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Unformatted text preview: Test Review Differential Equations: ODE vs PDE; Order. FOODE: y ( t ) = f ( t,y ( t ) ) IVP. Direction Fields. The Existence and Uniqueness Theorem. Four Special Classes FOLODE: y + p ( t ) y = g ( t ) . 2 Four Special Classes FOLODE: y + p ( t ) y = g ( t ) . Multiply with integrating factor e R p ( t ) dt . Separable FOODE: y = M ( x ) N ( y ) . 2 Four Special Classes FOLODE: y + p ( t ) y = g ( t ) . Multiply with integrating factor e R p ( t ) dt . Separable FOODE: y = M ( x ) N ( y ) . Write as M ( x ) dx + N ( y ) dy = 0 and integrate. Applications: Mixing; Escape Velocity. Pop ulation Dynamics. 2 Exact FOODE: M ( x,y ) dx + N ( x,y ) dy = 0 . 3 Exact FOODE: M ( x,y ) dx + N ( x,y ) dy = 0 . If M y = N x on a domain D without holes then there is a ψ ( x,y ) with ψ x = M and ψ y = N , and ψ ( x,y ) = c is an implicit solu tion. Integrating Factors: If M ( x,y ) dx + N ( x,y ) dy = 0 is not exact 3 Exact FOODE: M ( x,y ) dx + N ( x,y ) dy = 0 . If M y = N x on a domain D without holes then there is a ψ ( x,y ) with ψ x = M and ψ y = N , and ψ ( x,y ) = c is an implicit solu tion....
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 Spring '08
 Turner
 Uniqueness Theorem

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