TUT215 1 Fourier Series

TUT215 1 Fourier Series - Swinburne University of...

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Faculty of Engineering and Industrial Sciences M a t h e m a t i c s D i s c i p l i n e Tutorial 1: Fourier series 1. State the period of l x v l x iv nx iii x ii x i π sin ) ( 2 cos ) ( sin ) ( 2 cos ) ( sin ) ( 2. Graph each of the following periodic functions ). ( ) 2 ( 2 0 , ) ( ) ( ). ( ) 4 ( , 2 2 , 2 ) ( ) ( ). ( ) 2 ( , , ) ( ) ( 2 x h x h x x x h iii x g x g x x x g ii x f x f x x x f i = + < < = = + < < = = + < < = 3. For each of the following functions (i) graph the whole range Fourier series continuation for the interval specified, (ii) calculate the Fourier series. (a) < < = x x x f - , ) ( (b) 2 0 , ) ( < < = x x x f (c ) 2 2 - , 1 ) ( < < = x x f ). ( ) 2 ( , 2 3 2 , 1 x f x f x = + < < (d) 2 , ) ( < = x x x f . 2 3 2 - interval , 2 < < > x x x (e) < < = x x x f 0 , sin ) ( 0 ). ( < < 4. Find a Fourier series for the periodic function 1 x 1 - , ) ( < < = x x f Page 1 of 3
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TUT215 1 Fourier Series - Swinburne University of...

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