This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Practice problems for the Final, part 3 Note: Practice problems for the Final Exam, part 1 and part 2 are the same as Practice problems for Midterm 1 and Midterm 2. 1. Calculate Fourier Series for the function f ( x ), defined on [ 2 , 2], where f ( x ) = ( 1 , 2 x , 2 , < x 2 . 2. Calculate Fourier Series for the function f ( x ), defined on [ 5 , 5], where f ( x ) = 3 H ( x 2) . 3. Calculate Fourier Series for the function, f ( x ), defined as follows: (a) x [ 4 , 4], and f ( x ) = 5 . (b) x [ , ], and f ( x ) = 21 + 2sin5 x + 8cos2 x. (c) x [ , ], and f ( x ) = 8 X n =1 c n sin nx, with c n = 1 /n. (d) x [ 3 , 3], and f ( x ) = 4 + 6 X n =1 c n (sin( nx/ 3) + 7cos( nx/ 3)) , with c n = ( 1) n . 4. (a) Let f ( x ) = x + x 3 for x [0 , ]. What coefficients of the Fourier Series of f are zero? Which ones are nonzero? Why? (b) Let g ( x ) = cos( x 5 )+sin( x 2 ). What coefficients of the Fourier Series of g are zero? Which ones are nonzero? Why? 1 5. Let f ( x ) = 2 x + x 4 for x [0 , 5]. (a) Write down the function G ( x ), which is the odd continuation for f ( x ). Specify what terms will be zero and nonzero in the Fourier expansion for G ( x )....
View Full
Document
 Winter '07
 nataliakomarova
 Fourier Series

Click to edit the document details