lecturenotes11_10 - For Lab 11 We will use a Fourier series...

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11/7/2008 1 Introduction to Series November 10, 2008 Taylor Series Recall that a Taylor Series can be used to represent a function in a simpler, polynomial form: or , ) ( ! ) ( ) ( 0 ) ( = = n n n x a n a f x f ) ( ) 1 ( ! 4 ) ( ... ... ) ( ! 3 ) ( ' ' ' ) ( ! 2 ) ( ' ' ) )( ( ' ) ( ) ( 5 4 ) 4 ( 3 2 x O x a f a x a f a x a f a x a f a f x f + + + + +
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11/7/2008 2 Maclaurin Series A McLaurin Series is a Taylor series about a=0. or , ) ( ! ) 0 ( ) ( 0 ) ( = = n n n x n f x f An Example: The Maclaurin Series for sin(x) is given by: ... ! 7 ! 5 ! 3 ) sin( 7 5 3 + + x x x x x | This polynomial approximates sin(x) for values of x near zero.
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11/7/2008 3 Plot of sin(x) and 7 th order Maclaurin Series approximation of sin(x) (Ref: Wolfram Mathworld) Fourier Series Fourier series are also used to represent functions in polynomial form. Fourier series use the sum of trigonometric terms to represent Periodic Functions
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11/7/2008 4 In general form: where ) sin cos 1 b a a f ω + + = , )] sin( ) cos( [ 2 ) ( 0 0 t t t n n n n n = , 2 L n π = and , ) cos( ) ( 2 2 1 = t t n n dt t t f L a . ) sin( ) ( 2 2 1 = t t n n dt t t f L b We will implement this in a rather simpler way in the next lab…
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Unformatted text preview: For Lab 11 We will use a Fourier series to represent the environmental temperature (which will effect u max ). Do this with 3 terms of the series, and the coefficients are provided constants (see handout for values) Code this into an embedded Matlab function! 11/7/2008 5 Simulink Example: Next, we will build a simulink embedded function to plot sin(x) and its taylor series approximation. Compare this to the matlab function you might write to create the same plot? TIME is the key difference between them (and I dont mean how long it takes to code)...
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lecturenotes11_10 - For Lab 11 We will use a Fourier series...

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