7
\L{(_oJ1 r-vrJ~ ~"J~~ \:)( ./' \ ~0 ( (bJ ~J::: UJ II> A,) \.l~'~ vw \\ dt~-\-0S'--\-,U0 (r, ~0) . The rttlW,,~<II' ~ ~ ,,~ 0 S,\-Q(lv,'Vj tR S icJu~ L (~J~ ()-,s 6 r ~ ~'f:+ ("IC\Jv"Z_ - I ~0 w do, ~ ""L t.J< j-\;., f,vL., ~ L.,: L f:>' )', J ~~4 o: '3 f CI~' L W/I.. ~i)tn 1,,0 \-.~ (e'5' t: -Fi J,)f-0].J +-~) . ~0 W ~~ w e, L J.,' J-- ~<. "'{)w u) r '" :;, 5 u~) o-: cL-,J-r, ~0~\M ~ ~~ c_u~\~ s{.\\ "",\J'.)lA.Iif ~) ~J w e. \r-~ <Xcce>S 1-0 S"1' Ie:. ~'" ~) (,J r0 0~, l, 1-11 J:~.tr-, SJ ~, JV1 , I~ ('/'\)l\ ({l) w--Z_ l ' ""- 'J) 1 5' ,~, l 1- 'J S"''1\o) ~f1M.A- ~ \J\-ul\ CiA) Q,>+,~J l:W-vvee..s ~))U~v-) ~ I') V\J t~~) ~~ C~IA J J- "'''' '::21 ' ~- , .,J e>\' ""-+, J \\e_ ?-~U c~ J ("~ ') i~ 1 ~j , p(~) J ~ ?""..: μ; Of ~ -I\, 1) ,'" p..._ "If",,,J- \J.,. J-, ob ~'\A i>"'1~ ~JL); YrOc\'_k~ -} rJ V,->0r-t- p~ -:") fer l':::'- I, .-) b . ~~~ 0:'T \~\.s l /j fh\; ~) ~1T~ ~) \)'3~ 0~ l~s.

~0( UJ - CBCBcbcb.umd.edu/~hcorrada/CFG/lectures/lect7_DifferentialExpressionII/... · \L{(_oJ1 r-vrJ~ ~"J~ ~ \:)(\ ~0(./'(bJ ~J::: UJ II> A,) \.l~'~ vw \\ dt~-\-0S'--\-,U0 (r,~0)The

Embed Size (px)

Citation preview

\L{(_oJ1 r-vrJ~ ~"J~ ~\:)( ./'\ ~0 ( (bJ ~J::: UJ

II> A,) \.l~'~ vw \\ dt~-\-0S'--\-,U0 (r,~0). The rttlW,,~<II'~ ~ ,,~ 0 S,\-Q(lv,'Vj tR

S icJu~ L (~J ~ ()-,s 6 r ~ ~'f:+("IC\Jv"Z_ -

I ~0 w do,~ ""L t.J< j-\;. , f,vL., ~ L.,: L f:>' )',J ~~4o: '3 f¤CI~' L W/I.. ~i)tn1,,0 \-.~ (e'5' t: -Fi J,)f-0].J +-~) .~0W~~ w e, LJ .,' J-- ~<."'{)w u)r '" :;,5u ~) o-:

cL-,J-r, ~0~\M ~ ~~ c_u~\~ s{.\\ "",\J'.)lA.Iif ~)

~ J w e. \r-~ <Xcce>S 1-0 S"1' Ie:. ~'" ~)(,J r0 0 ~, l, 1-11 J:~.tr-,SJ~, JV1 , I~ ('/'\)l\ ({l) w--Z_l ' ""- 'J) 1 5 ' ,~, l 1- 'J

S"''1\o) ~f1M.A- ~ \J\-ul\ CiA) Q,>+,~J l:W-vvee..s~))U~v-) ~ I') V\J t~~) ~ ~ C~IA J J-"'''' '::21 ' ~- , .,J e>\'""-+, J \\e_ ?-~Uc ~J ("~ ')

i ~1~j », p(~)J~ ?""..:µ;Of ~ -I\, 1) ,'" p..._ "If",,,J- \J.,. J-,ob ~'\A i>"'1~ ~JL); YrOc\'_k~

-} rJ V,->0r-t- p~-:") fer l':::'- I, .-) b

. ~~~ 0:'T \~\.s l¤/j ·fh\;~)• ~1T~ ~) \)'3~ 0~ l~s.

1 Y - rEf\ {-\A'S fu->~C_ bj eVStY'l~ µ- ~ ")z._e5b~ ~ 5=('" u<- {Ii )~'"'- &-> i-lo>"L

L);)Q/~ ~ j* fl''jJe~,d~C. b h'o So.- d~"-I r\,;" ~~~UM.- lo.Q_0":>Q~ +-0 l~ r-vj~7 ~ C&<jJrz.-r

-fe.;,-'rs' 1;'. j' Ae.. d' ,}\-,.; ~J h'~ JJ: ik- ;o"'!W'.J

~ k. l-to~ ,µ,,-,,:S u>~cI'-' ~ -/\...)\D \I. J- »o o.."DO:~1')Y\ ~. hvcQ.v. p, _i cJ.c'<'t,,-~.J, ft["o iJ\.<-. ['<O,.,lo\--''''1 ~ 0-~JvL'> 'sJ~J 0[\ Jlv.- iW'>S~' 6+- ~k' ~ J~e d.

