MATH3060  Mathematical Analysis III  2016/17
Announcement
 Homework 1 due on Sep 21, 2016
 Homework 2 due on Sep 28, 2016 (For question 2, do only for n >0)
 Homework 3 due on Oct 5, 2016 (Revised: corrected typo in question 5)
 Homework 4 due on Oct 12, 2016
 Homework 5 due on Oct 24, 2016
 Midterm Oct 26 (up to section 2.3)
 Important revision on Lecture note 10 on the example of boundary of a metric ball
 Homework 6 due on Nov 9, 2016
 Midterm graded, can collect from TA, mean=49, SD=21
 Homework 7 due on Nov 16, 2016
 Homework 8 due on Nov 28, 2016
 Homework 9 no need to hand in
 Final Exam: Dec 7, 2016, 3:305:30pm, UC Gym [Download file]
 Solution of Q5 in HW 9 is revised.
 Solution of midterm is uploaded.
General Information
Lecturer

WAN, Yau Heng Tom
 Office: LSB215
 Tel: 3943 7986
 Email:
Teaching Assistant

Lo Chiu Hong
 Office: LSB 222A
 Tel: 3943 3575
 Email:
 Office Hours: M3,6; W34,6; H34,6

TSANG, Tin Yau
 Office: AB1 505
 Tel: 3943 4298
 Email:
 Office Hours: M79, W34 ,H79
Time and Venue
 Lecture: Mon 10:3011:15pm LSB C1; Wed 10:3012:15 MMW Engine Bldg LT;
 Tutorial: Mon 11:3012:15pm LSB C1
Course Description
This course is a continuation of MATH2060. It provides rigorous treatment on further topics in mathematical analysis. This course is essential for studying advanced mathematics, pure or applied, to the level beyond undergraduate. Topics include: Fourier series, pointwise and uniform convergence of Fourier series, $L^2$completeness of Fourier series. Parseval's identity; metric spaces, open sets and continuity, completion of a metric space, contraction mapping principle; the space of continuous functions, Weierstrass approximation theorem, StoneWeierstrass theorem, Baire category theorem, continuous but nowhere differentiable functions, equicontinuity and Ascoli's theorem; implicit and inverse function theorems, functional dependence and independence; fundamental existence and uniqueness theorem for differential equations, the continuous dependence of the solution on initial time and values.
References
Lecture Notes
 Lecture 1
 Lecture 2
 Lecture 3
 Lecture 4
 Lecture 5
 Lecture 6
 Lecture 7
 Lecture 8
 Lecture 9 (revised, minor note on notation)
 Lecture 10 (revised again on important example)
 Lecture 11
 Lecture 12
 Lecture 13
 Lecture 14
 Lecture 15 (revised)
 Lecture 16
 Lecture 17
 Lecture 18
 Lecture 19
 Lecture 20
 Lecture 21
 Lecture 22
 Lecture 23
Tutorial Notes
 Tutorial 1 (SEP 19)
 Tutorial 2 (SEP 26)
 Tutorial 3 (OCT 3)
 Tutorial 4 (OCT 17)
 Tutorial 5 (OCT 24)
 Tutorial 6 (OCT 31)
 Tutorial 7 (NOV 7)
 Tutorial 8 (NOV 14)
 Tutorial 9 (NOV 21)
 Tutorial 10 (NOV 28)
Assignments
 Homework 1 (due on Sep 21, 2016)
 Homework 2 (due on Sep 28, 2016)
 Homework 3 (due on Oct 5, 2016)
 Homework 4 (due on Oct 12, 2016)
 Homework 5 (due on Oct 24, 2016)
 Homework 6 (due on Nov 9, 2016)
 Homework 7 (due on Nov 16, 2016)
 Homework 8 (due on Nov 28, 2016)
 Homework 9 (no need to hand in)
Solutions
 HW1 Solution
 HW2 Solution
 HW3 Solution (Updated for Q1)
 HW4 Solution
 HW5 Solution
 HW6 Solution
 HW7 Solution
 HW8 Solution
 HW9 Solution (Q5 revised)
 Midterm Solution
Assessment Scheme
Homework (about once a week)  10%  
Midterm (Oct 26, 2016, 10:3012:15pm)  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.
Last updated: December 05, 2016 11:22:39