University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg9

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

Mtg 9: Thur, 10Sept09


Page 9-1

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(1)



Note: Symbol notations:

defined as equal by definition

Non-symmetric notation means equal by definition as well, better notation than

Goal: Derive mathematical structure of a class of exact N1_ODEs

Exact L1_ODE_VC:

(2)



Application: Just invent any
Let




Page 9-2

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(3)



HW: Show that Eq(3) L1_ODE_VC is "exact". See Note P.10-1

Question: How about N1_ODEs? Eq.(2)P.6-4

N1 means Nonlinear, 1st Order

(4)



(5)



Where

Eq.(2) P.6-4:


Page 9-3

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Eq.(4) P.9-2

Where

(6)



From Eq.(6) P.9-3 , Eq.(4) P.9-2 and Eq.(3) P.4-2 obtain:

(7)



Application: Consider the following







(8)



HW: Show Eq(8) is "exact" N1_ODE. Note P.10-1

Page 9-4

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L2_ODE_VC with missing dependant variable



Where due to missing dependant variable y.

Eq.(1)P.2-3 is a L1_ODE_VC

Solution: Eq.(4)P.8-2

Exact N2_ODEs:

General N2_ODEs:

Application:

is exact means such that

References[edit]