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


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%          The title and header.

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

\begin{center}
\large
Preparation guide for Quiz 03   
\normalsize
\end{center}
\noindent
% Oct 02, 2009. 
% \vspace{.3in}

% \bigskip

%           The questions!

Since the content of this quiz is very little,
the homework
problems are especially important, every one of them.

Here is the check list:

\begin{enumerate}

\item 
Those materials that I told you to skip, skip them.

\item 
Be able to write down the formulae for the Lagrange polynomials
and know their basic properties.

\item 
Given the data $(x_0,y_0), \cdots (x_n, y_n)$, know how to compute
all the divided differences. See Table 3.7 and 3.8 for example.

\item 
Know how to generate the interpolating polynomial
with the Lagrange polynomials, or with the
divided differences.

\item 
This time, you will need to do a self-contained programming,
on Newton divided difference. 
Write one from scratch.
More importantly, test it with the 'interp.m' on the course
homepage against polynomials where you know 
the exact solution of the interpolating polynomial.
People almost always make some mistake in the first programming
attempt. This one is short enough for you to debug.

You will need to do it again in the quiz. No more and no less.

\item
Memorize the formula of interpolation error. Be able to derive
basic error bounds.

\end{enumerate}

\end{document}


%  This is a LaTex file.

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


\documentclass[12pt]{article}

%          The page format, somewhat wider and taller page than in art12.sty.

\topmargin -0.1in \headsep 0in \textheight 8.9in \footskip 0.6in
\oddsidemargin 0in  \evensidemargin 0in  \textwidth 6.5in

\begin{document}
\thispagestyle{empty}

%          The title and header.

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

\begin{center}
\large
Preparation guide for Quiz 04   
\normalsize
\end{center}
\noindent
% Oct 02, 2009. 
% \vspace{.3in}

% \bigskip

%           The questions!

As usual, you need to go over your homework problems first.
When you are done, check if you have reached the following:
\begin{enumerate}

\item 
Understand the formula of Hermite interpolation.
For example, what is the degree of Hermite polynomials?
How to derive the 'basis functions', $H$ and $\hat H$?

\item 
Be able to implement the Hermite interpolation.

\item 
What are the continuity conditions for cubic splines?
Why do they give rise to piecewise cubic polynomials?
Why need two more conditions on the boundary?

What are 'free', 'clamped' and 'not-a-knot' boundary conditions, respectively?

\item 
Know how to use cubic splines of existing packages
such as those in matlab and octave 
(i.e. read the corresponding 'help' documents and make sure you
 understand them).

\end{enumerate}

\end{document}