1v1,\t._ vi j~ (0~ 0( ~ D .os: /~(\-\~l F~~~') ~ eX, I 50 0f("J 0(' Iv1 ~J6¤-

r~'J,,~A tn>-~'D~ Ie Q.. ~ 6A- c c)'b+- -:;.. s,ei;\l;.,..J-; '" ~

T"" \ev- ~ ~ W~: ?r-/J)?'5v<A ~ (_~ ~

) ~ ~ J- ~1 ,Jo-.

fw~t-.' 7(\)~ c"') bt 'I ':> t~e~ cc){'Ce(_\''W;ty I~\ 0. ~et0~~~ ~

-=') G,._Qj 3 7:)"''' ~ (.J, t- 'it

y MD -I~ l'Ao1

l' lI{\ - (- \-01-

5 I)A~S 1'\11_j

eD'>'~v CV 7/ :f..') .:; J.

PD V' ~~ ~ J- W'b-e.- ~B?J,Ves \IA tJ-- 5,\AM y:)-D\- ':> J~\. (.J c~ ~ (,IA HL. it:, ~':> f - e reu"1:tlv! /

b J ~ v-£- ~~ 'f ~ I~eh JJ U)J(_ ~ \~'::, ~

tte.'£ ~~ ~~> (eM'¤. ~ i 0-.. \~"'{ ~ cL?I-v<\~'v\)

0-.) (A..Y\. WW c« k La;'}-~? .

6~%1

r _.. - - . - - I ~ ~~ •• ~ -

yer .~UL-',,) 1. dJ", I ~ ~

~:>~ I ~ 'f ~e_ c CAJ- C60~

'B - - bT

\~()vJl- \)~,A- 'j \ V->e.. \;~ vL o; (.f'I},_~ t /cL~fyJ bu I--.~ o.c~b1}1

lJ-R- C--e>. "'- / J v--o

1J;,),~ ~ J loL.J r~ I C-'"" ~ ~~ ~~

",,\'bOt e- ~{l.~:\..t.- j.Q_~ j(':>t\\) I>":;'~\ \-\i)c\~j): l)",6er ~ c-.SS<Mf,~~ ~+ ~ d ~,

v. <' , -1' \..c r / oJ i!_<\""";~u-f..,' 'M ;5 J. '"t,.;~'k"[.I.~~"1M~t/It ,'- ,_t\.. H...h). ~e. ~~ ~ p-v.,j'-'L 'S'9'v J<:lW\A

~ l,~+- ~\roul.L b-e.. C.or

::::- '") L.,.,_.Q_Q "> ; ~ ""~ \-' (~ "~ r~ L. ~J • ...... M..~

05 ~ pU'l-e...-~\.~ ('l>.M1z o~ 5~v--¤_ j r-vJ.v-L$~;'>MJ ~ Yw 1-1) \\-

i-Iyi"1

-rl ':> c~ k ~~~ ~ b.o ;'v-c.lu i~ Xo;~ rk~~?~ lA- 5~~+W- ~ d: Of

(S~J I J-.J.)

~.

- '1- f:o, , ~ jl I \ I J /'() l c 1-).) 1.

1C.,().):; ~ t Pi ., ~ : ~"-', .~.~~~W'( (. ( -;t)

TeJ.",.--..._j: we ~j w-t- iDe!) 5.\.c~ ~ tc:_,w t..- so"L +tJ-S. ~\ l. ~~ vwU I Lt- lAot tM'->vl ~,.h.._ ~. (j~t_ d:le:»

-"0~ .

fDru [I;) -:;._'J(;_.::--VI' _. _t~lPL ~:}

'"1-' vcJ~ (_p~"):; VA~ _,A. 0/~ 7, i1 r D t"\.__t-)

CD A.,.. ~4"rW ftlV\1-: r~ IJV iv-J,Je,. ~e..~.. uJ;~~

~ L p~)~ ~ kr'- Ll-s(l"'PfeJ,.cJba ') .fkp~?-

ot fk_ {;~t- ~ o: {lM-du +-~lv~ ~~~ ) j,"""1 ~ <)'A ~ I N<" ; s ~v.f~ t ~I)/" :J:~')..(_<'! ~ )

® Ik~ ~~U ~~Ii-: 9 cp,,) i> ~r';.v7~S ~_ ..-.

~ ~ jeM.-'>, c~~ F1)i2- ~ J! le..tk.

1--~ lf~) >~)i:~$p I tk J5~ttVA. lotl"w~ 16: .1: Dr ~u- 'r-"cJ".~ i)e,) ~ PC7-) ~ '" ~ rc",)

2: ~ ...k ~ ()...sJ "t ;t (t'J,l)fO,OI,cMJ." ") o- '1's)

pc (µ i!J I fa b (7 )

~

~! ~k 1-e{~ ~ ~')5 k f-.> Ct c"»' ~cf-~"'~~~'- ~\-~'v~~Cu.,.'t- JD f\v--s 0L~J~))~~ ;~~ f-\~~t~sJ- ~t -h,E>(~ fe c~ ~w tt- .J..e-b+~ o...-l G~~~~v.-~~~ \"'~r~~\ftM