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.
