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Lecture_17_differentiation_6p

Lecture_17_differentiation_6p - Illustration numerical...

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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
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