Leoture#6 - UIUC
Transcript of Leoture#6 - UIUC
09/11/17
Leoture#6_
Announcement : . iclickr Tf • first questions : Friday.
Is . register device
#ont.net#iFnE:m:nnt¥>comptv ,i)=v - projfriu )
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Finding proj and comp graphically :
More line until
#apewrgeaagliagular
it touches To
a¥;H→ sienna-
projftp.rojtcomp.Q#suppose iiandv are a linear
.
What B pro ;( Ii ) ?
¥ it
BFexpressveotorntrmsofamon.us )
The idea & of a basis is to have asntawndaayd
of writingand computing
with vectors .
pphim
.si#heo*
@Fso*#. YejtorisnEagles.rs?#enrT= a
,f + azf Components are
=p ,a + pzpo
w 't i. p
hell = vk.tn#=q2tqT"
t.ve/ample_:Tr=ze+2j Ifill = ZMZ
= ZR a +0.11=2 i.
Changinybasisst,
ah
iEEE¥c*sTo change to the { a ,
I } basis we
expresst and f in terms of these
.
e= projce ,a) + projk ,
d) = # an- fzf
g = projg ,a) tprojblo ) =
€ an xat I
Substitute into (D) for i & j :
=D a =3 # an - tat ) +2 # + fad )= Fa an - fefo ~
this is in the new
basis p. = Fmz
Check : 11 Ilk 113ft zy 11 =ftp.#2=tEilulk 11 Faa - FzToH=¥+# =P
.
Recall : Jr = Zf + Zf = zmz an
t.us = (21+21).(31+21)=6+4--10 -
t.u=(2Ra)•(Faan-faI)=|o]#|All vector operations are basis independent
.
CylindricalCoerdinatesnyyeyeEIYnImtYIIpp@syshortestfrisotannq.x.tshtEEp9Fn3einTd9IfIyeaueu.x
FEI .
"
£r= cosoe + sings ✓
• P'
×
e^o= Exner =E ( code + sin Of )
= cos OF xD + sin O knxf= - sin O
d#+co÷at ) could de changing .