MATH 1005 Study Guide - Midterm Guide: Fourier Series
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Any non-programmable calculator permitted, 1 blank sheet permitted for roughs. (cid:88) n=1 sin n n cos nx, (b) 2 sin n n cos nx: [2 marks] the rst term term, b1, of the fourier sine series of the function f (x) = x2 for 0 < x < is given by: (a) 0, (b) 8 sin x, (c) 2 8 sin x, (d) 2 + 8 sin x: [2 marks] find the rst term, a0, of the fourier cosine series of the function f (x) = 2 (b) a0 = 0, (c) a0 = 1, (d) a0 = Part ii: show all work here and give details. Find the fourier series of f in the form: [10 marks] let f (x) = where n 1. 2: [10 marks] let f (x) = x2 for 0 x 1. Find the an in the half-range cosine series of f (which is of the form an cos(n x))
