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Unformatted text preview: PDE EXAMPLES Math 21a An equation which involves partial derivatives for an unknown function f ( x, y ) is called a partial differential equation or shortly a PDE . The topic of PDEs would fill a course by itself. Finding and understanding solutions of PDEs can be difficult. The topic is introduced here in the context of partial differentiation . You should be able to verify that a given function f ( t, x ) satisfies a specific PDE and know some examples. It is useful as well to understand how these equations are derived. LAPLACE EQUATION. f xx + f yy = 0 . A stationary tempera- ture distribution on a plate satisfies this equation. 1) Verify that f ( x, y ) = x 3 3 xy 2 satisfies the Laplace equation. ADVECTION EQUATION. f t = f x . Models transport in a one- dimensional medium. It is also called a transport equation . 2) Verify that f ( t, x ) = e- ( x + t ) 2 satisfy the advection equation f t ( t, x ) = f x ( t, x )....
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This note was uploaded on 03/29/2008 for the course MATH 308 taught by Professor Comech during the Spring '08 term at Texas A&M.
- Spring '08