Multivariable calculus for first-year students with two terms of AP credit

The following is a **tentative** syllabus for the course.

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

1 | 12 Sep (M) | 12.1, 12.2 | Coordinates and vectors in R^{3}, spheres |

2 | 14 Sep (W) | 12.3, 12.4 | Dot and cross products |

3 | 16 Sep (F) | 12.5 | Lines and planes |

4 | 19 Sep (M) | 13.1, 13.2 | Space curves |

5 | 21 Sep (W) | 13.3 (pp. 901-903), 13.4 (pp. 910-913, 916-917) |
Arclength (no curvature, no normal/binormal vectors) and kinematics (no tangential and normal components of acceleration) |

6 | 23 Sep (F) | 14.1, 14.2 | Functions of two variables |

7 | 26 Sep (M) | 14.3 | Partial derivatives |

8 | 28 Sep (W) | 14.4 | Tangent planes and linear approximations |

9 | 30 Sep (F) | 14.5 | Chain rule (no implicit function theorem) |

10 | 3 Oct (M) | 14.6 | Directional derivative and gradient |

11 | 5 Oct (W) | 14.7 | Maxima and minima |

5 Oct (W) |
Exam 1: covers through 12.1-14.5 |
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12 | 7 Oct (F) | 14.8 | Lagrange multipliers |

13 | 10 Oct (M) | 15.1 | Double integrals over rectangles |

14 | 12 Oct (W) | 15.2 | General planar domains |

15 | 14 Oct (F) | 15.6 | Triple integrals |

16 | 17 Oct (M) | 15.3, 15.7 | Polar and cylindrical coordinates |

17 | 19 Oct (W) | 15.8 | Spherical coordinates |

18 | 21 Oct (F) | 15.9 | Change of variable, Jacobians |

19 | 24 Oct (M) | 16.1, 16.2 | Vector fields, scalar line integrals |

20 | 26 Oct (W) | 16.2 | Vector line integrals |

26 Oct (W) |
Exam 2: covers 14.6-15.9 |
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21 | 28 Oct (F) | 16.3 | Fundamental theorem of line integrals |

22 | 31 Oct (M) | 16.4 | Green's theorem |

23 | 2 Nov (W) | 16.5 | Divergence and curl |

24 | 4 Nov (F) | 16.6 | Parametrized surfaces |

25 | 7 Nov (M) | 16.7 | Surface integrals |

26 | 9 Nov (W) | 16.8 | Stokes's theorem |

27 | 11 Nov (F) | 16.9 | Divergence theorem |

28 | 14 Nov (M) | 16.10 | Wrap up |

18 Nov (F) |
Final Exam: comprehensive |