微分流形（英）（2018 秋季学期）
中国科学技术大学数学科学学院
课程公告
(12/07) Final Exam: Jan. 10, 15:00-17:00 @ 1302 Cover Lecture 1 - Lecture 28.
(01/04) Lecture 30 uploaded.
(01/04) Q/A by TA: Jan. 8, 19:30-21:00 @ 1302
(01/07) Solutions to PSet 6 and PSet 7 uploaded.
(01/07) Deadline to submit late PSets: Jan. 12, 15:00pm (strict!).
(01/07) To EVERYBODY: Please contact TA to double check your PSet Scores.
课程信息
授课老师：
王作勤 (wangzuoq at ustc dot edu dot cn)
上课时间：
星期二下午 15：55pm – 17：30pm; 星期四上午 9：45am – 11：20am;
上课地点：
一教 1302 （changed!）
办公室：
管研楼1601
助教：
Yiyu Wang and Yilin Gong (wangyiyu and gylustc at mail dot ustc dot edu dot cn)
答疑时间：
周日 3:55 pm -5:20 pm
答疑地点：
五教 5207
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
参考书籍
Serge Lang, Introduction to Differential Manifolds
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。
课程的讲义将在每堂课后上传。
| 序号 | 日期 | 内容 | 讲义 | 作业 | 参考答案 |
|---|---|---|---|---|---|
| Lecture 1 | 09/11 | Review of Topology, Topological Manifolds | Lect 1 | PSet 1, Part1 : Due Sep. 27. | PSet 1 Solutions (by Yiyu Wang) |
| Lecture 2 | 09/13 | Review of Analysis, Smooth Manifolds | Lect 2 | ||
| Lecture 3 | 09/18 | Smooth Functions, Partition of Unity | Lect 3 | PSet 1, Part2 : Due Sep. 27. | |
| Lecture 4 | 09/20 | Partition of Unity, Whitney Approximation Theorem | Lect 4 | ||
| Lecture 5 | 09/25 | Smooth Maps, The Differentials | Lect 5 | PSet 2 : Due Oct. 11. | PSet 2 Solutions (by Yiyu Wang) |
| Lecture 6 | 09/27 | Local Properties of Smooth Maps | Lect 6 | ||
| Lecture 7 | 09/29 | Sard's Theorem | Lect 7 | ||
| Lecture 8 | 10/09 | Smooth Submanifolds, Embeddings | Lect 8 | PSet 3, Part 1 : Due Oct. 25. | PSet 3 Solutions (by Yulin Gong) |
| Lecture 9 | 10/11 | The Whitney Embedding Theorem | Lect 9 | ||
| Lecture 10 | 10/16 | Tubular Neighborhoods | Lect 10 | PSet 3, Part 2 : Due Oct. 25. | |
| Lecture 11 | 10/18 | Transversality | Lect 11 | ||
| Lecture 12 | 10/23 | Smooth Vector Fields | Lect 12 | PSet 4, Part 1 : Due Nov. 8. | PSet 4 Solutions (by Yulin Gong) |
| Lecture 13 | 10/25 | Integral Curves | Lect 13 | ||
| Lecture 14 | 10/30 | Flows | Lect 14 | PSet 4, Part 2 : Due Nov. 8. | |
| Lecture 15 | 11/01 | Distributions | Lect 15 | ||
| Lecture 16 | 11/06 | Lie Groups and Lie Algebras | Lect 16 | PSet 5, Part 1 : Due Nov. 22. | PSet 5 Solutions (by Yiyu Wang) |
| Lecture 17 | 11/08 | The Exponential Map | Lect 17 | ||
| Lecture 18 | 11/13 | Lie Subgroups | Lect 18 | PSet 5, Part 2 : Due Nov. 22. | |
| Lecture 19 | 11/15 | Lie Group Actions | Lect 19 | ||
| Lecture 20 | 11/20 | Multilinear Algebra | Lect 20 | PSet 6 : Due Dec. 6 | PSet 6 Solutions (by Yiyu Wang) |
| 11/22 | Midterm 9:45-11:45 @ 1302 Cover: Lec 1 - Lec 19. | ||||
| Lecture 21 | 11/26 | Differential Forms | Lect 21 | ||
| Lecture 22 | 11/29 | Integrals of Differential Forms | Lect 22 | ||
| Lecture 23 | 12/04 | Stokes' Theorem | Lect 23 | PSet 7 Part 1 : Due Dec. 20 | PSet 7 Part 1 Solutions (by Yulin Gong) |
| Lecture 24 | 12/06 | De Rham Cohomology | Lect 24 | ||
| Lecture 25 | 12/11 | The Mayer-Vietoris Sequence | Lect 25 | PSet 7 Part 2 : Due Dec. 20 | PSet 7 Part 2 Solutions (by Yulin Gong) |
| Lecture 26 | 12/13 | De Rham Cohomology with Compact Supports | Lect 26 | ||
| Lecture 27 | 12/18 | Mapping Degree, Poincare Duality | Lect 27 | ||
| 12/20 | Problem Session by TAs | ||||
| Lecture 28 | 12/25 | Vector Bundles | Lect 28 | ||
| Lecture 29 | 12/27 | Connections and Curvatures | Lect 29 | ||
| Lecture 30 | 01/03 | Chern-Weil Theory | Lect 30 | ||
| 01/10 | Final 15:00-17:00 @ 1302 Cover: Lec 1 - Lec 28. |
[top]