# Math 222 Current Assignment

## Due Friday, March 8

This week's assignment involves the Diffeq, Phase Plane program
of MacMath 9.2.
The computer portion of the assignment is just item 3 of part c). For each
of the 5 cases mentioned, students are asked to produce a symmetric matrix
with the specified eigenvalues, and then look at (and print) some integral
curves of the vector field. (Non-diagonal would be more interesting,
except in the proper node cases....)

MacMath sometimes has trouble printing, so shift to screen dumps (cmd-shift 3)
if this arises.

Note that Macmath requires asterisks (*) for multiplication. (3+x+4*y rather
than 3x+4y.)

On part a), note that the vector field grad(Q) at the column vector
**(x,y)^transpose** is the matrix A times this column vector.

On part b), work in general matrix form. You need the definition of
eigenvectors and eigenvalues, but not their computation. The
asserted integral curve is \vec(r(t)) =

so the vector field at the point **(x,y)^transpose** is ...
and continue to verify the integral curve definition.

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Last Update: * March 7, 1996*