21C Lecture #23

21C Lecture #23 - 2 u lltlc rq dte,$ha (ot,U) /d#\ r r /ert...

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Nfrf hrfrt, f // lq v fu,W W f ( ^*ax, ,X: x(k) Y* YG) f (- k ror), f (rk), v0),2 x(u,v)t yr x(u,v) r V fu,rt (rh,u), v (a,rt f ftr4r> ? fft) r #k)dt *... a w,v) -= l ("vj * t^Q,v) Ax r $, (x,v) dy{,. . (hongc ( !o tto* x (t*A t>s x(*l *$x ox, # at v (tra t)= y&l * 6 y ay; elr at Yftroa)3 $ (xt-6x*.,. t yrarf ;' = I &,v) r S^(r,v) ax+ f, ft,v) Ay r,,, =(\ - t(h'r)+ fi (r,v)#^*+f (r,r)*6tr_, : f ft, yJ r frrkd# r { (r, o *]or *,, I I #+$ * Y (u,v) | Hr,, : $ Jv rr r | ,l a$ I P"'Iul Jo'nol'u' r* *{. * * J#'*^/, l}j*-vu,Y D "rr aAp *45*-al?r /g= )tt t( ,, dx N 'F N lf 'l^ l:,lri'rurnj x { #} #lu, # }# l, J A (r(r {r: 2f( 3u\ *t
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$ (x (u,v), y (u,', ? Lf c h { (xtu,u), vo+v))= | (*,u) 7 xz r vz '(xoy.) >g a tgl o fr, (o,b)s i T^ t,oh cQ fLafr' tr' H +r\ \t %/ #J t*o + # (r,,YiL X: Xo f Y'- yo {- N,t tt tost Y a v StnU 0u ?x Tu DY ;r r lxCos'tr tv'Utusd -' hn(05v, Caf u, lVSiqd.V(a; u( " lu toseu t X v'sind cosu F v'ginz $ (., costv,- u Zstntd : X u cotl v' # {uz std u cos tt Fyob fft,',J : x'r yz Conr;&e hon it cheqir in /irrrlfon *h,r,fli, f,,'4t ( folr)
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Unformatted text preview: 2 u lltlc rq dte,$ha (ot,U) /d#\ r r /ert od;'c of + ef (Yr$ i't (Trh (x,tro)' d,roc*") A : 4 f (xo*ton dh t & i-?t D( olt Dy $ (r,,v,)d y, r.rb>[ r -o ta tb-T X !r (a,t) ' (l, I fr$'(!,,-t @) Lrt * l<a,b) F(,qu); r 4V' [r' .Zx,q r Ayob (a,b) = 0,r) Ao + lb (a,tr> = b,) (a,1,) z (t,') (o,lr> z (t'-t) &,{r) a t;-t) (x,r to rv, + tb) I r :o (ro,u,>a r X&,,y")b dr;-,- -f,' dtt u )x h Hn> =-t It: Hr(v'D' vf?*i+xi hre'l'onal ^ *auohre ,$ t-qwl 6o,vo) in &rcc{tort X )$, e-r-.\ _. t 7 bv f (r,o ) .* u= lv*l F"stei vP (x,,y") o i exnsU ; X ?*r? :2x Vl (x,i' /ri { Arj vf. 1rar ,2v b Vf (x,y). fr = /v Pk,g I Noriaun pfun 7 i,r frt lvl I :?#;no$ chsorc / 2 t4-.tfi a rA al rb J aol fr y-tF Dr 5 o Vf iE dirc c{to n i n whtc h N in create s- V.f U di ,c6J; on I n uhr ch f dcc res cS A = "i ,r b3 lnl Cqss p= dngb bctuan o(trcr*ort y f. T"tlcrL d f In c!;re'{tn of mt vcchc lf no) r r' n y? ,ucct-o( vFL rrirAvjJ$'et/ =flr 'lr f =, xf *r3...
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This note was uploaded on 03/18/2011 for the course MATH 21C taught by Professor Milton during the Spring '08 term at UC Davis.

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21C Lecture #23 - 2 u lltlc rq dte,$ha (ot,U) /d#\ r r /ert...

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