This calendar is extremely tentative, but should give a general idea of what topics we will cover.
Course Textbooks:
| Date | Tentative class plan: |
| Mon, Feb 1 | Welcome! Folland § 1.1-1.2: Introduction to Metric Spaces and Euclidean Spaces. Also covering § 13 of Ross. |
| Wed, Feb 3 | Continuation of the prior topic. |
| Mon, Feb 8 | Quiz 1. Folland § 1.3-1.5: Limits, Continuity, Sequences, and Completeness. Also covering § 13 and 21 of Ross. |
| Wed, Feb 10 | § 1.6: Compactness. Also covering parts of § 13 and 21 of Ross. |
| Mon, Feb 15 | College closed |
| Wed, Feb 17 | § 1.7: Connectedness (also covering Ross § 22). § 1.8: Uniform Continuity. |
| Mon, Feb 22 | Quiz 2. § 2.1-2.2: Differentiability |
| Wed, Feb 24 | § 2.3: The chain rule § 2.10: Vector valued functions |
| Mon, Mar 1 | More on the chain rule § 2.4: The mean value theorem |
| Wed, Mar 3 | First Midterm. |
| Mon, Mar 8 | § 2.6: Higher-Order partial derivatives § 2.7: Taylor's Theorem (multiple variables) |
| Wed, Mar 10 | § 2.8: Critical Points |
| Mon, Mar 15 | Quiz 3. § 2.9: Extreme Values |
| Wed, Mar 17 | Quiz 4. § 3.1-3.2: The Implicit Function Theorem and curves in the plane |
| Mon, Mar 22 | § 3.1&3.3: The Implicit Function Theorem and Surfaces in R3 |
| Wed, Mar 24 | Quiz 5. § 3.4: Transformations and coordinate systems |
| Mon, Mar 29 | Spring break |
| Wed, Mar 31 | Spring break |
| Mon, Apr 5 | Proof of the Implicit Function Theorem |
| Wed, Apr 7 | 4.2: Integration in Rn |
| Mon, Apr 12 | Second Midterm. |
| Wed, Apr 14 | § 4.3: Multiple and iterated integrals |
| Mon, Apr 19 | § 4.4: Change of variables |
| Wed, Apr 21 | Quiz 6. § 5.1: Arc length and line integrals |
| Mon, Apr 26 | § 5.2: Green's Theorem |
| Wed, Apr 28 | Quiz 7. § 5.2: Green's Theorem |
| Mon, May 3 | Finish § 5.2: Green's Theorem § 5.3: Surface area and surface integrals § 5.4: Vector Derivatives |
| Wed, May 5 | Quiz 8. § 5.5: The Divergence Theorem |
| Mon, May 10 | § 5.7: Stoke's Theorem |
| Wed, May 12 | Quiz 9. § 5.8: Integrating vector derivatives |
| Mon, May 17 | § 5.9: Higher dimensions and differential forms |