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AMS 361: Calculus IV
Fall 2011
Lecture 11-15-2011
Linear System of DEs & Laplace Transforms
Goals for Tuesday (11/15/2011) lecture:
Understanding the solutions of the following systems of DEs:
Example 2
࠵
!
࠵
!
!
=
4
−
3
3
4
࠵
!
࠵
!
This example will show that the system has complex eigenvalues
࠵
!
=
4
+
࠵
3
࠵
!
=
4
−
࠵
3
and we can find the associated eigenvectors for the two eigenvalues.
Example 3
࠵
!
࠵
!
!
=
4
−
3
3
4
࠵
!
࠵
!
This example will show that the system has complex eigenvalues
࠵
!
=
4
=
࠵
!

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and we can find the associated eigenvector
࠵
!
for the eigenvalue
࠵
!
. We have to compose
the linearly independent solution by introducing
࠵
!
=
࠵
!
࠵
+
࠵
!
࠵
!"
Example 4
࠵
!
࠵
!
!
=
3
2
7
5
࠵
!
࠵
!
+
3
2
࠵
Example 5
Two coupling blocks by two massless springs on smooth horizontal bench.
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