Mtg 9: Thur, 10Sept09
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(1)
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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:
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(2)
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Application: Just invent any
Let
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(3)
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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
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(4)
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(5)
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Where
Eq.(2) P.6-4:
Eq.(4) P.9-2
Where
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(6)
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From Eq.(6) P.9-3 , Eq.(4) P.9-2 and Eq.(3) P.4-2 obtain:
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(7)
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Application: Consider the following
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(8)
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HW: Show Eq(8) is "exact" N1_ODE. Note P.10-1
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