Chemical Engineering Hand Written_Notes_Part_23

Chemical Engineering Hand Written_Notes_Part_23 - 48 2....

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48 2. FUNDAMENTALS OF FUNCTIONAL ANALYSIS which can be approximated in the neighborhood of x = h 11 i T using the Taylor series expansion as f ( x )= f ( x )+ ∂f 1 ∂x 1 ∂f 1 ∂x 2 ¸ x = x δ x +[ δ x ] T 2 f ∂x 2 1 2 f ∂x 1 ∂x 2 2 f ∂x 2 ∂x 1 2 f ∂x 2 2 x = x δ x + R 3 ( x x ) (5.23) =2 ( 1+ e 2 )+ h (2 + e 2 )( 2+ e 2 ) i " x 1 1 x 2 1 # + " x 1 1 x 2 1 # T " (2 + e 2 ) e 2 e 2 (2 + e 2 ) #" x 1 1 x 2 1 # + R 3 ( x x ) (5.24) Case B: Functionvector F ( x ): R n R n F ( x )= F ( x )+ ∂F ( x ) x ¸ δ x + R 2 ( x x ) (5.25) ∂F ( x ) x ¸ = ∂f 1 ∂x 1 ∂f 1 ∂x 2 ...... ∂f 1 ∂x n ∂f 2 ∂x 1 ∂f 2 ∂x 2 ...... ∂f 2 ∂x n ...... ...... ...... ...... ∂f n ∂x 1 ∂f n ∂x 2 ...... ∂f n ∂x n x = x Here matrix h ∂F ( x ) x

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This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

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Chemical Engineering Hand Written_Notes_Part_23 - 48 2....

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