MATH2028  Honours Advanced Calculus II  2023/24
Announcement
 The Final Exam will cover everything from Lecture Notes L1L19 (except L9) and Problem Sets 19.
 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 10:3011:15am and then tutorial from 11:30am12:15pm; on Nov 15 (Wed) we will have a double lecture from 10:30am12:15pm.
 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 10:40AM12:10PM. It covers all the topics in Lecture Notes L1L10 (except L9) and Problem Sets 15.
 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.
General Information
Lecturer

LI Manchun Martin
 Office: LSB 236
 Tel: 39431851
 Email:
 Office Hours: By appointment
Teaching Assistant

CUI, Han
 Office: AB1 614
 Tel: 39434109
 Email:
 Office Hours: Thursday 2:30pm5:30pm

WANG, Yizi
 Office: LSB 222A
 Tel: 39433575
 Email:
 Office Hours: Wednesday 2:00pm4:00pm
Time and Venue
 Lecture: Mon 10:30AM12:15PM, MMW 710; Wed 11:30AM12:15PM, WMY 301
 Tutorial: Wed 10:30AM11:15AM, WMY 301
Course Description
This is a continuation of MATH2018. The following topics will be discussed: multiple integrals in ndimensions: 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
 "Thomas' Calculus, Early Transcendentals" by G. Thomas et. al., 13th edition
 "Differential Forms" by V. Guillemin and P. Haine, World Scientific
Preclass Notes
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, 10:40AM12:10PM, inclass)  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.
Assessment Policy Last updated: November 21, 2023 09:06:04