# ICE: Matlab Flow

Recall that the three-term recurrence relation
for Chebyshev polynomials is given by
\[
T_{k+1}(x) = 2xT_k(x)-T_{k-1}(x),
\]
where we know that \(T_0(x) = 1,\) and \(T_1(x)=x,\)
for \(x\in[-1,1].\)
Given some maximal degree \(K\) that we choose, write a script that
uses this relation to generate a \((K+1)\times N\) array
`T`
whose \(k^\text{th}\) row comprises the values of \(T_{k-1}\)
at some vector \(x\) of length \(N\), which you provide.
In other words, `T(k+1,n)`\(=T_k(x_n)\)
for \(k=0,1,\dots,K\) and \(n=1,2,\dots,N\).
Your script should then plot the rows of
`T`.

Assignment 6 is posted.

The midterm exam will take place on Friday,
12 October. As always, you are permitted any paper
notes you find useful, but no electronic devices are
allowed. The test is cumulative, but emphasizes
the material covered in the last fours weeks.
A sample exam is
available.

You need to install
Matlab
on your computer by Wednesday.
You do not need Simulink or any particular toolboxes, though
you might find the Symbolic toolbox useful at some time
in the future (not in this class).