Date |
Lecture notes |
Exercises |

23 Sep | Smooth manifolds and smooth maps, tangent vectors. | Solve one of the Exercises from Sections 1.1 and 1.2. |

30 Sep | Commutator of vector fields, differential 1-forms. | Exercises 1 and 2 from the file above. |

7 Oct | Differential k-forms, exterior derivative. | Exercises 3 and 4. |

14 Oct | Exterior derivative, volume forms. | Exercise 5. |

21 Oct | Integration. | Exercises 6 and 7. |

28 Oct | Tensors. | Exercises 9 and 10. |

4 Nov | Trace and contraction, tensor fields, interior product. | Exercises 11, 12, and 13. |

11 Nov | Repetition. | Exercise 14. |

18 Nov | Products, quotients, immersions, submersions. | Exercise 15. |

25 Nov | Lie derivative. | Exercise 16. |

2 Dec | Covariant derivative. | Exercises 18 and 19. |

9 Dec | Riemannian metric. | Exercise 20. |

16 Dec | Levi-Civita connection. | Exercises 21 and 22. |

23 Dec | Levi-Civita connection on a submanifold. | Exercises 23 and 24. |