MATH2028 - Honours Advanced Calculus II - 2022/23

Announcement

• The Final Exam will cover everything, i.e. Lecture Notes L1-19 and Problem Sets 1-11 (except partition of unity L8).
• Problem Set 11 is posted and due on Dec 7 (Wed).
• Problem Set 10 is posted and due on Nov 30 (Wed).
• Problem Set 9 is posted and due on Nov 23 (Wed).
• Problem Set 8 is posted and due on Nov 16 (Wed).
• The statistics for midterm is as follow: mean=61.8, median=63, standard deviation=9.0. A suggested solution has been uploaded to Blackboard.
• Problem Set 7 is posted and due on Nov 9 (Wed).
• Problem Set 6 is posted and due on Nov 2 (Wed).
• Topics to be covered in the midterm: L2-L9 (except L8), Problem Set 1-5.
• Problem Set 5 is posted and due on Oct 21 (Fri).
• The revised midterm date is Oct 24 (Mon), 10:30AM-12:15PM in-class at CKB UG04.
• Problem Set 4 is posted and due on Oct 14 (Fri).
• Problem Set 3 is posted and due on Oct 5 (Wed).
• Problem Set 2 is posted and due on Sep 28 (Wed).
• The midterm date has been fixed as Oct 25, 2022 (Tuesday), 4:30-6:15PM, venue to be announced.
• Problem Set 1 is posted and due on Sep 21 (Wed) via Blackboard.
• The midterm is tentatively scheduled to take place in-class from 4:30-6:15PM on Oct 25, 2022. If you have any serious time conflict with this time, please let me know latest by Sep 16 (Friday).
• There is no class on Sep 5 (Mon) due to the university inauguration ceremony for undergraduates. The first lecture will be on Sep 6 (Tue). Since there are no Monday lectures in the first two weeks, we will instead have double lectures on the Tuesdays of Sep 6 and Sep 13 from 4:30 - 6:15PM instead.
• If you are not yet official registered on CUSIS, please send me an email to let me know so that I can keep you updated about the course via emails.

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General Information

Lecturer

• LI Man-chun Martin
  • Office: LSB 236
  • Tel: 3943-1851
  • Email:
  • Office Hours: By appointment

Teaching Assistant

• LO Chiu Hong
  • Office: LSB 228
  • Tel: 3943-7955
  • Email:
  • Office Hours: every Monday to Thursday 3:30 - 4:30PM

Time and Venue

• Lecture: Mon 10:30AM-12:15PM, CKB UG04; Tue 4:30PM-5:15PM, SC L3
• Tutorial: Tue 5:30PM-6:15PM, SC L3

Course Description

This is a continuation of MATH2018. The following topics will be discussed: multiple integrals in n-dimensions: 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.

References

• "Calculus on Manifolds" by M. Spivak, 5th edition, CRC press
• "Analysis on Manifolds" by J. Munkres, 1st edition, CRC press
• "Functions of Several Variables" by W. Fleming, 2nd edition, Springer
• "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach", J. Hubbard and B. B. Hubbard, 5th edition, Matrix Editions
• "Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds" by T. Shifrin, 1st edition, Wiley

Pre-class Notes

• Course outline

Lecture Notes

• L1 - Introduction and Overview
• L2 - Multiple Integrals
• L3 - Integrability Criteria
• L4 - Integration on Bounded Sets
• L5 - Iterated Integrals and Fubini's Theorem
• L6 - Applications of Fubini's Theorem
• L7 - Polar, Cylindrical and Spherical Coordinates
• L8 - Partition of Unity (optional)
• L9 - Change of Variables Theorem
• L10 - Proof of Change of Variables Theorem
• L11 - Line integrals
• L12 - Conservative Vector Fields
• L13 - Green's Theorem
• L14 - Surface Integrals in R^3
• L15 - Curl and Divergence
• L16 - Stokes and Divergence Theorem in R^3
• L17 - Differential Forms
• L18 - Integration on submanifolds of R^n
• L19 - Generalized Stokes Theorem

Assignments

• Problem Set 1 (due on Sep 21)
• Problem Set 2 (due on Sep 28)
• Problem Set 3 (due on Oct 5)
• Problem Set 4 (due on Oct 14)
• Problem Set 5 (due on Oct 21)
• Problem Set 6 (due on Nov 2)
• Problem Set 7 (due on Nov 9)
• Problem Set 8 (due on Nov 16)
• Problem Set 9 (due on Nov 23)
• Problem Set 10 (due on Nov 30)
• Problem Set 11 (due on Dec 7)

Assessment Scheme

Homework Assignments		10%
Midterm (Oct 25, 4:30-6:15PM, Oct 24, 10:30AM-12:15PM, in-class)		40%
Final Exam (centralized, please refer to RES webpage)		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.

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Assessment Policy

Last updated: November 20, 2022 23:40:45