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%  Homework for the undergraduate course "Numerical Analysus I", 
%  Spring semester, 2010, Wei-Cheng Wang.


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{\scriptsize Numerical Analysis I, Fall 2010 
(http://www.math.nthu.edu.tw/\~\,wangwc/)} \hfill 

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Preparation guide for Quiz 01   
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% Oct 02, 2009. 
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%           The questions!

Most of the exam problems will be closely related to your homework
problems. Make sure you understand all of them. 

You will need to do simple programming for the quiz, such as 
revising a (given) bisection code for a different problem.
Try it first.

\begin{enumerate}

\item 

Understand why it takes 
32 bits for single precision and 64 bits for double precision.

\item
Understand the source of loss of significance caused
by subtraction and how to avoid them.
Study the examples in the textbook.

\item
Understand the source of instability for recurrence formula.
Read example 3 on page 32.

\item 
Understand rate of convergence.

\item
Understand the principle of bisection and be
able to derive error estimate.

\end{enumerate}

{\bf Other remarks}:

\begin{enumerate}
These are things that will not appear in the exams, but you
may be curious and want to know about.
\item 
You may 
find different definitions for the machine epsilon,
since it is not officially put in IEEE standard.
We take the one adopted by Matlab for convenience.
Use `help eps' command in matlab to find out the details.

\item
Ragarding problem 11(c) and 12(c) of section 1.2,
be reminded that there is a theorem that gives
the error bound between an 'alternating series' and its 
finite term truncation. Which is ...?

\item
If you looked at the answer for problem 15 of section 1.2,
 you may wonder how to get that number calculated.
Try `vpa'. It is also in the sample code sent to you.

\item
\end{enumerate}

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