T 00 f(t) = + E an cos(nat/L) + b, sin(nat/L) (1) ÷TSt) cos(nat/L)dt, b =".S(t) sin(nat/L)dt (2) an and a, must be evaluated separately.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Fourier Series.
f(t)
*+E an cos(nat/L) + b, sin(nat/L)
2
(1)
T=1
iL re) cos(nat/L)dt,
=÷(, s() sin(nat/L)dt (2)
An =
and a, must be evaluated separately.
2. Fourier cosine series.
n=00
a0
S(t) =
+£ an cos(nat/L),
S(4) cos(nat/L)dt
(3)
an =
n=1
and ao must be evaluated separately.
3. Fourier sine series.
f(t) = E b sin(nat/L),
S) sin(nat/L)dt
(4)
b, =
4. Fourier series complex form.
1
T=00
f(t) = co +
E Geinzt/L
(5)
n=-0,n#0
and co must be evaluated separately.
Transcribed Image Text:1. Fourier Series. f(t) *+E an cos(nat/L) + b, sin(nat/L) 2 (1) T=1 iL re) cos(nat/L)dt, =÷(, s() sin(nat/L)dt (2) An = and a, must be evaluated separately. 2. Fourier cosine series. n=00 a0 S(t) = +£ an cos(nat/L), S(4) cos(nat/L)dt (3) an = n=1 and ao must be evaluated separately. 3. Fourier sine series. f(t) = E b sin(nat/L), S) sin(nat/L)dt (4) b, = 4. Fourier series complex form. 1 T=00 f(t) = co + E Geinzt/L (5) n=-0,n#0 and co must be evaluated separately.
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