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MAT244 Math--Lectures / Phase portraits - Improper nodes
« on: November 19, 2014, 11:02:48 AM »
Prof, how about direction of improper node?
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Quiz 4 / Q4 problem 2
« on: November 12, 2014, 09:03:38 PM »
Q2: 7.6 #6
r2+9=0
r1=3i, r2=-3i
pure imaginary eigenvalue, so it's stable center
also whole soln is in the q1 fisrt post.
r2+9=0
r1=3i, r2=-3i
pure imaginary eigenvalue, so it's stable center
also whole soln is in the q1 fisrt post.
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Quiz 4 / Q4 problem 1
« on: November 12, 2014, 08:56:10 PM »
7.5 p 407 # 5
Draw a full phase portrait and describe completely the type of the stationary point indicating if it is stable or unstable and in the case of the center and focus indicate orientation (clockwise or counter-clockwise)
\begin{equation*}
\textbf{x}'=\begin{pmatrix}
-2 & \hphantom{-}1\\ \hphantom{-}1 &-2
\end{pmatrix}\textbf{x}\ .
\end{equation*}
![](http://<a href="http://www.imagebam.com/image/f84041363999992" target="_blank"><img src="http://thumbnails109.imagebam.com/36400/f84041363999992.jpg" alt="imagebam.com"></a>)
![](http://<a href="http://www.imagebam.com/image/64d11b364003377" target="_blank"><img src="http://thumbnails111.imagebam.com/36401/64d11b364003377.jpg" alt="imagebam.com"></a>)
sorry two picture can't see normally, there are two links of picture of q1 and q2
http://www.imagebam.com/image/f84041363999992
http://www.imagebam.com/image/64d11b364003377
Draw a full phase portrait and describe completely the type of the stationary point indicating if it is stable or unstable and in the case of the center and focus indicate orientation (clockwise or counter-clockwise)
\begin{equation*}
\textbf{x}'=\begin{pmatrix}
-2 & \hphantom{-}1\\ \hphantom{-}1 &-2
\end{pmatrix}\textbf{x}\ .
\end{equation*}
sorry two picture can't see normally, there are two links of picture of q1 and q2
http://www.imagebam.com/image/f84041363999992
http://www.imagebam.com/image/64d11b364003377
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