Calculus of functions of one and several variables

The following is a **tentative** schedule for the course.
Please check back regularly for updates as the term progresses.

Day | Lectures | Sections in Text | Brief Description |
---|---|---|---|

1 | 11 Sep (M) | 4.1-4.5 | Review of Math 3: Riemann sums and the Fundamental Theorem of Calculus |

2 | 13 Sep (W) | 11.2 | Infinite series; geometric series |

3 | 15 Sep (F) | 11.3 | The integral test |

4 | 18 Sep (M) | 11.4, 11.6 | Comparison tests; ratio test |

5 | 20 Sep (W) | 11.6, 11.8 | Power series; ratio test and radius of convergence |

6 | 22 Sep (F) | 11.9 | Functions as power series (incl. differentiation and integration) |

7 | 25 Sep (M) | 11.10 | Taylor and Maclaurin series, I |

8 | 27 Sep (W) | 11.10 | Taylor and Maclaurin series, II |

9 | 29 Sep (F) | 11.11 | Taylor polynomials; remainder estimates |

10 | 2 Oct (M) | Review | |

11 | 4 Oct (W) | 12.1-12.2 | Coordinates in R^n as a vector space; distance forrmula; simple surfaces |

4 Oct (W) |
Exam 1 |
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12 | 6 Oct (F) | 12.3 | Dot products and projections, I |

13 | 9 Oct (M) | 12.3 | Dot products and projections, II |

14 | 11 Oct (W) | 12.4 | Cross products and geometry; relation to volume/area |

15 | 13 Oct (F) | 12.5 | Lines in different forms; planes in vector and standard forms |

16 | 16 Oct (M) | 12.5 | Equation of a plane in different forms |

17 | 18 Oct (W) | 13.1-13.3 | Derivatives and integrals along curves, arc length |

18 | 20 Oct (F) | 14.1-14.2 | Limits and continuity in 2- and 3-D |

19 | 23 Oct (M) | Review | |

20 | 25 Oct (W) | 14.3 | Partial derivatives |

25 Oct (W) |
Exam 2 |
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21 | 27 Oct (F) | 14.4 | Tangent planes and normal lines |

22 | 30 Oct (M) | 14.5 | Chain rule |

23 | 1 Nov (W) | 14.6 | Gradients and directional derivatives, I |

24 | 3 Nov (F) | 14.6 | Gradients and directional derivatives, II |

25 | 6 Nov (M) | 14.7 | Extreme values, I |

26 | 8 Nov (W) | 14.7-14.8 | Extreme values, II; Lagrange multipliers, I |

27 | 10 Nov (F) | 14.8 | Lagrange multipliers, II |

28 | 13 Nov (M) | Wrap up | |

TBA |
Final Exam |