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has a 1 times y<sub>1</sub> in that spot. I think it's easier to use the
 
has a 1 times y<sub>1</sub> in that spot. I think it's easier to use the
 
Jacobian matrix the way I demonstrated in class to see this.
 
Jacobian matrix the way I demonstrated in class to see this.
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Response from [[User:Rrusson|Ryan Russon]]
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Thanks Steve! Using the Jacobian is how I approached it and it is a lot more intuitive for me to approach it that way.
  
 
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[[2013_Fall_MA_527_Bell|Back to MA527, Fall 2013]]
 
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Revision as of 15:25, 21 September 2013


Homework 5 collaboration area

MA527 Fall 2013


Question from Ryan Russon

For problems p.159: 4,7,11 are we supposed to accompany each solution with a sketch of the what is happening at the critical points or are we fine just stating what is happening at those points based on the eigenvalues of the linearized system? My confusion is stemming from the answer in the back of the book for #11 which says, "Use -cos(+- 1/2...)," you get the picture.

Answer from Steve Bell :

Those problems don't seem to ask for a sketch, so don't bother. (If you wanted to practice for the exam, testing yourself to see if you would know how to draw a sketch if you had to would be therapeutic.)

That cryptic remark about the trig identity can be used like so

$ -\cos(\frac{\pi}{2}+ x)=\sin x = x -\frac{1}{3!}x ^3 +\dots \approx x $

(when x is small) to realize that the linearized system at the critical point (pi/2,0) has a 1 times y1 in that spot. I think it's easier to use the Jacobian matrix the way I demonstrated in class to see this.

Response from Ryan Russon

Thanks Steve! Using the Jacobian is how I approached it and it is a lot more intuitive for me to approach it that way.


Back to MA527, Fall 2013

Alumni Liaison

Questions/answers with a recent ECE grad

Ryne Rayburn