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 LT1YIA 505 , 4:306:00PM. It will cover all the topics in lecture notes L1L9L8 (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 18Oct 22Oct 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), 4:306:15PM, inclass.
 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, Manchun Martin
 Office: LSB 236
 Tel: 39431851
 Email:
 Office Hours: By appointment
Teaching Assistant

LEUNG, Ho Tin
 Office: LSB G08
 Tel: 39437954
 Email:
 Office Hours: Mon 1:003:00PM; Tue 1:005:00PM; Wed 12:002:00PM
Time and Venue
 Lecture: Mon 10:30AM12:15PM, MMW 702; Tue 4:30PM5:15PM, LSK LT1
 Tutorial: Tue 5:30PM6:15PM, LSK LT1
Course Description
This is a continuation of MATH2018. The following topics will be discussed: multiple integrals in n dimensions: areas and nvolumes, surface areas, volumes of submanifolds and hypersurfaces in nspace, change of variables; vector analysis: line integrals, surface integrals, integration on submanifolds, Green theorem, divergence theorem and Stokes theorem in ndimensions.
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
Preclass Notes
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, 4:306:15PM, inclass)  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