Lecture_17_differentiation_6p

Lecture_17_differentiation_6p - 4/10/2011 1 Derivative,...

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Unformatted text preview: 4/10/2011 1 Derivative, what does it mean physically Finite differences using Taylor series Forward differencing Backward differencing Central differencing Lecture 17: Numerical differentiation Interpretation of finite differences Higher order derivatives Example: NGSIM data set: computation of velocity Be careful of noise... Differentiation Definition of the derivative Most basic way to define the derivative: as the slope of the tangent, defined by the limit below: x x f x f x Idea of finite differencing: discretization Create a grid along which the function will be discretized, and the limit of the ratio in the previous slide will be approximated. Illustration: numerical approx of ratio (1) If h is small, this should provide a good approximation of the derivative Illustration: numerical approx of ratio (2) If h is small, this should provide a good approximation of the derivative Illustration: numerical approx of ratio (3) If h is small, this should provide a good approximation of the derivative 4/10/2011 2 Formal expression: Taylor series Remember, approximations of functions with small variations can be expressed with Taylor series. We use the following notation Remember, approximations of functions with small variations can be expressed with Taylor series. We use the following notation Formal expression: Taylor series Remember, approximations of functions with small variations can be...
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This note was uploaded on 09/07/2011 for the course ENGIN 7 taught by Professor Horowitz during the Spring '08 term at University of California, Berkeley.

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Lecture_17_differentiation_6p - 4/10/2011 1 Derivative,...

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