MATH4030 - Differential Geometry - 2015/16
Announcement
- Tutorial will begin on Sep 10.
- Homework 1 is posted and due on Sep 15 at 5PM.
- The lecture notes is posted. Please note that the lecture notes will be revised continuously as the class goes on.
- Homework 2 is posted and due on Sep 23 (Wed) at 5PM.
- Midterm 1 will take place in the second half of the class next Tuesday (Sep 22). It will cover all the materials up to and including the lectures and tutorials this Thursday (Sep 17). There will still be lecture in the first half of the class before the midterm.
- Homework 2 typo: #5, the power on the right hand side should be "n-i" instead of "n-1".
- Homework 3 is posted.
- The statistics for midterm 1 is as follows: mean=11.05, median=11, highest=16, standard deviation=3.23. If you have not got back your midterm, please come to my office to pick it up.
- Homework 4 is posted.
- There is a mistake in HW4 Q2 (b). The revised version has been uploaded.
- Midterm 2 is changed to Oct 27 (Tuesday) in class. Please make sure to attend the midterm.
- Homework 5 is posted.
- The due date of Homework 5 is postponed to Oct 15.
- For question 2 in HW5, the curve is arc-length parametrized. The revised version has been uploaded.
- Homework 6 is posted.
- In HW5 Suggested Exercise 1(a), the sign in front of epsilon should be "plus". The revised version has been uploaded.
- Homework 7 & 8 are posted. Please note that HW 7 is due on Wednesday, the day after midterm 2.
- Midterm 2 will be held in class on Oct 27, 10:30-11:30AM. There will be no lecture on that day. The test will cover all the materials up to and including the lecture on Oct 22.
- In Q.1 of Homework 6, there should be no "squared" of the integrand. The revised version has been uploaded.
- Homework 9 is posted.
- Midterm 2 has been returned in class today. Here are the statistics: mean = 17.3, median = 18, standard deviation = 2.63. If you missed class today, please come to my office to pick up your midterm.
- In suggested solution to HW 7 Q.3(b), the semi-circles need to be reparametrized suitably to satisfy the geodesic equations.
- The final exam has been scheduled on Dec 15, 2015 (Tuesday) 9:30am - 12:00pm at Indoor Multi-purpose Sports Hall, Shaw College. Please refer to the RGS webpage for the most up-to-date information.
- Homework 10 is posted.
- The last homework assignment 11 is posted. Please note that the due date is on Nov 26, Thursday.
General Information
Lecturer
-
Li Man-chun Martin
- Office: LSB 236
- Tel: 3943-1851
- Email:
Teaching Assistant
-
Huang Shaochuang
- Office: LSB 222A
- Tel: 3943-3575
- Email:
- Office Hours: Tu 1:30-6:15PM, W 8:30AM-12:15PM, F 8:30AM-12:15PM
-
Wang Qizhi
- Office: LSB 233
- Tel: 3943-7957
- Email:
- Office Hours: M 2:30-5:00PM, W 2:30-5:00PM, F 8:30AM-12:00PM
Time and Venue
- Lecture: Tu 10:30AM - 12:15PM, LSB C2; Th 10:30AM - 11:15AM, LSB C2
- Tutorial: Th 11:30AM - 12:15PM, LSB C2
Course Description
This course covers basic theory on curves, and surfaces in the Euclidean three space. Topics include: regular curves, Frenet formulas, local theory of curves, global properties of curves such as isoperimetric inequality, regular surfaces, 1st and 2nd fundamental form, Gaussian curvature and mean curvature, Gauss map, special surfaces such as ruled surfaces, surfaces of revolution, minimal surfaces, intrinsic geometry: geodesic, and Gauss-Bonnet Theorem. Students taking this course are expected to have knowledge in advanced calculus, linear algebra, and elementary differential equations.
Textbooks
- "Differential Geometry: Curves - Surfaces - Manifolds" (2nd edition) by Wolfgang Kuhnel
References
- "Differential Geometry of Curves and Surfaces" by Manfredo do Carmo
- "Differential Forms and Applications" by Manfredo do Carmo
Pre-class Notes
Lecture Notes
- Lecture Notes Part 1(last revised on Sep 28)
- Lecture Notes Part 2(last revised on Oct 14)
- Lecture Notes Part 3(last revised on Nov 25)
- Lecture Notes Part 4(last revised on Dec 4)
Tutorial Notes
- Tutorial Notes 1 (Sep 10)
- Tutorial Notes 2 (Sep 17)
- Tutorial Notes 3 (Sep 24)
- Tutorial Notes 4 (Oct 8)
- Tutorial Notes 5 (Oct 15)
- Tutorial Notes 6 (Oct 22)
- Tutorial Notes 7 (Oct 29)
- Tutorial Notes 8 (Nov 5)
- Tutorial Notes 9 (Nov 12)
- Tutorial Notes 10 (Nov 26)
- Tutorial Notes 11 (Dec 3)
Assignments
- Homework 1 (due on Sep 15 at 5PM)
- Homework 2 - revised (due on Sep 23 at 5PM, note different date!)
- Homework 3 (due on Sep 29 at 5PM)
- Homework 4 (due on Oct 6 at 5PM) - revised on Oct 6
- Homework 5 -revised (due on Oct 15 at 5PM)
- Homework 6 -revised (due on Oct 20 at 5PM)
- Homework 7 (due on Oct 28 at 5PM)
- Homework 8 (due on Nov 3 at 5PM)
- Homework 9 (due on Nov 10 at 5PM)
- Homework 10 (due on Nov 17 at 5PM)
- Homework 11 (due on Nov 26 (Thursday) at 5PM)
Solutions
- Solutions to HW1
- Solutions to HW2
- Solutions to Midterm 1
- Solutions to HW3 (For Q5a, please refer to the back of the solution for a more precise treatment.)
- Solutions to HW4
- Solutions to HW5
- Solutions to HW6
- Solutions to HW7
- Solutions to Midterm 2
- Solutions to HW8
- Solutions to HW9
- Solutions to HW10
- Solutions to HW11
Assessment Scheme
| Weekly Homework Assignment | 10% | |
| Midterms (Sep 22 and Oct 27) | 40% | |
| Final Exam (Dec 15 9:30AM-12:00PM, please refer to RGS's webpage for the most updated information) | 50% |
Honesty in Academic Work
The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Last updated: December 03, 2015 13:40:00