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Unformatted text preview: f ( x ) = a 2 + X n =1 a n cos nx (19) = 1 (20) 18 1 Figure 3: graph of the function to which the series con-verges f ( x ) = 1 , < x < ; sine series period 2 (21) To obtain the sine series we take the odd extension of f ( x ) and hence all the cosine coecients , a n , will be zero. Computing b n , b n = 2 L Z f ( x ) sin nx L dx (22) = 2 Z sin nxdx (23) = 2 n-cos nx (24) = 2 n 2 , n = odd , n = even (25) the corresponding Fourier sine series is, f ( x ) = X n =1 b n sin nx (26) = 4 X n = odd sin nx n (27) = 4 X n =1 sin(2 n-1) x 2 n-1 (28) Figure 4: graph of the function to which the series con-verges 2...
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This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).
- Spring '07