4
Ilo4qQc 1.. tora1*o{nr.a E_n*,,..^clio.. (rr.^!.: $a1.J, o^-\ A^Ar* X -l- ea*t,.^le At?\ tor E tSt ) ?A: ct.A .*.^ A\ n u. : A* "\ 4lI V <l qzA -tL* Lo.n rrc allo.se.t oJ\ e AA,,^^^JI. d a to t ttr\ [ov "6rur1 \^ f,e,ncvJl) 6,.$-{J e,AAt,"^cJ Nu,^^o,.^i bd En+ii#,iii ) To'' 4*a ) r *) A \rv. Sol"th.+7 \.^,e.o..rtqlnct"/ \,^^+.r1"'^44.".t \"" A.^brte-tzt "t a4, h.lru .[ \."\1'.r.^ \ e \ 11 iA c\ ^6'.v. C>.vvoa\o,^Ar.^{ -}- /f t('\> t -*t*--. / ttA\r)= ?"[]reo), N="4 N\ * bllq. vvr^l I t= L: t\^1 ) lde J'.t \t^,,'n"" Yar"'ls'*rl- ] otr'^ \l I ere ,, Jc ^1 \ Ya.,'.-\-*. o! ncvv^Jtt" \ r 4''l 4< to , \1. ^ 4-\+,,"^Je d ttrt [o' ]Q\ I , \-\o",,- R"r^,)*,*^t5cL E.nrx*.Jrov. N T{^^L--1tyJ Ufo+.*.,.*.- t t- t>t J4^+ b, €--ao\ )e x 4q|-c't b^01 v*[,^q o o\r \ t ,.o - \", €-<cr^ 1 A fL \\ \'l 0\ A'{e'^o,roJe ltr't,l he..ro, ^\e o\aeVvrrrl -hA d'''dr I (zI,A'n)) l'^t( utA,*.J< tt? \ [ o' ? ts \ ) \'] k4*^"ri" T.v. r;- . \r . a\ 8" (\ > 4\>t ) '! +14 u.c w) *^s.- eyt\t.^^Jc -\." \a 0"t!). T["4 G L-'on-Y^nI'-"tyJ €A*t.,..**-.r C-r'- \c A4^* J- b.- a \*^'-\t"' t:, ^yqd A L ^' ['^ v-lt-^ Ya-t^'I-""iXJto"'l cA L.21."tvta \' E

r)= ?[]reo), N=4home.iitk.ac.in/~neeraj/mth515a/module2.pdf · E,t n*t t" 0 e@2 iiL 'r^ Xt, X r-.-./ *^ ,L t nK xrs6\ *. rf b:!, n

  • Upload
    others

  • View
    1

  • Download
    0

Embed Size (px)

Citation preview

Ilo4qQc 1.. tora1*o{nr.a E_n*,,..^clio..

(rr.^!.: $a1.J, o^-\ A^Ar* X -l- ea*t,.^le At?\ tor E tSt )

?A: ct.A .*.^ A\ n u. : A* "\ 4lI V <l qzA -tL* Lo.n rrc

allo.se.t oJ\ e AA,,^^^JI. d a to t

ttr\ [ov "6rur1 \^ f,e,ncvJl) 6,.$-{J e,AAt,"^cJ

Nu,^^o,.^i bd En+ii#,iii ) To'' 4*a ) r *) A \rv. Sol"th.+7

\.^,e.o..rtqlnct"/ \,^^+.r1"'^44.".t \"" A.^brte-tzt "t a4,

h.lru .[ \."\1'.r.^ \ e \ 11 iA c\ ^6'.v. C>.vvoa\o,^Ar.^{ -}-/f

t('\> t -*t*--./ttA\r)= ?"[]reo), N="4

N\ * bllq. vvr^l I t= L: t\^1 ) lde J'.t \t^,,'n"" Yar"'ls'*rl-

] otr'^ \l I ere ,, Jc ^1 \ Ya.,'.-\-*. o! ncvv^Jtt" \ r 4''l

4< to , \1. ^ 4-\+,,"^Je d ttrt [o' ]Q\ I ,

\-\o",,- R"r^,)*,*^t5cL E.nrx*.Jrov. N T{^^L--1tyJ Ufo+.*.,.*.-

t t- t>t J4^+ b, €--ao\ )e x 4q|-c't b^01 v*[,^q oo\r \ t ,.o - \", €-<cr^ 1 A fL \\ \'l 0\ A'{e'^o,roJe ltr't,l

he..ro, ^\e o\aeVvrrrl -hA d'''dr I (zI,A'n)) l'^t(

utA,*.J< tt? \ [ o' ? ts \ ) \'] k4*^"ri" T.v. r;- .

\r . a\ 8" (\ > 4\>t ) '! +14 u.c w) *^s.-

eyt\t.^^Jc -\." \a 0"t!). T["4 G L-'on-Y^nI'-"tyJ

€A*t.,..**-.r C-r'- \c A4^* J- b.- a \*^'-\t"'t:, ^yqd A L ^' ['^ v-lt-^ Ya-t^'I-""iXJto"'l cA L.21."tvta \'

E

E,t n*t t"0 e@2 iiL 'r^

Xt, X r-.-./ *^ ,Lt nK xrs6\

*. rf

b:!, n <Al*.de flts):

N,*,o,^ A\ ',..0 eA; (E > \f

Arax.IF*[email protected], !: * I *t n'^A t:, :

t:

h.sr.r-fantrot^t@

t', r,o\. N (g/ \ ) t'". A \"9{..^€

s otr\IL

T r t'

,: 1:".^ !&+, IJ lr',-

\\ t->'')' "'c"nn'{""'

sts\\): l"\\'eu) be:

T- \au.A-.^.tsf, '*"*^^i: "l;"::l:o\lt'i[,?,,,t"Jt;l.;

'-t; c^A '\\'* ",n;'*^*-f, -t s

ffi J.v. 4), '\n

t * \'r !2'L[,--1l -*nJ. *t r '

{ aeg, , / V=''4o 0 Jfu'a::\^a./

-$- btrntvvzJ Vd''f4 v _Y. !_.

