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HW1 2017171081 이상민

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1. (a)
p=cxtY)az
"
]ÑÑ
[ ¥]=[¥¥É¥§]y]
"
0
An
( ) :(
0
Seiocoso
⊖¢
-5m¢
Ao
A∅
sin D- sing
2
.
.io#gfBaaoie*azsaordiaate%aemEEk&%Ea&-
@ ) A- D=
2-
④
coso-sio-s.jo
/
A- ✗ D=
5+3.4+(-211-1)=10-112+2--24
coordinate system
cylindrical
i.
5
3
2
4
-
de
de
(-4+5)%-1120-6)dz
+
-1
2
-1dg -114oz
IAI-F-i-E-TFP-cx-flaz-H-vE-z.fi
system
④
spherical coordinate
p-cxc-yjcoso-dr-cx-vflsin.cl#-,
(b)
-21=(-3+8)
aeacxaz
=5
i.
Az
-
⇔
cos-0
cosy
/ B=2ae -14dg
A=5aet3d∅ -2oz
'
1-(b)
Q=Yax+XZay+cxtY)dz
→
cylindrical
Q=¢os∅y+sin∅xz)d±(-sñ∅Yt∅≥z)d∅+GᵗY)dzg
☆
spherical
①
(
=
4€
Cos⊖cos∅tkZc◦s⊖sm∅
( f.
+
f- Ls'm∅+kZcos∅)a∅
-
At Hyde -12 czay Yaz
>
.
(a)
O≤ KEIO ,
y.sinfcoso-xzsin0-s.tn/+cxtY)cos0-)dr
+
c◦s0-=⇒go→⊖=sec(•?
24
'
f. A-
CXTY)sei⊖)d⊖
=
JP Adv
"
-
◦
≤
(5) F-
-
yes
,
F.
i-t-yi-T-z.KZ/tEZR,
ᵈ" " "F=
O≤z≤
to
+5%-1%-1,4%50
y -10-10--4
=
fiiidx
.fi?idz-.fo5ydy--lo-lo--E--
1250
,
≈
Axyax-izxz-ay-fd2-F-2-edxdydz3.la
( Determine the
)
,É≤∅≤ É
ded∅dz
)e=2qo≤
2- ≤
area
to
8- A-
3
£
÷i¥ÉÉ¥÷¥
=L
=
=
0
=
⇔
-225
.
-
≥
50=0-1,
rsénocoso
rsg-s.io/Z=ras0So-a-dr=SiisESEy.r2sio-dod0-dr¥¥÷÷
D- A- =L
;
(b) z=o,o≤e≤ 5 ,0≤∅≤
-
sixdo.sjede.SE 'd
:
x
g- esio
So.Adu=S% :S 'iydzded∅
"
e.
✗
=
g-
=Sj%ᵗ"S¥rˢsii0sé∅d∅d0dr
IT
=f%r'dr
2-
.
siio-da.fi"sé∅d∅
÷%ᵈⁿ
5xftayzpv-5yaxtlloxy-4H-ay-4Y.dz?cCb)V=2eCltxYs
5.ot.to?T-hegradiento-ss#ie
(d) f-
(c)
r-r.co
,
D- ≤
¥
:÷ ÷ ÷:?÷ ÷¥÷:
'm∅
=
_
&e+2e%5∅)sin∅
DV-simoc2-6ekoszojae-2.co/CltE(cosH-2sii0D.I
"
{%
x=ecos∅
"
(c) ✓ =2r2cos⊖c◦s∅
-
dt-deae-edoao-dz-az.tt
(d) 0=-5 ,0≤r≤ 5,0
≤
0=22
¥¥¥ay
dxaxtdyay-d2-az-drar-rdo-ao-rs.in
=
⊖d∅d∅
PV=4rcosocos∅ar-2rsis⊖c◦s∅a⊖-2r¥%I
,
⇔
.
06
A= @ Ya
"
(a)
07
.
≥
+
cos
✗
Yaytsdn
:( 2-
Az
.
V=x2y2e✗ᵗ
(d)I
divA-P-A-2y.EL-xsinxL-sinzxt.NO -0k¥ / safe"ᵗ+x'y2ze"ᵗ)
curllt-JXA-o-ckx-fzsinxz-cos.cz 7) Ay
-
+
(b)
A_
+
fYsisxy-2xe"Yja#
ezzcosoapi-zs-a.hr?Ke
*÷⇔⇔+÷*⇔⇔ ]
,
ii. *
=
card # ☐
✗
E'
d-
(
✗
2eÉos∅
#
=
+
esiho
1¥
a≥
¥ ¥
2- said
0
ez%s∅
"
/
=
d-
✗
(
Z∅de
+
)
Zézasoaq
tezsinoaz
diva:P
-
+
curl #
¥
+
=3É∅¥Éa◦⇐÷
P✗A=,✗|÷
/
¥
.
€X[
"
-
Isn:O
4z(C0S2∅tsm∅
TPV=¥j
( Ncos ⊖ )
÷
*
Exist
11
r30s20-drtfreso-sio-3-zrsin-ojrao-tfrsi-0.co
( x3y2e×ᵗ)
/
+
2-
C- said
-40520
'
2- +
le
?
@ 24+401 )
to
" "" "" ∅
" " "" "
A=É¥(r%s⊖⇔H+¥f¥sii⊖ )
'
-1¥
⇔⇔⇔,
=
=EE∅aet2ezc◦s∅a∅+Ésin∅
(c) A- rcoso-a.si/ar--jstsO-do--r2cos0-Ao
"""""
"
p.py.j.gyfe.zezkoszo-s.az#-ig2-y(coso-2si)z0/
)=2Z%s∅-e⇔
eat
Ziyi )
=é"(2y44xy2Ztx2y2z2+2n1x"y
11
,
Ig
(
+
=
,
( is# tzérsaocoso) )
✗
✗
)
( ⇒ ( sñG.éKa⊖cos∅ )
Éo✗(¥s÷ .ee#o-sioy
-
"" ⊖
i-H.e-wf.zrizr.i-zs-i-s.no
+
-
etr
-
r⇒
) rsuioao
-
e
"%Y
cosy
§ A. all 5,0×-1-1.15
L
=
IF
☐✗
A'
-
=
-
faze
de
'
e-
a-
DA
ea∅
/
art
¥ ¥
,
easy 2
0
.
=É(6e?sñ∅)az
fzltdt-fg-6etsiodd-sifE-toe-sioledo.de
=
,
'
°
, :c .se#e.siE
2
=
5,2
_
⇐
eye de
-
"
"
[
-
Tie
?É ]
?=É_
09 A=xyaiyay Evaluate §£A-d2
,
.
dJ=+azdA
Y
t.EE
*
=\ :;:t
E. Ey ¥
§Ad1=§
7
?⃝
?⃝
?⃝
=e∅aet=t§+=¥{⇔"É¥⇒
-
'
-
✗
-
DA
s
=f↑
¥0
" "
-
-
xdydr
⇔
It
ftp.%Edgdx-isjsjiecosoedode
0
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