Unformatted text preview: respect to x , so that I xx ( t, x, y ) = ∂ 2 I ( t, x, y ) /∂x 2 . (a) Since Taylor series expansion yields I ( t ) i − 1 ,j = I ( t, x, y ) − hI x ( t, x, y ) + h 2 2 I xx ( t, x, y ) − h 3 6 I xxx ( t, x, y ) + O ( h 4 ) , I ( t ) i +1 ,j = I ( t, x, y ) + hI x ( t, x, y ) + h 2 2 I xx ( t, x, y ) + h 3 6 I xxx ( t, x, y ) + O ( h 4 ) , we see that I ( t ) i − 1 ,j − 2 I ( t ) ij + I ( t ) i +1 ,j h 2 = h 2 I xx ( t, x, y ) + O ( h 4 ) h 2 = I xx ( t, x, y ) + O ( h 2 ) . 129...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.
 Fall '11
 Dr.Robin

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