Suppose that f(t) is periodic with period (-x, a) and has the following real Fourier coefficients: a1 = 1, az= 3, az = 3, bi = 2, by = -3, by = 0, ao - 4, ... ... (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) = f(t) = (B) Give the real Fourier coefficients for the following functions: () The derivative f'(t) do = , ag bị = , by= .... (ii) The function f(t) - 2 do = ... bị = b2 = bz = , ... (ii) The antiderivative of (f(t) – 2) (with C = 0) do = , a = , az = . ... bs= (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) ao = ,... by = , bz = , by= ... (Iv) The function f(2t) , az= , as= ... bị = b = ba = , ...

Suppose that f(t) is periodic with period (-x, a) and has the following real Fourier coefficients: a1 = 1, az= 3, az = 3, bi = 2, by = -3, by = 0, ao - 4, ... ... (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) = f(t) = (B) Give the real Fourier coefficients for the following functions: () The derivative f'(t) do = , ag bị = , by= .... (ii) The function f(t) - 2 do = ... bị = b2 = bz = , ... (ii) The antiderivative of (f(t) – 2) (with C = 0) do = , a = , az = . ... bs= (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) ao = ,... by = , bz = , by= ... (Iv) The function f(2t) , az= , as= ... bị = b = ba = , ...

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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Question

Suppose that f(t) is periodic with period [-n, 7) and has the following real Fourier coefficients:
4,
а1 3D 1, а2 — 3, аз — 3,
an
...
b1 = 2, b2 = -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)
ao =
, a1 =
, a2 =
, a3 =
bi =
b2 =
, b3 =
(ii) The function f(t) – 2
a0 =
, a1 =
> a2 =
, a3 =
bị
b2 =
, b3 =
| (iii) The antiderivative of (f(t)
2) (with C = 0)
an =
> a1 =
, a2 =
, аз —
b, =
b2 =
b3 =
(iv) The function f(t) + 3 sin(3t) +3 cos(2t)
ao =
, a1 =
, a2 =
, a3 =
b1 =
b2 =
, 63 =
(iv) The function f(2t)
an =
, a1 =
, a2 =
, аз —
b, =
, b2 =
b3 =

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