Readings listed in the table below are from the following textbooks and notes:

(M) Munkres, J. *Analysis on Manifolds*. Cambridge, MA: Perseus Publishing, 1991. ISBN: 0201510359, ISBN: 0201315963 (paperback).

(S) Spivak, M. *Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus*. Cambridge, MA: Perseus Publishing, 1965. ISBN: 0805390219.

(MLA) Notes on Multi-linear Algebra (PDF)

(SN) Supplementary Notes (PDF)

LEC # | TOPICS | READINGS |
---|---|---|

2 | Compactness, Connectedness | M, sections 1 and 2 |

3 | Differentiation in n Dimensions | M, end of section 4 on connectedness |

8 | Reimann Integrals of Several Variables, Conditions for Integrability | M, section 10 |

10 | Fubini Theorem, Properties of Reimann Integrals Graded | M, section 11 |

13 | Exhaustions | M, theorem 15.3 and following paragraph |

15 | Partitions of Unity (cont.), Exhaustions (cont.) |
M, sections 1 and 2
MLA |

22 | The d Operator (cont.), Pullback Operator on Exterior Forms | M, section 29 |

24 | Poincare Theorem | SN, section 1 |

34 | Orientations of Manifolds | MLA, section 7 |

35 | Integration on Manifolds, Degree on Manifolds | M, section 34, pp. 281-286 only |