ł%�(� t) - "tt�(� t) = 0
r, r,
(r, �, Ć)
d2R(r) dR(r)
r2 + 2r + [k2r2 - l(l + 1)]R(r) = 0.
dr2 dr
Z(kr)
"
R(r) =
kr
(l + 1/2)
� = ą1, ą3, ą5...
2 2 2
y(x) = xŁn="cnxn,
n=0
 = ą�
R(r)
(J, Y )
"
Jl+1/2(x)
jl(x) = Ą/2 " ,
x
"
Yl+1/2(x)
yl(x) = Ą/2 "
x
sin x sin x cos x
j0(x) = , j1(x) = - ,
x x2 x
cos x - sin x cos x
y0(x) = , j1(x) = - ,
x x x2
 j0(x) x = 0 y0(x)
(a, b) ś(x, y, t)
ś(x, y, 0) = ś0 sin(2Ąx/a) sin(3Ąy/b)
ś(x, y) = 0
8
"tś(x, y, 0) = 0
w1 = (-6, 6) w2 = (-1, 9)
� �
w1 = (0, 1, -1) w2 = (2, -3, 9) w3 = (6, 0, 0)
� � �
w1 = (2, -2, -6, 4) w2 = (9, -5, 3, -7) w3 = (-8, -1, 5, -5) w4 = (7, -7, -3, 8)
� � � �
1, x, x2, x3, x4...
-1 d" x d" 1
f(x) = x(1 - x) -1 d" x d" 1
1
2 2
"xxu = "ttu,
v2
u(0, t) = u(l, t) = 0 u(x, 0) = 0 '" "tu(x, 0) = ut0
1
2 2
"xxu - "ttu = F (x, t),
v2
"
F (x, t) = sin �t + cos( 2�t)
f(x, y) = xy 0 d" x < Ą 0 d" y < Ą
f(x, y) = 1 0 d" x < a 0 d" y < b
f(x, y) = x2y2 -a d" x < a -b d" y < b
f(x, y) = cos(2Ąx/a) cos3(2Ąy/b) -a d" x < a -b d" y < b a, b " R
1
2 2 2
"xxu + "yyu = "ttu, 0 < x < a, 0 < y < b,
v2
u(0, y, t) = u(a, y, t) = 0 "yu(x, 0, t) = "yu(x, b, t) = 0
u(x, y, 0) = f(x, y) "tu(x, y, 0) = 0
f(x, y) = sin3(Ąx/a) cos2(2Ąy/b)
a > 0, b > 0
A
"
u(ń, t) = sin(kń - �t)
ń
ł%�(� t) - "tt�(� t) = 0,
r, r,
u (ń, Ć, z)