## Real Analysis – Consultation

Posted: April 19, 2013 in General

Do note that I would be overseas from 26 Apr (Fri). Hence, I would not be available for consultation nor be able to answer an queries (including emails).

Good Luck for the Examinations!

## Real Analysis – Student Feedback

Posted: April 15, 2013 in Real Analysis Spring 2013

For students taking MH3100/MTH311, I sincerely like to seek your feedback on the the conduct of the tutorials.

Please access this link to provide your feedback. Feel free to make ANY comments and your feedback will be taken seriously and taken into consideration (if I ever get to teach again).

Note that the link is only available until 21 Apr (Sun).

Regards,
HanMao

## Real Analysis – Tutorial 9

Posted: March 27, 2013 in Real Analysis Spring 2013

As mentioned by Prof Chan and Prof Zhao, the definitions of limits can be interpreted as a challenge-and-respond’ process and Prof Zhao further elaborated ${\epsilon}$ as a standard of proximity’. In the tutorial, I gave another (similar) interpretation of the definition.

In general, most’ theorems and definitions in mathematics can be interpreted as a machine’ that produces some output given every input of certain type. For example, the definition of functional limits can be interpreted as the following machine.

Here, the input is a positive ${\epsilon}$ and the output (highlighted in blue) is a ${\delta}$. We notice the output has to fulfill certain conditions that are dependent on the input. This is highlighted in yellow.

In other words, the machine is a ${\lim_{x\rightarrow c} f(x)=L}$‘ machine if given input ${\epsilon>0}$, the machine outputs a ${\delta>0}$ such that ${|f(x)-L|<\epsilon}$ whenever ${0< |x-c|<\delta}$.

## Practice Problems for Real Analysis

Posted: March 22, 2013 in Real Analysis Spring 2013

Please feedback if the questions are sufficiently simple’ or if hints are sufficiently strong’.
Practice Problems for Lecture 11
Practice Problems for Lecture 10
Practice Problems for Lecture 9 Take note of Q4/Q5 in Section 4.
Practice Problems for Lecture 8
Practice Problems for Lecture 6
Practice Problems for Lecture 5

## Real Analysis – Tutorials

Posted: March 19, 2013 in Real Analysis Spring 2013

Tutorial 12
Worksheet with blanks
Completed worksheet
(Please take note that $\lim_{n\to\infty} f'_n$ need not equal $(\lim_{n\to\infty} f_n)'$ even if $f_n$ converges uniformly.
However, $\lim_{n\to\infty} f'_n=(\lim_{n\to\infty} f_n)'$ if $f'_n$ converges uniformly.)

Tutorial 11
Edited Worksheet with blanks
(Correction due to Jin Bin.)
Completed worksheet

Tutorial 10
Worksheet with blanks
Completed worksheet

Tutorial 9
See this post for explanation of the diagrams.
Worksheet with blanks
Completed worksheet

Tutorial 1
Completed worksheet.

## Real Analysis – Practice Problems 8

Posted: March 14, 2013 in Real Analysis Spring 2013

Note that there is some overlap with the tutorial problems.

Also, please feedback if these problems are simple’ enough.

## Real Analysis – Tutorial 7

Posted: March 11, 2013 in Real Analysis Spring 2013