# MATH3060 - Mathematical Analysis III - 2016/17

Course Year:
2016/17
Term:
1

### 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
• 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.

### 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%