\ L 1l wth L5t I Pf*r,r r Qet^'eut . The SePnraFcow i ("c P Dt^, ol vo-rt -btct '.,^ett -cl J., * grs,aetts: -Th. hee-t e*. -Thc o.ne el- ( Fr"a* frc- .. .cvet5 *l( s.at"o\t - 15 probleqr J ' - A\qlfiple c|or'ce --\
* kevicw t f!? lef -rg,f"e: *_!-t!4 a, E BvP Eor '.lve (.t.x) u- . b w-k) u(t, x)= I cu u tt\ 11't t 44 rl I f sq"r-f.'.- 1 f F"u.r.ri fave I II /t> | "{ v*c.*urer I ls"^."r I I e-u".tue I e,et\,"4 [ ["""re I L I e-e4'ctbe I o0 | ?-t"te * I vtt,x) w, (k) V"te\ 2 - h'r4f I ( e.-*al I eve I I e-vaae I sa "t I c4...h0,- I c L or" J - I J ? robt..t. | +" i rc ...1 Foq-rac so.,'er L €r^ ,r. *b.t.-?Y ."ar\.
s"(. c" the r Evll * E_!2'4P3 €€ ec. hart ttr a xeL",zJ qtt,tt) IL l^ u(t tk J' s.." (L:) Lt Io tX\ : q (a 2) s-e!- Tlv> P. D. fla*l €. ult /r\ -- c\ v,lt l w\ &) (x \u" uht?l I u\ Lt,vt - (t,x) un tt,k \ /1 w,&t u: ftt = ur tt 'l w:tt .
.4 vettl wekt DrwJt the e?. bv u, tt\ wll 4 w"txt ulttl . I tv u, (a u/rty) 4I(\ w\k) q uJftt w." tx1 u\ u./1t ltt tt<t .-ty t )l u; ltl -2, wftl w." *) 4txt 24 rt/, (,<) : O v;1.\ + lt V"[tl =o
..€ wj' tx > + )" \u,t*t Bvf i : <> wt, (2_) r o v" f,VP r Itl Va(t1 = o v vh Io) BVP (to,t v-e R'."v.' ) lu. Ld"l, ,|z Wnlx) -o w,. q) . Sofj. -'la-:;2".1 P(r) ; 12 t terre er1 s.tatft\ , .t <os (/\)c ) + c, S|w (7-x1
( . e\ o. v(a) B., wr(x) : .L slia U,E) | C.: I z) s,- (,,,. o' v/r(L) r s..- (7- z) = o k- qs) --'- "ts4 I V*erl |
r.(. ,t:ftt v,(t)-- o I /e. L" r "f a ut , u^""' l ,t I F'. I"r I" fe f;" I 1r..r 2q rat e ulnt + e v,ft) i. ? Lta e V"(t) )' )"ttl e v-(tt Tp. (o\ ,| Vr uLv2 a/ t -tt t' vttlt\ e -
{ 2 /w? xl r^tt,x\: cae S4 \2 / s.naot .<) t ll Aa f.r (r e- u(tt o I u(t,t) 2 () so (',r) =o t o. Frr qr ta 2 ^to/ x) . s,n z s*(irx ) : .q (.Lx) r*f hetl rrac *tt^"1"--h'ty €ra-ct,.., t Tht st' (\4ry) sd-(4t) s \ .l* \_ ro I z- ./ .s..* t / w. {x sdu (tl irx I 7x\ c^ -L L'7)
.q \ L.f{ f,t^a,'. (v) re \'l. I thev =, (f)' ., (t) lt,xl : U s,. (xt)
s.zr,eJ - 1 IE ? * Re"."r-h wt th ft"e uo-"r'4ble lf wt e ai seS+eat tL Da?.er,-r"e e 11" "," bcl ..sa./.! vnr,:o-loGt zd!' 'nett^"4 "1 + |c )a (rh,x/ -a ;\ f.a (t -r 2t' )>r- ttae",. vatl vtt') wu\ vttl() (0" z) -ta v" tt1 w" cx1 /l*r \ -d v(tl k t ,r-ol t( o.
( It Renrrh . sa7*reh'"t" The FDc- o&'zr tt od ,nae v..!Lr tt e fra.'. le t 4 Fxt'qp Ftul tt^e d TR/P ttn ae. ("e tt"e l" ult,x1 f utt,x) tt, a,3r1 x e L taLo,e).u.>o. ,", I I Lu (o, x ) I >t "l ( r,( Re .. f, o) "l ult,3tr
*rs r: (F.,,.....1 fr.,r rat tt^e lnunS e?. e? . Th,:t .t . s/aye ( Ber*"th. ) ! t Jer.rr'lotr ou e. Sar.-t wo-qer .r' +F) { t.e}.f ( erc - ,, ?he.e 4.e bwo c.r,. f,..{l. c.r.1..6'ot^s, ,vh.( . tt., l^ft'ql. 7otttu.,. -€ a Ft"rtL( ve(ouly of tu., r f-"-11- t (t,x\ = u w" (x) u,, |t) '1 1 I /. .t _l 6dk.d( r.1.1 | Bvp. I .t.- ooE | e-*,. t | I L c-f4q.I.I wr (&) . u- t(l De ".fc t(, : v" u,' u, ty.tl (x) !t)
{ tt) wJ'rxt 0." l_ WIx) utt) v; /t) I 2, tt) u- wJ 0(, - 2", w-(xt i! rtt , y-ltt = o 2, 4'
w:o<, r )- whkt =o 8VP i wrtot Fo w-(gV).o t ue ft) v- It) =O sJl. s:{ rf (p.r) i" )o .x\ - oz I - ," 'l r.ol e Dc Solr .' P(r\ = \^e ral Ge S a(: wn k) = a, c"s (7-x) + cz gc:
(t- nr) ( .T\ Wr sdt 1" (r- Ba.J =- .zl o F> S.v = uT /-t" l-","-;(*;l 7." i- li -o I i,^ ttt + n" !./. of . 6.r?F.l I _/ t se.t\.( ot-dci- o,t'. rt i- ttt . --) ftrt = -2- ,-,1.r=tu/"'l (u"/" t) v\ Itl ( v./"t) ces
& utrx\. 2 fc" .a (utt) + r, s.u(Y) "*("3r1 lr u lt, o) 1 sc\ ao) sO ('aJ I s.. ii u l't, lv ) (k, Ut", e) ct) Sav. u' (o) 6-) o x) ."{4!t)f%! sr.(Y) f- ,. s,, t 4- (t /t) . I^' {"tt1 I I cu ',"(Y) (r) : q(o/X) = Sre (Ll | { t nt ut 7o,xt 4h la
\ /1af lY: hLltt, The xo F+ . ( ll It n ['"'-1g1 (4\ Stv S.' (*) I ) J 3 , tratu -l '- (Y) =) o tttw \.:! / -Tf c, 8T -v L (ul El. *l r3o t r.-({) n- o(* I 5.q / hx\ ( =-l J. o t7' 7
.(r nl::('t ' ti (v..t-t) c"5 ar. st",(u.V"t)l u(t,xl I s,,.let1 u(t,xt t /t- tL It ,xl
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