University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg19
EGM6321 - Principles of Engineering Analysis 1, Fall 2009
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
(1) | |
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.
(1) | |
(2) | |
Where are known
(3) | |
Where
(4) | |
Where