The instructor for this section is Professor Yanyan Li.

Office Hour: Thursday, 3:20pm to 4:40pm, Via Canvas Conference* Manfredo P. Do Carmo *; **
Differential Geometry of Curves and Surfaces
** (second edition);

* Homework (10%); Exam 1 (20%);
Exam 2 (20%); Final Exam (50%).
*
(for homework, the lowest will be dropped; no late homework)

Date | Section | Homework |
---|---|---|

Jan. 21 | 1.1, , 1.2, 1.3. Parametrized curves, regular curves and arc length | 1.2: 1, 4, 5 1.3: 1, 3, 6 |

Jan. 23 | 1.4. The vector product in R^3 | 1.4: 3, 5 |

Jan. 28 | 1.5. The local theory of curves parametrized by arc length | 1.5: 1, 2, 5, 9, 11, 12 |

Jan.30 | 1.7. Global properties of plane curves | 1.7: 1, 2 |

Feb. 4 | 2.1, 2.2. Regular surfaces, inverse image of regular values | 2.1: 2.2: 1, 2, 3, 5, 7 |

Feb. 6 | 2.3. Change of parameters; differentiable functions on surfaces | 2.3: 2, 3, 4 |

Feb. 11 | 2.4. The tangent plane; the differential of a map | 2.4: 1, 2, 3, 4, 6 |

Feb. 13 | 2.5. The first fundamental form; area | 2.5: 1, 2, 4, 5, 10 |

Feb. 18 | 2.5 and 3.1. | |

Feb. 20 | Review for the Exam 1 | |

Feb. 25 | Exam 1 | |

Feb. 27 | 3.2. The definition of Gauss map and its fundamental properties | 3.2: 1, 2, 3, 5, 6, 7, 8, 11, 12. |

March 3 | 3.3. The Gauss map in local coord. | 3.3: 1, 4, 5 |

March 5 | 3.3. The Gauss map in local coord. | 3.3: 6, 7, 13, 14 |

March 10 | 3.4. Vector fields | 3.4: 1, 3, 4, 5, 6, 10 |

March 12 | Cancelled by the University | |

March 24 | 3.5. Ruled surfaces and minimal surfaces | 3.5: 2, 3, 4, 6 |

March 26 | 3.5. and 4.1. | 3.5: 11, 12 |

March31 | 4.2. Isometries; conformal maps | 4.2: 1, 2, 3, 7. |

April 2 | Exam 2 | |

April 7 | 4.3. The Gauss theorem and the equation of compatibility | 4.3: 1, 3, 4, 5, 6, 7, 8 |

April 9 | 4.4. Parallel transport, geodesics | 4.4: 1, 2, 3, 4, 5 |

April 14 | 4.4. Parallel transport, geodesics | 4.4: 7, 14 |

April 16 | 4.4. Parallel transport, geodesics | 4.4: 17 |

April 21 | 4.5. The Gauss-Bonnet theorem and its applications | 4.5: 1, 2, 3, 4 |

April 23 | 4.6. The exponential map, geodesic polar coordinates | 4.6: 1, 2, 3, 4, 5 |

April 28 | 4.6. The exponential map, geodesic polar coordinates | 4.6: |

April 30 | Review for the Final Exam | |