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Unformatted text preview: Mathematica to make a graph of the x-y the solution trajectory. You should obtain a spiral solution. Next, use Mathematica to generate a direction (or slope) ﬁeld plot of x vs. y (recall how you did something very similar to this in Homework #2). Finally, overlay the two plots so that you can see how the trajectory threads the direction ﬁeld plot. Describe in words how the trajectory would change if we have diﬀerent initial conditions from those given above. Do you expect all trajectories to have the same end point? (c) Rewrite equations (1) and (2) as a single equation in matrix form. Then use Mathematica to ﬁnd the eigenvalues and eigenvectors of the coeﬃcient matrix that appears in your equation. What do your results tell you about the nature of the solutions to equations (1) and (2)? Are they consistent with the particular solutions you found in part (a)?...
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This note was uploaded on 12/29/2011 for the course ENGR 5a taught by Professor Brewer during the Fall '09 term at UCSB.
- Fall '09
- Chemical Engineering