Last updated February 29, 2004

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

Day 1: 1/5 | Sections 1 & 2 | Review of linear algebra |

Day 2: 1/7 | Section 2 | Review of linear algebra: determinants |

Day 3: 1/12 | Section 3 | Review of topology of R^n |

Day 4: 1/13 | Section 4 | Compact sets in R^n |

Day 5: 1/14 | Section 5 | Differentiable functions |

Day 6: 1/16 | Sections 5 & 6 | Continuously differentiable functions |

Day 7: 1/20 | Section 7 | The chain rule |

Day 8: 1/21 | Section 8 | The inverse function theorem |

Day 9: 1/23 | Sections 8 & 10 | The inverse function theorem; Integral over a rectangle |

Day 10: 1/26 | Sections 11 and 12 | Existence and evaluation of Riemann integral
(Lebesgue's and Fubini's theorem) |

Day 11: 1/27 | Section 13 | Integral over a bounded set |

Day 12: 1/28 | Section 14 | Rectifiable sets |

Day 13: 2/2 | Section 15 | Improper integrals |

Day 14: 2/3 | Section 17 | Change of variables |

Day 15: 2/4 | Section 18 | Diffeomorphisms of R^n |

Day 16: 2/6 | Section 20 | Applications of change of variables |

Day 17: 2/9 | Section 20 | Invariance of the volume under isometries of R^n |

Day 18: 2/10 | Sections 21 and 22 | The volume of parametrized manifolds |

Day 19: 2/11 | Sections 22 and 23 | Parametrized manifolds and manifolds in R^n |

Day 20: 2/16 | Sections 23 and 24 | Manifolds and manifolds with boundary |

Day 21: 2/18 | --- | Play with coordinate patches :o) |

Day 22: 2/20 | Section 29 | Tangent vectors and tangent plane |

Day 23: 2/23 | Sections 29 and 26 | Tangent vectors and tangent plane; Multilinear algebra |

Day 24: 2/25 | Section 27 | Alternating tensors |

Day 25: 2/27 | Section 28 | Wedge product |

Day 26: 3/1 | Sections 29 and 30 | Differential forms; The differential operator |

Day 27: 3/2 | Section 32 | The action of a differentiable map |

Day 28: 3/3 | Section 33 | Integration of forms over parametrized manifolds |

Day 29: 3/5 | Sections 34 and 35 | Orientable manifolds; Integration of forms over oriented manifolds |

Day 30: 3/8 | Section 37 | Stokes' theorem |

Day 31: 3/9 | --- | Wrap up ... |