微分流形（2023 秋季学期）
中国科学技术大学数学科学学院
课程公告
(12/16) Lecture 23 and Lecture 24 uploaded!
(12/16) PSet 7，part 1 uploaded. Due: Dec. 28.
(12/25) Lecture 25 and Lecture 26 uploaded!
(12/25) PSet 7，part 2 uploaded. Due: Dec. 28.
(12/25) 考前答疑： Jan 02, 19:30-21:30 at 5501
(1/2) Lecture 27 and Lecture 28 uploaded!
(1/2) ： 期末考试：19:30-21:30 覆盖：Lecture1-Lecture28 （updated）教室：5501
课程信息
授课老师：
王作勤 (wangzuoq at ustc dot edu dot cn)
上课时间：
星期二晚上 19：30 – 21：05; 星期四下午 15：55 – 17：30;
上课地点：
五教 5501
办公室：
管研楼1601
助教：
YE Xingchen （yexkif_1oclock at mail dot ustc dot edu dot cn） ZHOU Yipeng (zhouyp612 at mail dot ustc dot edu dot cn)
答疑时间：
周五，19:30-21:30pm
答疑地点：
5501
参考书籍
John Lee, Introduction to Smooth Manifolds (Second Edition)
参考书籍
Loring Tu, An Introduction to Manifolds
参考书籍
Victor Guillemin and Alan Pollack, Differential Topology
课程安排，讲义以及习题
课程安排可能会随着课程的进行而略有变动。
课程的讲义将在课后上传。
作业在标明的日期(通常是周二)课前交。
小论文：期中考试100分(含)以上选做，A+必要条件。
小论文选题
| 序号 | 日期 | 内容 | 讲义 | 作业 |
|---|---|---|---|---|
| Lecture 1 | 09/12 | Review of Topology, Topological Manifolds | Lect 1 | PSet 1, Part1 : Due Sep. 26. |
| Lecture 2 | 09/19 | Smooth manifolds and smooth maps (extended lecture) | Lect 2 | PSet 1, Part2 : Due Sep. 26 |
| Lecture 3 | 09/21 | Partition of unity and applications (extended lecture) | Lect 3 | |
| Lecture 4 | 09/26 | The tangent space and the differential | Lect 4 | PSet 2, Part1 : Due Oct. 17 |
| Lecture 5 | 09/28 | Local behavior of smooth maps | Lect 5 | |
| Lecture 6 | 10/10 | Sard's theorem | Lect 6 | PSet 2, Part2 : Due Oct. 17 |
| Lecture 7 | 10/12 | Smooth submanifolds | Lect 7 | |
| Lecture 8 | 10/17 | Whitney Embedding Theorem | Lect 8 | PSet 3, Part1 : Due Oct. 31 |
| Lecture 9 | 10/19 | Tubular Neighborhood Theorem | Lect 9 | |
| Lecture 10 | 10/24 | Transversality | Lect 10 | PSet 3, Part2 : Due Oct. 31 |
| Lecture 11 | 10/26 | Smooth Vector Fields | Lect 11 | PSet 4, Part1 : Due Nov. 14 |
| Lecture 12 | 10/31 | Integral curves | Lect 12 | |
| Lecture 13 | 11/02 | Flows | Lect 13 | PSet 4, Part2 : Due Nov. 14 |
| Lecture 14 | 11/07 | Distributions | Lect 14 | |
| Lecture 15 | 11/09 | Lie groups and its Lie algebras | Lect 15 | PSet 5, Part1 : Due Nov. 28 |
| Lecture 16 | 11/14 | Lie homomorphisms and the exponential map | Lect 16 | |
| Lecture 17 | 11/16 | Lie subgroups and Lie subalgebras | Lect 17 | |
| Lecture 18 | 11/21 | Lie group actions | Lect 18 | PSet 5, Part2 : Due Nov. 28 |
| 11/23 | Midterm | |||
| Lecture 19 | 11/28 | Tensors and linear k-forms | Lect 19 | PSet 6, Part1 : Due Dec. 14（updated） |
| Lecture 20 | 11/30 | Differential forms and exterior derivative | Lect 20 | |
| Lecture 21 | 12/05 | Integrations of differential forms | Lect 21 | PSet 6, Part2 : Due Dec. 14 |
| Lecture 22 | 12/07 | Stokes formula | Lect 22 | |
| Lecture 23 | 12/12 | De Rham cohomology groups | Lect 23 | PSet 7, Part1 : Due Dec. 28 |
| Lecture 24 | 12/14 | Mayer-Vietoris sequence | Lect 24 | |
| Lecture 25 | 12/19 | Compactly supported de Rham cohomology groups | Lect 25 | PSet 7, Part2 : Due Dec. 28 |
| Lecture 26 | 12/21 | Degree theory and applications | Lect 26 | |
| Lecture 27 | 12/26 | Poincare Duality | Lect 27 | |
| Lecture 28 | 12/28 | Thom class | Lect 28 | |
| 01/02 | 考前答疑 | |||
| 01/05 | 期末考试：19:30-21:30 at 5501 覆盖：Lecture1-Lecture28 updated |
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