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Unformatted text preview: Differentiation - 1 19 - Numerical Differentiation Recall that the derivative of a function y(x) is defined as h x y h x y x y h ) ( ) ( lim ) ( ' + = This implies that if we have a series of points, (x j , y j ) and we want to compute an approximate set of points (x j , y j ) for the slope, we need to do the following: 1. At each point, compute the slope between it and a neighboring point: ( ) ( ) j j j j x x y y y + + 1 1 ' 2. Output the computed slope at each point as an approximation to y j . The process of computing a derivative in this fashion is known as numerical differentiation or more commonly, finite difference . Once we have computed the slope, we must assign the slope to a particular value of j . A forward difference at x j is defined as: ( ) ( ) j j j j j x x y y y = + + 1 1 ' A backward difference at x j is defined as: ( ) ( ) 1 1 ' = j j j j j x x y y y And a central difference at x j is defined as: ( ) ( ) 1 1 1 1 '...
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This note was uploaded on 02/12/2011 for the course E 7 taught by Professor Patzek during the Spring '08 term at University of California, Berkeley.
- Spring '08