Suppose that f(t) is periodic with period [-a, *) and has the following real Fourier coefficients: ao = 4, a1 = 1, az = 3, az = 3, b = 2, by = -3, by = 0, .. (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) (B) Give the real Fourier coefficients for the following functions: (1) The derivative '(t) -6 b, = b = -6 b = (1) The function f(t) – 2 ag = .... b, = , b = by = (iii) The antiderivative of (f(t) – 2) (with C = 0) 3/2 az = b, = by= 3/2 by %3D (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) do 1 , ds = 3 .... b, =2 b2 =-3 3 (iv) The function /(2t) , ag = bz =
Suppose that f(t) is periodic with period [-a, *) and has the following real Fourier coefficients: ao = 4, a1 = 1, az = 3, az = 3, b = 2, by = -3, by = 0, .. (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) (B) Give the real Fourier coefficients for the following functions: (1) The derivative '(t) -6 b, = b = -6 b = (1) The function f(t) – 2 ag = .... b, = , b = by = (iii) The antiderivative of (f(t) – 2) (with C = 0) 3/2 az = b, = by= 3/2 by %3D (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) do 1 , ds = 3 .... b, =2 b2 =-3 3 (iv) The function /(2t) , ag = bz =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that f(t) is periodic with period [-n, 7) and has the following real Fourier coefficients:
a1 = 1,
b1
an = 4,
a2 = 3, az = 3,
2, b, =
-3, bz = 0,
(A) Write the beginning of the real Fourier series of f(t) (through frequency 3):
f(t) =
(B) Give the real Fourier coefficients for the following functions:
(i) The derivative f' (t)
, a1 =
a2 =
-6
az =
b1 =
, b2 =
-6
b3 =
(ii) The function f(t) – 2
, a1 =
, a2 = 3
, az =
3
b, =
, b2 =
, b3 =
(iii) The antiderivative of (f(t) – 2) (with C
0)
an =
, a1 =
, a2
3/2
, аз —
b, =
b2 = 3/2
, b3 =
(iv) The function f(t) + 3 sin(3t) +3 cos(2t)
an =
, a1 = 1
, a2 = 6
, az = 3
b, = 2
, b2 = -3
bz =
3
(iv) The function f(2t)
an =
, a1 =
, a2 =
, аз —
b1 =
b2 =
bz = 0
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