MATH3060 - Mathematical Analysis III - 2021/22

Course Name: 
Mathematical Analysis III
Teacher: 
Prof. Tom Yau Heng WAN
Course Year: 
2021/22
Term: 
1

Announcement

  • No tutorial in the 1st week
  • Face-to-face classes, midterm, and final exam. However, homework will be assigned and collected using Gradescope (in the tool of Blackboard)
  • Homework 1 (due on Sep 24, 2021, 12:00noon, submit via Gradescope system)
  • Homework 2 (due on Oct 8, 2021 at 12:00noon, submit via Gradescope system)
  • Homework 3 (due on Oct 15, 2021 at 12:00noon, submit via Gradescope system)
  • Homework 4 (due on Thursday Oct 21, 2021 at 12:00noon, submit via Gradescope system)
  • Midterm exam next Friday Oct 22, 2021 during class (9:30-11:00am), covers material up to Oct 15 and homework 4.
  • Homework 5 (due on Wednesday Nov 10, 2021 at 12:00noon, submit via Gradescope system)
  • Mid-term statistics: average=48.97, SD=18.33, Max=90, Min=7
  • Homework 6 (due on Nov 19, 2021 at 12:00noon, submit via Gradescope system)
  • Homework 7 (due on Nov 26, 2021 at 12:00noon, submit via Gradescope system)
  • Homework 8 (No need to hand-in, solution will be posted on Dec 8, 2021)
  • Final exam: 18:30-20:30, Dec 16, 2021, University Gym; covers all materials with emphasis on those after the midterm exam

General Information

Lecturer

  • Tom Yau-heng Wan
    • Office: LSB 215
    • Tel: x 37986
    • Email:

Teaching Assistant

  • Chan Ki Fung
    • Office: AB1 505
    • Tel: 394 34298
    • Email:

Time and Venue

  • Lecture: Wed 9:30-10:15am ERB703; Fri 9:30-11:15am WMY305
  • Tutorial: Wed 08:30-09:15am ERB703

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


Tutorial Notes


Assignments


Solutions


Assessment Scheme

Homework 10%
Mid-term (Oct 22, 2021, 9:30-11:15am) 40%
Final (18:30-20:30, Dec 16, 2021 University Gym) 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 08, 2021 18:38:45