MATH2028 - Honours Advanced Calculus II - 2025/26

Course Name: 
Honours Advanced Calculus II
Teacher: 
Prof. Tom Yau Heng WAN
Course Year: 
2025/26
Term: 
1

Announcement

  • In this term, we will follow the treatment of Prof Martin Li in the 23-24 academic year in order to maintain consistency. Lecture notes and other teaching materials can be downloaded in the corresponding course webpage: https://www.math.cuhk.edu.hk/course/2324/math2028
  • Concerning "Use of AI Tools", this course adopts, by default, the "Approach 1 - Prohibit all use of AI tools". Since there is no method to ensure no one uses AI tools in homework, homework will not be counted towards the final grades. Instead, 4 classwork, each with a couple of questions, during scheduled tutorial sessions (see below) will be counted 10% towards the final grades. (Suggested problems will be provided before each classwork session for study proposes.)
  • All classwork and midterm will be graded online using the Gradescope system. The link of the Gradescope system can be found in the Blackboard system.
  • The following arrangement at the end of the classwork sessions and the midterm will be implemented: 1. Stop writing when "pen-down" is announced by the instructor. 2. Use your "smartphone" to capture images of all the (non-empty) pages of your answers when instructed by the instructor. 3. Then convert the images of your answers into a pdf file. 4. Submit the pdf file of your answers into the "Classwork" or "Midterm" in the Gradescope system. (You will have around 15 minutes for steps 3-5.) 5. Submit your answer book to the instructor.
  • Midterm and Final exams are traditional closed book exams. Classwork is open book in the sense that hard copies of lecture notes/reference books and even discussions among classmates reference books are allowed, but no computers, smart devices or internet (including AI) tools.
  • No tutorial in the 1st week
  • Reminder: Classwork 1 will be held this Thursday's tutorlal (Sep 25). In case that there is a typhoon signal higher than or equal to 8, it will be cancelled. And only CW2, 3, 4 will be counted toward the final grade.
  • Suggested problems for study: Prof Li's problem set 1 [Download file]
  • Suggested problems for study: Prof Li's problem set 2 [Download file]
  • Problems in Classwork will be in the similar level of problems in "Problems to hand in" and "Suggested Exercises" in the above 2 problems.
  • Reminder: Classwork 2 will be held this Thursday's tutorlal (Oct 9).
  • Suggested problems for study: Prof Li's problem set 3 [Download file]
  • Suggested problems for study: Prof Li's problem set 4 (excluding partition of unity) [Download file]
  • Problems in Classwork will be in the similar level of problems in "Problems to hand in" and "Suggested Exercises" in the above 2 problems.
  • As requested, solutions of problem sets 3 & 4 are provided
  • Reminder: Midterm will be held next Monday Oct 20 at 10:30-12:00noon in the usual classroom.
  • Midterm coverage: From the beginning up to Change of Variables Thm. (Proof of Change of Variables Thm excluded.)
  • Suggested problems for study: Prof Li's problem set 5 (with solutions) [Download file]
  • According to the grade descriptors, there will be some difficult/unfamiliar questions in the midterm.
  • Midterm result has been published in the Gradescope system. Please check your papers and make regrade requests if necessary. However, any regrade request needs to be submitted within one week on or before Nov 6, 2025
  • Midterm Stat (before any regrade request): Mean=58.64, SD=12.41, Max=80, Med=61, Min=35
  • Reminder: Classwork 3 will be held coming Thursday's tutorlal (Nov 13).
  • Suggested problems for study: Prof Li's problem set 6. (Solutions will be provided after CW3.) [Download file]
  • Problems in Classwork 3 will be in the similar level of problems in "Problems to hand in" and "Suggested Exercises" in the above problem set.

General Information

Lecturer

  • Tom Yau-heng Wan
    • Office: LSB 202A
    • Tel: x 37969
    • Email:

Teaching Assistant

  • Song Wang
    • Office: LSB 232
    • Tel: 9064 7466
    • Email:
    • Office Hours: Monday 10:00am-12:00am
  • Shengze Xu
    • Office: LSB 222B
    • Tel: 3943 7963
    • Email:

Time and Venue

  • Lecture: Mon 10:30-12:15, Mong Man Wai Bldg 710; Thu 9:30-10:15, Lai Chan Pui Ngong LT
  • Tutorial: Thu 8:30-9:15, Lai Chan Pui Ngong LT

Course Description

This is a continuation of MATH2018. The following topics will be discussed: multiple integrals in ndimensions: areas and n-volumes, surface areas, volumes of submanifolds and hypersurfaces in n-space, change of variables; vector analysis: line integrals, surface integrals, integration on submanifolds, Green theorem, divergence theorem and Stokes theorem in n-dimensions.

We will not be using just one single textbook for the course. Instead, we will roughly go through Chapters 3-5 of Spivak’s book (the main reference) in terms of content, but supplemented with more expanded details and with a more modern treatment on differential forms.


References

  • M. Spivak, Calculus on Manifolds, 5th edition, CRC press (Main reference, the course will covers Ch3-5 of this book in terms of content, but with modifications)
  • V. Guillemin and P. Haine, Differential Forms, World Scientific (For modern approach of differential forms)
  • J. Munkres, Analysis on Manifolds, 1st edition, CRC press (For classical theoretical treatment)
  • W. Fleming, Functions of Several Variables, 2nd edition, Springer (For classical theoretical treatment)
  • Thomas’ Calculus, Early Transcendentals, 13th edition (For computational examples and applications)
  • J. Hubbard and B.B. Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, 5th edition, Matrix Editions (For computational examples and applications)
  • T. Shifrin, Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds, 1st edition, Wiley (For computational examples and applications)

Lecture Notes


Tutorial Notes


Assessment Scheme

Classwork (in tutorials, Sep 25, Oct 9, Nov 13 and Nov 27) 10%
Mid-term (Oct 20, 2025 during class) 40%
Final (date to be determined by university) 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.

Assessment Policy

Last updated: November 13, 2025 10:47:10