MATH3060 - Mathematical Analysis III - 2022/23
Announcement
- No tutorial in the 1st week
- Homework 1 (due Sept 23, 2022, 11:00am, via Gradescope) [Download file]
- Homework 2 (due Oct 5, 2022, 11:00am, via Gradescope) [Download file]
- Homework 3 (due Oct 14, 2022, 11:00am, via Gradescope) Typos in question 3(d) have been corrected in the revised file. [Download file]
- Homework 4 (due Oct 19, 2022, 11:00am, via Gradescope) [Download file]
- Reminder: Midterm on Oct 21, 2022, 9:30-11:00am; coverage Ch 1 & 2, Homework 1-4
- Arrangement of submit midterm: It is a usual face-to-face examination. However, in order to avoid argument after the grading, you will be required to do the following steps at the end of the midterm: (1) Stop writing when "pen-down" is announced by the instructor. (2) Use your "smartphone" to capture images of all the (non-empty) pages of your answers when instructed by the instructor. You will have around 5 minutes to do so. (3) Submit your answer book to the instructor. (4) Then convert the images of your answers into a pdf file. (5) Submit the pdf file of your answers into the "midterm" in the Gradescope system for record keeping before 11:59am (same morning). (We will check the "record" when grading.)
- Homework 5 (due on Nov 4, 2022 at 11:00am, via Gradescope) [Download file]
- Typos in the notes of Lecture 12, please see revised file below.
- Homework 6 (due on Nov 18, 2022 at 11:00am, via Gradescope) [Download file]
- Midterm Stat: Mean=55.41, Median=60, SD=22.39, Max=98, Min=18
- Homework 7 (due on Nov 25, 2022 at 11:00am, via Gradescope) [Download file]
- Homework 8 (No need to hand in, solution will be posted.)(Typo corrected) [Download file]
- Final exam on Dec 15, 2022 Thursday, 9:30-11:30am; Multi-purpose Hall, Pommerenke Student Centre. Coverage: Lecture notes Ch1-4 and homework 1-8, with emphasis on those material not included in the midterm.
General Information
Lecturer
-
Tom Yau-heng Wan
- Office: LSB 202A
- Email:
Teaching Assistant
-
Chan Ki Fung
- Office: AB1 505
- Tel: 39434298
- Email:
Time and Venue
- Lecture: Wed 9:30-10:15am YC Liang Hall G04; Fri 9:30-11:15am YC Liang Hall 106
- Tutorial: Wed 8:30-9:15am YC Liang Hall G04
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.
(Basic knowledge of (continuous) functions and sequences of (continuous) functions are expected including convergence, uniform convergence, differentiability, and integrability)
References
- Lecture Notes of Prof KS Chou (see below in Pre-class Notes)
- Stein & Shakarchi, Fourier Analysis, An Introduction, Princeton Lectures in Analysis I, Princeton University Press
- Rudin, Principles of Mathematical Analysis, McGraw Hill
- Copson, Metric Spaces, Cambridge University Press
- B. Thomson, J Bruckner, & A Bruckner, Elementary Real Analysis, Prentice Hall
Pre-class Notes
- Lecture Notes of Prof KS Chou, Chapter 0
- Lecture Notes of Prof KS Chou, Chapter 1
- Lecture Notes of Prof KS Chou, Chapter 2
- Lecture Notes of Prof KS Chou, Chapter 3
- Lecture Notes of Prof KS Chou, Chapter 4
Lecture Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12 (typos revised)
- Lecture 13
- Lecture 14
- Lecture 15
- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
Tutorial Notes
- Tutorial 1
- Tutorial 2
- Tutorial 3
- Tutorial 4
- Tutorial 5
- Tutorial 6
- Tutorial 7 (with solutions of some questions)
- Tutorial 8
- Tutorial 9
- Tutorial 10 (with some amendment on Q4, will discuss it next time)
- Tutorial 11
- Tutorial 12
Assignments
- Homework 1 (due on Sep 23, 2022 11:00am)
- Homework 2 (due on Oct 5, 2022 at 11:00am)
- Homework 3 (due on Oct 14, 2022 at 11:00am)
- Homework 4 (due on Oct 19, 2022 at 11:00am)
- Homework 5 (due on Nov 4, 2022 at 11:00am)
- Homework 6 (due on Nov 18, 2022 at 11:00am)
- Homework 7 (due on Nov 25, 2022 at 11:00am)
- Homework 8 (No need to hand-in, solution will be posted)(typo corrected)
Solutions
Assessment Scheme
| Homework | 10% | |
| Mid-term (Oct 21, 2022, 9:30-11:15am) | 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: December 02, 2022 12:04:08