f (t) = 3,0988[5,57+0,64Cos (3,34573 − x) + Sin (3,94198− 94198 − x2 )]
T T
f ( f (t) = f ( f (t + T + T ))
f ( f (t) = f ( f (t + nT + nT )), n = 0, ±1, ±2,...
f ( f (t) f ( f (t) =
1 a0 + a + a1 cos( cos(ω0 t) + a + a2 cos( cos(ω0 t) + ... + ... + + b b1 sen( sen(ω0 t) + b + b2 sen( sen(ω0 t) + ... + ... 2 ∞
1 = a0 + (an cos( cos(nω0 t) + b + bn sen( sen(nω0 t)), )), 2 n=1
ω0 = 2π/T, 2 a0 = T an =
2
T
2 bn = T
T 2
−T
f ( f (t)dt,
2
T 2
−T
f ( f (t)cos( cos(nω0 t)dt,
2
T 2
f ( f (t)sen( sen(nω0 t)dt.
−T 2
∞ n t 2πi T
C e
f ( f (t) =
n
n−∞
iπ
e
+1=0
.
∞
C cos(nω t − θ ) f (t) = C + 0
0
n
n
n=1
ωn = nω0 ω0 = 2πf 0 = 2π/T
C n
θn
∞
(A cos(ω t) − θ ) f (t) = A + 0
n
n
n
n=1
A0 = An =
a0 2
a + b 2 n
θn = tan −1 =
2 n
bn an
f ∈ C ∞ ( ) f (0) = f n
k p lim|x|→∞ P (x)f (n) (x) = 0
f, g ∈ S ( )
ˆ ) = f (x)e f (γ ˇ
−2πinxγ
f (x) =
dx
f (γ )e−2πiγx dγ f
f f → f ˆ f ˇ = f ∀f ∈ S ( ) ˆ ∀f ∈ S ( ||f ||2 = || f ||
lim|x|→∞ (1 + x2 )k f ( p) = 0 P (x)
78 %
3,6 %
2,8 %
46,6 % 2,6 %
27,7 % 2,1 %
8,1 %
5,0 %
f (t) = 3,0988[5,57 + 0,64Cos(3,34573 − x) + Sin(3,94198 −
x )] 2
f (t) = 3,0988[5 ,57 + 0 ,64Cos (3,34573 − x) + Sin (3,94198 −
x 2
)]
t
u(t, x) t
t
0
x
|u| ≤ ||f ||∞ 1 ≤ x < 70000 70000m
1m
0 u(t, x)
x u(t, x) =
c (x)e
2πint
n
dt
n∈Z
1
cn (x) =
u(t, x)e−2πintdt.
0
u ∂u 1 ∂ 2 u = ( 2) ∂t 2 ∂x
cn =
1
0
∂ 2 u ( 2 )e−2πintdt = 2 ∂x
1
0
(
∂u −2πint )e dt = 4πincn ∂t
4πincn cn = [(2πn)1/2 (1 + i)]2cn , cn cn
0 1
cn (0) =
ˆ f (t)e−2πint dt = f (n)
0
f (t) = u(t, 0)
ˆ f (n)
(2πn) ˆ cn = f (n)e
u(t, x) =
1/2
(1+i)x
(2π|n|)1/2 x 2πint+(2π|n|)1/2 ix
f (n)e ˆ
e
n∈Z
f (t) = 3,0988[5,57 + 0,64Cos(3,34573 − x) + Sin(3,94198 − x2 )]
