数学物理方程-第5讲（2.4-2.4）.doc

文档介绍：Mathematical Physics Equations
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3
° ® u u
| 0,
=
x = 0
°
¯
w u
u xx
| (), | ()
= =
M ψ
t t
= = 0 0 w t
2 2
w w
uu
2
=+ <<>
afxtxl t
( ,) 0 0
2 2
w w
tx
0 ()

| 0
, | 0
u = =
xxl == 0
w u
| 0 , | 0
==
tt == 0 0 w t
()
u xx
| (), | ()
= =
M ψ
t t
= =
0 0
¯ w t
U(x,t)=V(x,t)+W(x,t)V(x,t)
22
- w w
u u
2
° w w = + < < >
a fxtxlt
(,)00
22
° t x
22
- w w
u u
2
° w w = < < >
a xlt
0
2 2
t x
° ® = =
u u
| 0, | 0
xxl == 0
°
w u
6
f x t
(,) =
()
()
()()
f
ð
Vx tv t x
( , ) ( ) sin n
= ¦ ()
n l
n = 1
f
ð
¦ ft x
( ) sin n
n l
n = 1
l
2 n ð
fn tl f x t l xdx
( ) ( , ) sin
= ³ 0

()()()
{ 0 ()
222
an ð ()
t + 2
l
n ð
v t ft x
() ()sin
º
- l n n ¼
"
v
n
222
anð v tf t
() ()
=
l n n
2
'
vn (0) v= = 0 (0) 0
10
v t
" () +
n
2 2 2
a n ð
2
l
vtft
( ) ( )
= ()
n n
vn (0) =
'
v = 0 (0) 0
Up
( ) =
n
2 l
1 Fp
( )
222
2 n
an ð
p +
Laplace()
2 2 2