MATH3060 - Mathematical Analysis III - 2022/23

Course Name: 
Mathematical Analysis III
Teacher: 
Prof. Tom Yau Heng WAN
Course Year: 
2022/23
Term: 
1

Announcement

  • No tutorial in the 1st week

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 Wong Foo Yuan Bldg UG01 (new location LHC G04 to be updated on CUSIS); Fri 9:30-11:15am YC Liang Hall 106
  • Tutorial: Wed 8:30-9:15am Wong Foo Yuan Bldg UG01 (new location LHC G04 to be updated on CUSIS)

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


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: August 29, 2022 14:48:06