4/10/2011
1
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Derivative, what does it mean physically
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Finite differences using Taylor series
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Forward differencing
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Backward differencing
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Central differencing
Lecture 17: Numerical differentiation
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Interpretation of finite differences
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Higher order derivatives
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Example: NGSIM data set: computation of velocity
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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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