séries de Fourier - IMJ-PRG

cos3xsin(2x)−3 cos(3x) cos xsin x
Sn=
n
X
k=0
eikx Sn=ein
2xsin(n+1
2x)
sin(x
2)
2 cos x−1
3sin(4x)
eix −e−2ix + 5
2
+∞
X
k=1
1
k2(cos(kx)−sin(kx))
+∞
X
k=1
1
2kcos(kx) + eikx 
x∈R\2πZS(x) =
+∞
X
k=0
coskx
S
+∞
X
k=1
cos(kx)
k·2kz=reiθ
ln(z) = ln(r) + iθ
f:R→R2π
f(x) = −1−π < x ≤0
1 0 < x ≤π.
f k ak(f)=0 bk(f) =
2
πZπ
0
f(t) sin(kt)dt
f f

f S0(x)S2(x)S4(x)
f
f:R→R2π f(x) = x x ∈[−π, π[
f
f f
+∞
X
k=1
1
k2
f g
R R 2π
f(x)g(x)x∈[0, π]
f g f g
f:R→R2π1−x2
π2[−π, π]
akbkf
∞
X
k=1
1
k2
∞
X
k=1
(−1)k
k2
∞
X
k=1
1
k4

0π
k0
π
1
f
0π/2π
1
g
f:R→R2π f(x) = ch x x ∈[−π, π[
f
f f
+∞
X
k=1
1
k2+ 1
+∞
X
k=1
(−1)k
k2+ 1
f:R→Rf(x) = 
sin(nx) f
f
uC(t)e(t)τ=RC
e(t) = eiωt
uC(t)uC(t)
e(t) = f(t)f uC(t)
e(t)uC(t)
uC(t)e(t)τ=RC
e(t) = eiωt
uC(t)uC(t)
e(t) = g(t)g
uC(t)e(t)uC(t)
e(t)
R
i(t)
CuC(t)e(t)
R
i(t)
C
L
uC(t)