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