EGM6321 - Principles of Engineering Analysis 1, Fall 2009
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Mtg 19: Tues, 5Oct09
HW: Legendre differential Eq.(1) P.14-2 with , such that homogeneous solution .
Use reduction of order method 2 (undetermined factor) to find , second homgenous solution
HW: K. p28, pb. 1.1.b.
Variation of parameters (continued) P.18-4
Use expression for Eq.(2) P.18-4 and Eq.(3) P.18-4 in non-homogeneous L2_ODE_VC Eq.(1) P.3-1
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(1)
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Where , because is a homogeneous solution
Where , because is a homogeneous solution
2 equations Eq.(1) P.18-4 and Eq.(1) P.19-1 for two unknowns
In matrix form:
Where is the Wronskian matrix designated as
The Wronskian, W, is the determinant of
If , then exists and
Theorem: (function of x) are linearly independant if , where zero function.
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(1)
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(2)
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Where are known
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(3)
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Where
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(4)
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Where