The table below indicates which topics we will cover in each class. **Before each class**, you should read the lecture notes up to and including the place indicated below.

Lec | Date | Notes | Topics | |
---|---|---|---|---|

1 | Sep 8 | 1.1, 1.2 | Open sets, boundaries, limits | |

2 | Sep 10 | 1.3, 1.4, 1.5 | Affine approximations, the derivative | |

3 | Sep 15 | 1.6, 1.7 | Differentiation rules; paths, curves, and surfaces | |

4 | Sep 17 | 1.8, 1.9, 1.10 | Directional derivatives, higher order derivatives, Taylor's theorem | |

5 | Sep 22 | 1.11, 1.12 | The implicit function theorem, the inverse function theorem | |

6 | Sep 24 | 2.1, 2.2, 2.3 | Extrema, the second derivative test | |

7 | Sep 29 | 2.4, 2.5 | Lagrange multipliers, multiple constraints | |

8 | Oct 1 | 2.6, 3.1 | Global extrema, double integrals by vertical slices | |

9 | Oct 6 | 3.2, 3.3, 3.4 | Double integrals by horizontal slices, Fubini's theorem | |

10 | Oct 8 | 3.5, 3.6 | Double integrals over general regions, examples and applications | |

11 | Oct 13 | 3.7 | Triple integrals | |

12 | Oct 15 | 4.1, 4.2, 4.3 | Change of variables, polar coordinates | |

13 | Oct 20 | 4.4, 4.5, 5.1 | Cylindrical and spherical coordinates, vector fields | |

14 | Oct 22 | 5.2, 5.3 | Conservative vector fields, curl | |

Oct 25–29 | Reading week | |||

15 | Nov 3 | 1.1–4.5 | Midterm exam | |

16 | Nov 5 | 6.1, 6.2, 6.3 | Path and line integrals, reparameterization | |

17 | Nov 10 | 6.4, 6.5 | Line integrals of conservative vector fields, path independence | |

18 | Nov 12 | 7.1, 7.2, 7.3 | Parameterized surfaces, tangent planes, surface area | |

19 | Nov 17 | 7.4, 7.6 | Surface integrals | |

20 | Nov 19 | 7.5, 7.7 | Centre of mass and moment of inertia; reparameterization and orientation | |

21 | Nov 24 | 8.1 | Gradient, divergence, and curl | |

22 | Nov 26 | 8.2 | Divergence theorem | |

23 | Dec 1 | 8.3 | Green's theorem | |

24 | Dec 3 | 8.4 | Stokes' theorem |