This calendar is extremely tentative, but should give a general idea of what topics we will cover.

Course Textbooks:

**Folland:**Folland, Gerald B.*Advanced Calculus,*Pearson, 2002**Ross:**Kenneth A. Ross,*Elementary Analysis: The Theory of Calculus*, 2nd edition, Springer, 2013.**Pugh:**Charles C. Pugh,*Real Mathematical Analysis*, Springer, 2015.

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 R^{3} |

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 R^{n} |

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 |

Relevant links: