# MATH3060 - Mathematical Analysis III - 2022/23

Course Year:
2022/23
Term:
1

### Announcement

• No tutorial in the 1st week
• Homework 3 (due Oct 14, 2022, 11:00am, via Gradescope) Typos in question 3(d) have been corrected in the revised file. [Download file]
• Reminder: Midterm on Oct 21, 2022, 9:30-11:00am; coverage Ch 1 & 2, Homework 1-4
• Typos in the notes of Lecture 12, please see revised file below.
• Midterm Stat: Mean=55.41, Median=60, SD=22.39, Max=98, Min=18
• 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

### Assessment Scheme

 Homework 10% Mid-term (Oct 21, 2022, 9:30-11:15am) 40% Final (date to be determined by university)) 50%