MATH2010C  Advanced Calculus I  2017/18
Announcement
 (8/1) Welcome to MATH2010C!
 (10/1) Homework 1 is posted. (due Jan 18, 2018, 12:00noon)
 (12/1) Tutorials with start next week.
 (17/1) Homework 2 is posted. (due Jan 25, 2018, 12:00noon)
 (23/1) Homework 3 is posted. (due Feb 1, 2018, 12:00noon)
 (29/1) Tutorial notes for week 3 has been revised. The arclength and the curvature for polar curves have been corrected.
 (30/1) Homework 4 is posted. (due Feb 8, 2018, 12:00noon)
 (7/2) Homework 5 is posted. (due Feb 22, 2018, 12:00noon)
 (7/2) Quiz 1 at 2:303:15pm, (Wed) Feb 14, 2018; covers material of weeks 14 up to Sandwich Theorem
 (23/2) Homework 6 is posted. (due Mar 8, 2018, 12:00noon)
 (23/2) Quiz 1 will be returned during the breaks between the lectures and tutorials on Feb 26 and 28.
 (6/3) Homework 7 is posted. (due Mar 15, 2018, 12:00noon)
 (13/3) Homework 8 is posted. (due Mar 22, 2018, 12:00noon)
 (22/3) Quiz 2 at 2:303:15pm, (Wed) Mar 28, 2018; covers material up to the lecture on Mar 14 and HW8 (up to max/min on closed and bounded region)
 (23/3) Homework 9 is posted. (due Apr 12, 2018, 12:00noon)
 (10/4) Homework 10 is posted. (due Apr 19, 2018, 12:00noon)
 Final exam: May 10 (Thursday) 9:3011:30am, University Gym
 All materials (lecture and tutorial notes, textbooks, and homeworks) up to Lagrange Multipliers with multiple constraints
 Materials before quizzes will also be tested.
 "Theory" (basic concept and computation of limits, continuity, partial derivatives, differentiability, and etc) will be tested but no epsilondelta proof.
General Information
Lecturer

CHENG, Man Chuen
 Office: LSB 210
 Tel: 3943 7985
 Email:
Teaching Assistant

SIU, Chun Yin
 Office: LSB 222A
 Tel: 3943 3575
 Email:
 Office Hours: Tue 15301630 (MathGym)

XIN, Jing
 Office: AB1 614
 Tel: 3943 4109
 Email:
 Office Hours: Mon 13301530 (MathGym)

YEUNG, Chin Ching
 Office: AB1 614
 Tel: 3943 4109
 Email:
 Office Hours: Thur 13301530 (MathGym)
Time and Venue
 Lecture: Monday 1:302:15pm, LSB LT2; Wednesday 2:304:15pm, LSB LT5
 Tutorial: Monday 12:301:15pm, LSB LT2; Wednesday 4:305:15pm, LSB LT5
Course Description
Functions of several variables, partial differentiation, differential and its geometric meaning, chain rule, maxima and minima, Lagrange multiplier, mean value theorem, Taylor series, and implicit function theorem.
Mainly follow the Textbook by Prof Thomas KK Au for general ndimension, and supplemented by the Thomas' Calculus on examples, special cases for 2 and 3 dimensions, and exercises.
Textbooks
 Thomas KwokKeung AU, Differential Multivariable Calculus, Asian Customized Edition, McGraw Hill Education
 Thomas, Weir & Hass, Thomas' Calculus, 12th Ed., Pearson
References
 S. Lang, Calculus of Several Variables, 3th Ed., Springer
Lecture Notes
 Week 1
 Week 2 (updated on 31/1: Defn of closed curve fixed)
 Week 3 (updated on 12/2: A mistake in the table on P9 has been fixed. The exterior of empty set should be R^2.
 Week 4
 Week 5
 Week 6
 Week 7 (updated on 23/3: A typo on the last line has been fixed. The correct statement should be: D_u f(0,0) DNE for u other than plus or minus e1, e2)
 Week 8
 Week 9
 Week 10
 Week 11
 Week 12
 Week 13
Tutorial Notes
 Tutorial 2
 Tutorial 3 (typo in arclength and curvature of polar curves corrected at 29 Jan 18:20)
 Tutorial 4
 Tutorial 5 (proposition on polar form removed, uniqueness of symmetric harmonic functions reproven on 12 Feb 15:25)
 Tutorial 6
 Tutorial 7
 Tutorial 8
 Tutorial 9 (A number of mistakes were made during the tutorials. They have been corrected in the note.)
 Tutorial 10
 Tutorial 11 (A student's query on whether a unique critical point that is a local minimum of a C1 function is a global minimum is addressed in a remark following the relevant example.)
 Tutorial 12
Assignments
 Homework 1 (due Jan 18, 2018, 12:00noon)
 Homework 2 (due Jan 25, 2018, 12:00noon)
 Homework 3 (due Feb 1, 2018, 12:00noon)
 Homework 4 (due Feb 8, 2018, 12:00noon)
 Homework 5 (due Feb 22, 2018, 12:00noon)
 Homework 6 (due Mar 8, 2018, 12:00noon)
 Homework 7 (due Mar 15, 2018, 12:00noon)
 Homework 8 (due Mar 22, 2018, 12:00noon)
 Homework 9 (due Apr 12, 2018, 12:00noon)
 Homework 10 (due Apr 19, 2018, 12:00noon)
Quizzes and Exams
Solutions
 Suggested solution of Homework 1
 Suggested solution of Homework 2
 Suggested solution of Homework 3
 Suggested solution of Homework 4
 Suggested solution of Homework 5
 Suggested solution of Homework 6
 Suggested solution of Homework 7
 Suggested solution of Homework 8
 Suggested solution of Homework 9
 Suggested solution of Homework 10
Assessment Scheme
Homework (about once a week)  10%  
2 Quizzes (Feb 14, 2018, 2:303:15pm; and Mar 28, 2018, 2:303:15pm)  40%  
Final (date to be determined by University)  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: April 24, 2018 10:14:34