NM7_numdiff - Numerical Differentiation and Integration...

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1 Numerical Differentiation and Integration Chapter 7
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2 Numerical Differentiation
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3 Why numerical? Sometimes an analytical function is known but the derivative is not easily found. Sometimes an analytical function is not known, such as with experimental data. What is known is data pairs (t, x(t))
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4 How to If the analytical function is known, the value of the function can be computed at t and t+ t; t is normally a constant. A simple rise/run can be computed as an estimate of the derivative. ( 29 ( 29 t t x t t x ( dt dx D - D + =
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5 For Example • If x(t)=sin(t), t 0 = 1 and t = 0.1, then: 1 . ) 1 sin( ) 1 . 1 sin( dt dx - =
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6 How to If only t and x(t) data pairs are known, a similar rise/run calculation can be done or… In this case, t is set by the parameters used at data acquisition time. If data is taken every 1 second, there may be a significant event that was missed. t data data run rise t 1 t - = +
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How to A curve fitting algorithm can be used to “fit” the data with a “simple” function for which the derivative can be found. For example, use polyfit to find the coefficients of
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This note was uploaded on 10/13/2010 for the course MECH 342 taught by Professor Vemaganti during the Winter '05 term at University of Cincinnati.

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NM7_numdiff - Numerical Differentiation and Integration...

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