MATH2028 - Honours Advanced Calculus II - 2021/22

Announcement

• For Q3 in Problem Set 10, the forms are defined on an arbitrary open subset of R^n.
• Problem Set 11 is posted and due on Dec 6 at 11:59PM.
• Problem Set 10 is posted and due on Nov 29 at 11:59PM.
• Problem Set 9 is posted and due on Nov 22 at 11:59PM.
• Problem Set 8 is posted and due on Nov 15 at 11:59PM.
• Problem Set 7 is posted and due on Nov 8 at 11:59PM.
• The statistics for midterm is as follow: mean=27.7, median=27, standard deviation=5.7. A suggested solution has been uploaded to Blackboard.
• Problem Set 6 is posted and due on Nov 1 at 11:59PM.
• Correction: A typo in Q.8 (b) of Suggested Exercises in Problem Set 3 has been fixed.
• Midterm will take place on Oct 19, 2021 at LSK LT1 YIA 505 , 4:30-6:00PM. It will cover all the topics in lecture notes L1- L9 L8 (excluding the proof of partition of unity). Please arrive at the test venue at least 10 minutes before 4:30PM and bring your student ID.
• Problem Set 5 is posted and due on Oct 18 Oct 22 Oct 25 at 11:59PM.
• Problem Set 4 is posted and due on Oct 11 at 11:59PM.
• Problem Set 3 is posted and due on Oct 4 at 11:59PM.
• To facilitate the grading process, please submit your Problem Sets via Gradescope.
• Problem Set 2 is posted and due on Sep 27 at 11:59PM.
• Problem Set 1 is posted and due on Sep 20 at 11:59PM.
• The midterm has been set on Oct 19, 2021 (Tue), 4:30-6:15PM, in-class.
• There is no tutorial in the first week. The first lecture will be on Sep 6 (Mon) from 10:30am to 12:15pm. 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.

---

General Information

Lecturer

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

Teaching Assistant

• LEUNG, Ho Tin
  • Office: LSB G08
  • Tel: 3943-7954
  • Email:
  • Office Hours: Mon 1:00-3:00PM; Tue 1:00-5:00PM; Wed 12:00-2:00PM

Time and Venue

• Lecture: Mon 10:30AM-12:15PM, MMW 702; Tue 4:30PM-5:15PM, LSK LT1
• Tutorial: Tue 5:30PM-6:15PM, LSK LT1

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 (revised on Sep 15)
• 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
• 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

Tutorial Notes

• Tutorial notes 1 (Sep 14)
• Tutorial notes 2 (Sep 21)
• Tutorial notes 3 (Sep 28)
• Tutorial notes 4 (Oct 5)
• Tutorial notes 5 (Oct 27)
• Tutorial notes 6 (Nov 2)
• Tutorial notes 7 (Nov 9)
• Tutorial notes 8 (Nov 16)
• Tutorial notes 9 (Nov 23)
• Tutorial notes 10 (Nov 30)

Assignments

• Problem Set 1 (due on Sep 20) - revised on Sep 16
• Problem Set 2 (due on Sep 27)
• Problem Set 3 (due on Oct 4) - revised on Oct 18
• Problem Set 4 (due on Oct 11)
• Problem Set 5 (due on Oct 25) - revised on Oct 12
• Problem Set 6 (due on Nov 1)
• Problem Set 7 (due on Nov 8)
• Problem Set 8 (due on Nov 15)
• Problem Set 9 (due on Nov 22)
• Problem Set 10 (due on Nov 29)
• Problem Set 11 (due on Dec 6)

Assessment Scheme

Homework Assignments		10%
Midterm (Oct 19, 4:30-6:15PM, in-class)		40%
Final Exam		50%

Useful Links

• .

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 28, 2021 13:07:47