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{\bf Math 325, Spring, 2001}

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It is time to organize groups for the group projects.
By Wednesday, February  28, please form a group with 2 or 3
other  students in the class (so a group has 3 or 4 members).
Each group should give me a list of the members of
the group by February 28.

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{\bf Assignment 5, due March 2}


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Read 
Boyce and DiPrima, Sections 7.7-7.9, 9.1, 9.2, and {\it Differential
Equations with Maple}, Chapter 12.

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In Boyce and DiPrima, do (by hand, unless otherwise indicated)
p.\ 400  \#1, p. 407\ \#17,19,   p.\ 417 \#1.
 On p.\ 407 \#17
also use Maple to find the matrices $T\/$ and $J\/$.
The Maple command  {\bf jordan}(A,$'$P$'$) will find the
Jordan canonical form  $J\/$ of $A\/$.  The command  {\bf eval}(P) will
then give the matrix  $T\/$.  The
command  {\bf jordan}
is in the {\bf linalg} package.  (Use the command: {\bf with(linalg)} to load
it.)

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In {\it Differential Equations with Maple} do Problem Set F \#1,4.


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Also solve the following problems.

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1. Solve:
$$
{\bf y}'=
\left [\begin {array}{ccccc} 2&1&0&0&0\\0&2&0&0&0\\0&0&3&1&0\\0&0&0&3&
1\\0&0&0&0&3\end {array}\right ] {\bf y}, \qquad {\bf y}(0)=
\left [\begin {array}{c} 1\\2\\3\\4\\5\end {array}\right ].
$$

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\noindent
2.  Find the general soluion of   
$$
{\bf y}'=\left [\begin {array}{ccc} 3&1&0\\0&3&1\\0&0&3\end
{array}\right ]
{\bf y}.
$$

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For the problems from Problem Set F, 
you may work in groups, following the same 
rules as for Assignment 2.
If you do work in a group, turn these problems in separately from the
rest of the assignment.


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