MATH2028 - Honours Advanced Calculus II - 2023/24

Announcement

• The Final Exam will cover everything from Lecture Notes L1-L19 (except L9) and Problem Sets 1-9.
• Problem Set 9, the last one, is posted and due on Dec 1.
• Problem Set 8 is posted and due on Nov 24.
• Special arrangements: on Nov 13 (Mon) we will have lecture from 10:30-11:15am and then tutorial from 11:30am-12:15pm; on Nov 15 (Wed) we will have a double lecture from 10:30am-12:15pm.
• Problem Set 7 is posted and due on Nov 17.
• The statistics for midterm are as follow: mean=65.5, median=66, SD=7, highest=80.
• Problem Set 6 is posted and due on Nov 8.
• The midterm will take place in class on Oct 25, 2023, from 10:40AM-12:10PM. It covers all the topics in Lecture Notes L1-L10 (except L9) and Problem Sets 1-5.
• Problem Set 5 is posted and due on Oct 20.
• Problem Set 4 is posted and due on Oct 13.
• Problem Set 3 is posted and due on Oct 4.
• Problem Set 2 is posted and due on Sep 27.
• Problem Set 1 is posted and due on Sep 20 via Blackboard.
• There is no class on Sep 4 (Mon) due to the university inauguration ceremony for undergraduates. The first lecture will be on Sep 6 (Wed). Since there are no Monday lectures on Sep 4, we will instead have double lectures on the Wednesdays of Sep 6 from 10:30AM - 12:15PM 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

• CUI, Han
  • Office: AB1 614
  • Tel: 3943-4109
  • Email:
  • Office Hours: Thursday 2:30pm-5:30pm
• WANG, Yizi
  • Office: LSB 222A
  • Tel: 3943-3575
  • Email:
  • Office Hours: Wednesday 2:00pm-4:00pm

Time and Venue

• Lecture: Mon 10:30AM-12:15PM, MMW 710; Wed 11:30AM-12:15PM, WMY 301
• Tutorial: Wed 10:30AM-11:15AM, WMY 301

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
• "Thomas' Calculus, Early Transcendentals" by G. Thomas et. al., 13th edition
• "Differential Forms" by V. Guillemin and P. Haine, World Scientific

Pre-class Notes

• Course outline (as of Sep 5)

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 - Chang of Variables Theorem
• L9 - Partition of Unity (optional)
• 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 20)
• Problem Set 2 (due on Sep 27)
• Problem Set 3 (due on Oct 4)
• Problem Set 4 (due on Oct 13)
• Problem Set 5 (due on Oct 20)
• Problem Set 6 (due on Nov 8)
• Problem Set 7 (due on Nov 17)
• Problem Set 8 (due on Nov 24)
• Problem Set 9 (due on Dec 1)

Assessment Scheme

Homework Assignments		10%
Midterm (Oct 25, 10:40AM-12:10PM, 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 21, 2023 09:06:04