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approximation of the function f[x] up to and including the terms in ",
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first n terms of the Fourier series."
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Cell[TextData[{
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range -\[Pi] \[LessEqual] x \[LessEqual] \[Pi]. When using the Plot function \
with the usual syntax, Plot[{f1[x],...f3[x]}, {x,-\[Pi],\[Pi]},...], you may \
need to use ",
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{x,-\[Pi],\[Pi]},...], so that you force the evaluation of the user-defined \
functions in the list before the sampling for the variable x takes place. \
Observe that the series with more terms is a better approximation but also \
oscillates wildly toward the end of the region."
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the function h against its Fourier Series with 1, 5 and 20 terms in different \
colors in the range -\[Pi] \[LessEqual] x \[LessEqual] \[Pi]. "
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 " source file ",
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Cell[TextData[{
 StyleBox["Demonstrate that two matrices do not commute in general, i.e. that \
AB \[NotEqual] BA, by defining two 5x5 random matrices using the function \
Table, computing both sides (AB and BA) and comparing the outputs using the \
function TrueQ[...] in ",
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BA",
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Cell[TextData[{
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Cell[TextData[StyleBox["Write a function g[A_,B_] that takes as input two \
matrices A and B (not necessarily square) and checks whether the number of \
columns of A is the same as the number of rows of B. If the dimensions match, \
then the function returns the product AB, otherwise it returns the message \
\[OpenCurlyDoubleQuote]Error, the matrices cannot be multiplied\
\[CloseCurlyDoubleQuote].  Test your function on a couple of matrices.", \
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Cell[TextData[{
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eigenvectors (Real and Complex) of a numerical square matrix. If A is an n \
\[Times] n matrix, then the number \[Lambda] is an eigenvalue of A if there \
exists a non-zero vector x such that ",
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There are at most n distinct eigenvalues of the matrix A, and at most n \
linearly independent eigenvectors with Real or Complex entries. "
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done using the function ",
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eigenvectors for each eigenvalue. The output is given in the form: { list of \
eigenvalues, list of eigenvectors }"
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Cell[TextData[{
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Cell["\<\
Use the function Eigensystem[...] to find the eigenvalues and a set of \
linearly independent eigenvectors for the matrix M that you defined in part \
I. \
\>", "ItemNumbered",
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Cell[TextData[{
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Eigensystem[...]."
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 "."
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