lecturenotes11_10

# lecturenotes11_10 - For Lab 11 • We will use a Fourier...

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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.
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 don’t mean how long it takes to code)...
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## This note was uploaded on 02/25/2009 for the course BEE 1510 taught by Professor Staff during the Fall '05 term at Cornell.

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

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