Unformatted text preview: ∂F ∂y 00 = const 3. Find the curve y ( x ) joining the two points (0 , 0) and (1 , 0) for which the functional J ( y ) = Z 1 y 00 2 dx is minimum if (i) y (0) = a and y (1) = b , (ii) no other conditions are prescribed. Hint: In the latter case, use two natural boundary conditions as suggested by the derivation of the EulerPoisson equation in Problem 2. 4. Find the curve y ( x ) such the functional J ( y ) = Z 11 y dx has an extremum, subject to the conditions y (1) = 0 , y (1) = 0 , Z 11 p 1 + y 2 dx = 4...
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This note was uploaded on 02/20/2011 for the course MATH 503 taught by Professor Schleiniger,g during the Fall '08 term at University of Delaware.
 Fall '08
 Schleiniger,G
 Math, Calculus

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