Calculus on Manifolds
PDF for the syllabus: [here]
Final Exam (2018):
Office Hours:
Instructor: Tuesday, Thursday 12pm-1pm @ Room 3488
TA (Nicholas Chin): Monday 12:15pm-1:15pm @ Room 3209D
Reference Materials:
Major Reference:
- Instructor's Lecture Notes: [here]
Solutions to selected exercises (typed by former students) can be found in the following website (Q&A):
https://piazza.com/ust.hk/spring2017/math4033/home
[If you cannot access the Q&A tab, send me (frederick.fong@ust.hk) an Email.]
Recommended References:
- Introduction to Smooth Manifolds (John M. Lee): [here]
- Differential Forms and Applications (Manfredo Do Carmo): [here]
- Prof. Hitchin's Lecture Notes on Differentiable Manifolds: [here]
- A Comprehensive Introduction to Differential Geometry, Vol. 1 (Michael Spivak): Buy [here (Amazon)]
- Lectures on Differential Geometry (S.S. Chern, Weihuan Chen, K.S. Lam): Buy [here at Amazon for the English version] or《微分幾何講義》陳省身、陳維桓: Buy [here at Taobao for the Simplified Chinese version]
Class Log:
| Week | |
| #1 |
Ref: pp1-13 [Blackboard Notes] |
| #2 |
Ref: pp12-21 [Blackboard Notes] |
| #3 |
Ref: pp23-31 [Blackboard Notes] |
| #4 |
Ref: pp32-46 [Blackboard Notes] |
| #5 |
Ref: pp47-58 [Blackboard Notes] |
| #6 |
Ref: pp61-74 [Blackboard Notes] |
| #7 |
Ref: pp75-94 [Blackboard Notes] |
| #8 |
Ref: pp95-114 [Blackboard Notes] |
| #9 |
Ref: pp115-127 [Blackboard Notes] |
| #10 |
Ref: pp128-138 [Blackboard Notes] |
| #11 |
Ref: pp139-151 [Blackboard Notes] |
| #12 |
Ref: pp152-158 [Blackboard Notes] |
Presentations
Click [here].
Problem Sets (Optional)
Submit any part of it before the due date in "Assignments" page of Canvas. Follow the instructions there.
Chapter 1: [Problems][Solutions]
Chapter 2: [Problems][Solutions]
Chapter 3: [Problems][Solutions]
Chapter 4: [Problems][Solutions]
Chapter 5: [Problems]
Past Final Exam
Spring 2017: [Exam][Solutions]
Class Photos
Course Summary:
| Date | Details | Due |
|---|---|---|