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
- Mid-term 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, 3:30-5:30pm, 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; W3-4,6; H3-4,6
-
TSANG, Tin Yau
- Office: AB1 505
- Tel: 3943 4298
- Email:
- Office Hours: M7-9, W3-4 ,H7-9
Time and Venue
- Lecture: Mon 10:30-11:15pm LSB C1; Wed 10:30-12:15 MMW Engine Bldg LT;
- Tutorial: Mon 11:30-12:15pm 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, Stone-Weierstrass 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, 10:30-12:15pm) | 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