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

From Wikiversity
Jump to navigation Jump to search

EGM6321 - Principles of Engineering Analysis 1, Fall 2009[edit]

Mtg 19: Tues, 5Oct09


Page 19-1

[edit]

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

[edit]

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

[edit]

(1)



(2)



Where are known

(3)



Where

(4)



Where

References[edit]