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TUT215 2 Half range Fourier Series

# TUT215 2 Half range Fourier Series - Swinburne University...

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Swinburne University of Technology Faculty of Engineering and Industrial Sciences Mathematics Discipline Tutorial 2: Half range Fourier series 1. Classify each of the following functions according as they are even, odd or neither. (i) 4 Period , 2 0 , 4 0 2 - , 4 ) ( = < < < < = x x x f (ii) . 2 Period , 2 , 0 0 , cos ) ( π π π π = < < < < = x x x x f (ii) . 2 Period , 2 0 ), 2 ( ) ( = < < = x x x x f 2. Consider the periodic function 4 2 , 2 2 0 , 4 ) ( < < < < = x x x f (i) Find the Fourier series for the above function. Graph the periodic extension on the interval -12< x <12. (ii) Find the Fourier sine series for the above function. Graph the periodic extension on the interval -12< x <12. (iii) Find the Fourier cosine series for the above function. Graph the periodic extension on the interval -12< x <12. 3. Consider the periodic function 2 1 , 0 1 0 , 1 ) ( < < < < = x x x f (i) Find the Fourier sine series for the above function. Graph the periodic extension on the interval -6< x <6. (ii) Find the Fourier cosine series for the above function. Graph the periodic extension on the interval -6< x <6.

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TUT215 2 Half range Fourier Series - Swinburne University...

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