University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg19

EGM6321 - Principles of Engineering Analysis 1, Fall 2009Edit

Mtg 19: Tues, 5Oct09


Page 19-1

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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

 

(1)


Where   , because   is a homogeneous solution

Where   , because   is a homogeneous solution

Page 19-2

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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.

Page 19-3

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(1)



 

(2)



Where   are known

 

(3)



Where  

 

(4)



Where  

ReferencesEdit