MATH4033 (L1) - Calculus on Manifolds

Syllabus PDF: [here]

Contact of Instructor and TA:

Instructor: Frederick Tsz-Ho Fong (frederick.fong@ust.hk)
TA: Duan Xiuqing (xduanad@connect.ust.hk)

Reference Materials:

Major Reference:

  • Instructor's Lecture Notes: [here]
    (MATH 4033 covers Chapters 1 ~ 5)

Recommended References:

  • Introduction to Smooth Manifolds (John M. Lee): [here]
  • Differential Forms and Applications (Manfredo Do Carmo): [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]

Should I take this course?

Visit this page.

Homework and Solutions

Problem Set 1 (Due 28/02)
Problem Set 2 (Due 21/03)
Problem Set 3 (Due 15/05)
Problem Set 4 (Optional, not to turn in)

Selected Solutions to Lecture Notes exercises (Chapters 1, 2, 3): [here]
(written by former 4033 students, not guaranteed to be perfect)

Lecture and Tutorial Slides and Videos

[Week 1][2.2: Slide, Video][2.4: Slide, Video]
[Week 2][2.9: Slide, Video][2.9: Slide, Video][Tutorial: Slide, Video]
[Week 3][2.16: Slide, Video][2.18: Slide, Video][Tutorial: Slide, Video]
[Week 4][2.23: Slide, Video][2.25: Slide, Video][Tutorial: Slide, Video]
[Week 5][3.2: Slide, Video][3.4: Slide, Video][Tutorial: Slide, Video]
[Week 6][3.9: Slide, Video][3.11: Slide, Video][Tutorial: Slide, Video]
[Week 7][3.16: Slide, Video][3.18: Slide Video]
[Week 8][3.24: Slide, Video][3.25: Slide, Video]
[Week 9][3.30: Slide, Video][4.8: Slide, Video]
[Week 10][4.13: Slide, Video][4.15: Slide, Video]
[Week 11][4.20: Slide, Video][4.22: Slide, Video]
[Week 12][4.27: Slide, Video][4.29: Slide, Video]
[Week 13][5.4: Slide, Video][5.6: Slide, Video]

Student Presentations

Click here

Exams (2021)

[Final Exam][Solution to Final Exam][Anonymous Scores Table]

Past Final Exams

Spring 2019: [Exam][Solutions]
Spring 2018: [Exam][Solutions]
Spring 2017: [Exam][Solutions]

Grades

 

Course Summary:

Date Details Due