[^rke< 5u>.] L\e

,tq 1x-r-^**e fl tOt> e

4b F^ ..Y< A*c

Ls"t,K an1+1x^''Je-

N

{tu\}\', \' \r; er\)

hu,,. lc, Fni"l^^::*t -\tr t | "^oD*-Y

l'^ 1-'-'\ 5Jt'-

I , ,t 0'."z) b< c'^ C-^ }{ct<-A)

gr a^ t'rgt r X ,

.:.4

€nA t'*J-"(A Vell\vcA

td( C...q

n

Lolr: \o^ u'r(>u\ ; L; QtoA -+ \"-^)ov

L: @ ;'A -t \"- ')se&\

Lo r,a ( u. c-trv YYr<L t n

!t'd wLc'n 0 trt

\ot ..* s*v rc v ^l*n ^l

.'^.,r e ) ,

-l L-m (nct''vrzr--'\

I t^ c1*tunq4\Fl

J tt.) [o,' Ztst)

a*z oA.

L tt, ^

a^-r ?eR [o"

\ Dv L\D ^\4A\t'-J(i\^tr ,t$ \

-\v { v'a 't l+ "lo "'t

f",t

["r cr Yar'A.t^tj<-\ t \. \ l. ), a,.{,,^n

)rt ( a\l \

eA+t,. Ol " "

Jtr,t, I)= J L(F^/1OV

,n t$ t )-)> -t L\s'

l_\//,+0A^) d.$tf"\|1,

Tor 6\ Yanf'-<ryJ e^ti*J" ttr'-) Lsc A"^ra

J\Frt,b) - L[F-tt1t)D\T

t'\o-t-I) 1 L\9t(r\)

h"^u.rJ{J lra f ^-r.r" A s \FK a^J' C-nnt AtT A [o- \t^'^'*i",'

Lts<) JtrJ,-(," u,t*) ge@ '\ csnvQA',^^ o"QeA'IhA*t,."

N{.n.},s^n t4-' A*'lyt- i.,l +- Count &-v Ot^'[1 hrn- yanl'at]'el

en+r..^J.-vn(.W,..}l.,l^^i^}J&.^.n0.^t^t.x,aryud('+]/

[*r"l*. ,p.v ft^) F€ A, LtF a\ \^ A (rrv(rr {"''^"\t"*

t(

lerr'e ''/ 2

. t \,A ^ $tvct^ \a'd-*n'\o*i'<AAi"^Jo't-'AJIAIJ(^J

Jttltt A'sfrr)'t <o1- v )€'tA

\4t^ottl ))) >

(c,. d..ttt\>\ >co'-\

--- /d*

T..^ Lte, $; t>\ )

cf L "A A\'rr c4 [1

Ya xls "^l gc-l

I tF, Er

* >aAC>nvc )r

Ll r>Yt

A^X

l-\.'l<

\"'

Ro.. $!-"cs,,.rJt lf,.a.uo,^: St\-r.c- -|qJr :

' A SnI t' 4-"'v()r-' r^.. r ra

' bo, a'tr F e ? \ow oeo) LLF ^) [ou Lts'(\ ) \'^ A

(p*.v( )'- \r^",'io'^ 4 A u A" r. r-r r a L.-

' Ti TLt) 'L^ cr" A-\'{rcrr'^* N+Jrn't'' L" r€C

.t"e\ift^A}rqh-Yc^'n,r..,^.y;"{;\\t.z.Ja,IAe.-rnio.xJr-1

A.^-.',^ )r-^J' LoL\\ 5" ttll\ ) < a, '

o o.;La\' u[t"\]) \ 1 )

\^)\-c.re $.a Lit'-' ' '

!9'v-\ '

\rtr\ !Io, \s,\s) t

I)

v*l

s"v- Fe0sato)

L *- f*"-:.J^";:?L'B LouQ '

tA\n

n Ur \'...'A AJtAtuJ

nt "." qt'a^'"'e-Lt+2

{d- \ ,Q.x'*,u /ra (.,.'"'r''"&-','

T';;-;"r\5Jue u r"'.1 -i n*hr-o^^t\

l,r.ri\rt"^" NrJtn*t.*

C-*(f-\A rf {, r-Lu^i AA\b:}t^*) A*}t 5"'}t\tc'rc"^c7 Ju-",..*l'c

No * n" *lr;_' ''; Jr-4 . \a--.r.r,-, , io^ ^tr r^ er"-^"'^Jt 'r'r

{41v.- r,-..1 \a ::W,--f**il ha,"}l;t &

3;.,*"i:; "# ^x)r^in.? i"\,--41 rn-L {r'lAk-

!- s,tP)

I r-\o! v

,AAWo- 0^""1or\

b:Itr.r

av$'

=-)plt*?aO-tr^ 5

ulNer,^-

tr.t \

,pE "t ($nua )r

LLt- ct I 'n C>^tn

eA

\rin