Chemical Engineering Hand Written_Notes_Part_23

Chemical Engineering Hand Written_Notes_Part_23 - 48 2....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

Chemical Engineering Hand Written_Notes_Part_23 - 48 2....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online