tutorial3 fourier
DESCRIPTION
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PC2174
Tutorial 3: Fourier Series
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1. Prove the following orthogonality relations: x0+Lx0
sin(2pirx
L
)cos
(2pipx
L
)dx = 0
x0+Lx0
cos(2pirx
L
)cos
(2pipx
L
)dx =
L, r = p = 012L, r = p > 00, r 6= p
x0+Lx0
sin(2pirx
L
)sin
(2pipx
L
)dx =
0, r = p = 012L, r = p > 00, r 6= p
2. Find the Fourier series of the functions f(x) = x in the range pi