structure of $\mathbf{R}^n$ | Note on $\mathbf{R}^n$ |
09/11 | Metric spaces | Note on metric topology | |
09/13 | Basic topology | Homework 2 and a solution | |
4 | 09/16 | Compactness | |
09/18 | Compactness in $\mathbb{R}^n$ | ||
09/20 | Connectedness | Homework 3 and a solution | |
5 | 09/23 | Sequences | |
09/25 | Limits | Homework 4 and a solution | |
09/27 | Subsequences and compactness | ||
6 | 09/30 | Cauchy sequences and completeness | |
10/02 | Comparison, relative rates | ||
10/04 | Monotonicity, infinite limits | ||
7 | 10/07 | Midterm 1 | Solution |
10/09 | Superior and inferior limits, series | Homework 5 and a solution | |
10/11 | Series of positive terms | ||
8 | 10/14 | Fall break | |
10/16 | The Root and Ratio tests | Homework 6 and a solution | |
10/18 | Operations on series | Euler's number $e$ | |
9 | 10/21 | Conditional convergence, rearrangement | |
10/23 | Limits of functions | ||
10/25 | Continuous functions | ||
10 | 10/28 | Continuity and compactness | Homework 7 and a solution |
10/30 | Continuity and connectednessThe Intermediate Value Theorem | ||
11/01 | Differentiability | ||
11 | 11/04 | The Chain Rule, local extrema | |
11/06 | Mean value theorems | ||
11/08 | Midterm 2 | Solution | |
12 | 11/11 | Taylor approximations | Homework 8 and a solution |
11/13 | Local behavior | Note on comparison relations | |
11/15 | Power series | Note on sequences of functions | |
13 | 11/18 | Analytic functions | |
11/20 | Riemann sums | ||
11/22 | Riemann integrals | ||
14 | 11/25 | Integrable functions | Homework 9 and a solution |
11/27 | Thanksgiving Break | ||
11/29 | Thanksgiving Break | ||
15 | 12/02 | Properties of the integral | Note on the properties of the Riemann integral |
12/04 | The Fundamental Theorem of Calculus | ||
12/06 | The exponential and logarithmic functions |