BQ GIAO
DUC
VA
DAO
TAO
t
DAI HQC HUE
aPq6
Hp
vd
tln thi sinh:
Sii
Uao
danh;
xV rul TUYEN sINH sAu
DAI
Hgc
xau 2012
(Dqt
l)
Mdn
thi: TOAN CHO
VAT
LV
(Danh
cho
cao hqc)
Tl4di
gian
ldm bdi.'
180
phut
Ciu
l.
Tinh V'
(i
f
(r)),trong
do F
-
xi +
yj
+
ti
ld
b6n
kinh
vecto,
r
:
lil,
f
(r)
la ham v6 hucrng chi
phU
thudc
vdo r
vd
V
ld to6n
tu Nabla.
Ap dung
kOt
qua
tr6n dti
tintr
r
'
1
i
\
\
r:
orv
\,,/
va
grad
[ai"
(;)]
Cflu
2.
GiAi bdi
todn
bdne
cach ddI
u
:
{*" 2,
01x1n
tw(0)
-
0,
w(n)
-
0.
CAu
3,
Cho mQt thanh m6ng, ddng chht, chi6u
diri l;
dAu x
-
0
cua thanh dugc
git
o
nhiQt d0 kh6ng d6i bing ?nr, dAu x
=
t dugc
giti
o
nhiQt d0 khdng
ddi bdng
?"r.
Tim
ph6n
bd nhiqt tr€n thanh hic f
> 0? Bi6t
ring
nhiet
dQ ban
dAu cua thanh bing 0.
CAu
4.
Tim nghi€m
u(x,y)
cua
phuong
trinh
Laplace
u*,
*
,X,
=
0 trong hinh
cht
nh4t D
-
{(x,y)
€
IRz[0
< x
I
Tr,0 <
y
<n]
thoa
mdn c6c
di€u kiQn bi6n sau:
{u(0,!)
:
o,
lu(x,0)
:
sin x,
u(r,!):0,
03ySTt,
u(x,tt)=0,
05;x1rc.
(urt:uxx+2,
0<x1Tt,f
>0
1u@,0)
:0,
ut(x,o)=0,
o<xSn
fr(0,
t)
:
0, u(n,f)
:
0,
f
>
0,
v
*
w trong do w
-
w(x)
la nghiQrn
cua
bdi
todn
CAU 5,
1.
Tinh luu s6 cua hirm
vecto: F
@y)i+
(bx)i,
(a,b
la hing sO; Ogc theo
ducrng
trdn b6n kinh
^R
nim trong
mflt
phing
xq,
co
tAm trung
vdi
g6c
tqa d0.
2. MQt
sqi
dAy vd hpn
(-m
I x 1+oo)
dugc
kich thfch
dao dQng
tU
do boi
mQt d0
lQch ban
dAu co dang:
(
.
hlxl
u(x,o):lh-
,
khi o<lxllc
[o
khi
c<lxl<*oo.
Hdy vE dpng
cua sgi
ddy
tai
c6c thdi
iliOm
tr,
=
ki
voi k
=
1vi
k
=
2 n6u vdn
tdc
truydn
song tr6n
ddy a,
-
2, con
vfln
t6c
ban
dAu cua
dAy bing
0.
Ghi
chil: Cdn bo coi thi kh6ng
giai
thfch
gi th€m.