Tentative Schedule of Lectures
This schedule is your instructor's estimate, as of the start of the semester, of what chapter-sections of the textbook will be covered when. In addition to the dates only being estimates, there may be changes to the set of chapter-sections represented below, and there may be some detours from the book.
| week of semester |
dates | book sections | |
|---|---|---|---|
| Week 1 | M 1/11 | Section 1.1 (metric spaces: definitions and examples) begun | |
| W 1/13 | Sections 1.1 cont'd | ||
| F 1/15 | Section 1.1 concluded; Section 1.2 (metric-space topology intro) begun | ||
| Week 2 | M 1/18 | MLK Day (no class) | |
| W 1/20 | Section 1.2 cont'd | ||
| F 1/22 | Section 1.2 concluded; Section 1.3 (relative topology) begun | ||
| Week 3 | M 1/25 | Section 1.3 concluded; Section 1.4 (Cauchy sequences and completeness) begun | |
| W 1/27 | Section 1.4 concluded; Section 1.5 (compactness) begun | ||
| F 1/29 | Section 1.5 (compactness) cont'd | ||
| Week 4 | M 2/1 | Section 1.5 concluded; Section 2.1 (continuity of functions between metric spaces) begun | |
| W 2/3 | Section 2.1 concluded; Section 2.2 (continuity and product spaces) begun | ||
| F 2/5 | Section 2.2 concluded; Section 2.3 (continuity and compactness) begun | ||
| Week 5 | M 2/8 | Section 2.3 cont'd | |
| W 2/10 | Section 2.3 concluded; Section 2.4 (continuity and connectedness) begun | ||
| F 2/12 | Section 2.4 concluded | ||
| Week 6 | M 2/15 | Section 3.1 (limits of functions); Section 3.2 (sequences of functions; pointwise and uniform convergence) | |
| W 2/17 | Section 3.3 (uniform convergence and continuity) | ||
| F 2/19 | Section 3.4 (uniform metric) | ||
| Week 7 | M 2/22 | Section 3.5 (series of real-valued functions on a metric space) | |
| W 2/24 | Section 4.1 (formal power series) | ||
| F 2/26 | Section 4.2 (real analytic functions) begun | ||
| Week 8 | M 3/1 | Section 4.2 concluded; Section 4.3 (Abel's Theorem) begun | |
| W 3/3 | Section 4.3 concluded; Section 4.4 (multiplication of power series) begun | ||
| F 3/5 | Section 4.4 concluded; Section 4.5 (exp and log) reviewed | ||
| Week 9 | M 3/8 | Section 4.6 (complex numbers; complex-valued series) | |
| W 3/10 | Section 4.7 (trig functions) | ||
| F 3/12 | Section 6.1 (linear algebra review) | ||
| Week 10 | M 3/15 | Section 6.2 ("grown-up" derivatives) | |
| W 3/17 | Section 6.3 (partial and directional derivatives) begun | ||
| F 3/19 | Section 6.3 concluded; Section 6.4 ("grown-up" Chain Rule) begun | ||
| Week 11 | M 3/22 | Section 6.4 concluded; Section 6.5 (equality of cross-partials) | |
| W 3/24 | Spring "recharge day" (no class) | ||
| F 3/26 | Section 6.6 (Contracting-Mapping Theorem) | ||
| Week 12 | M 3/29 | Section 6.7 (Inverse Function Theorem) begun | |
| W 3/31 | Section 6.7 concluded; Section 6.8 (Implicit Function Theorem) begun | ||
| F 4/2 | Section 6.8 concluded; Section 7.1 (Lebesgue measure: intro) begun | ||
| Week 13 | M 4/5 | Section 7.1 concluded; Section 7.2 (outer measure) begun | |
| W 4/7 | Section 7.2 concluded; Section 7.3 (non-additivity of outer measure) | ||
| F 4/9 | Section 7.4 (measurable sets) | ||
| Week 14 | M 4/12 | Section 7.5 (measurable functions) | |
| M 4/14 | Section 8.1 (Lebesgue integral of simple functions) | ||
| F 4/16 | Section 8.2 (Lebesgue integration of measurable functions) begun | ||
| Week 15 | M 4/19 | Section 8.2 concluded; Section 8.3 (absolutely integrable functions) begun | |
| W 4/21 (last day of classes) |
Section 8.3 concluded; Section 8.4 (comparison with Riemann integral) |