AM II Cursuri

76
t'ie a'.f* , H 6**aq 'or&,d tr ,,b66'# t Y ffE'1'rl Con pk + 6, *b.X) t-rd'T*$A*J R(4 lrn TLo s I (T ,r )-n + P5t? (ruqa llqv J-cou n*J* )[n).-a bo.a =r .',"4;:: (- L ah cob n'x I ilo, = Lr fp flZfr,,*rlOtE Ue nj J r.&i, Ju- Jo, J- J dne'ena , l:Jw J, &.ci I qrs ffa"oL k, ^,,L *+J*, o.zl r.rat ot*'f; lr*rys; 00 ".-# { = o 2.n?o -* Io',1,., + -,, t41 '! I Np mxCX ,/oz./ =+ l,'l* J^ cfl r+1,'J*'. il: I*coD ,*Ji, a 9 = 7 )o {*l coD mx dxr/)*e l- ILr.q ,(D2./ I -:r- r +- - f"'';*Jr,/o

description

analiza matematica

Transcript of AM II Cursuri

Page 1: AM II Cursuri

t'ie

a'.f*, H 6**aq'or&,d tr ,,b66'#t Y ffE'1'rlCon pk + 6, *b.X)

t-rd'T*$A*J R(4lrnTLo

sI (T,r )-n+P5t?

(ruqa

llqvJ-cou n*J* )[n).-a

bo.a

=r.',"4;::

(-L ah cob n'x

I ilo, =Lr

fp flZfr,,*rlOtE Ue nj

J r.&i, Ju- Jo, J-

J dne'ena , l:Jw J,

&.ci I qrs ffa"oL

k, ^,,L *+J*, o.zl

r.rat ot*'f; lr*rys;

00".-#{

= o 2.n?o-* Io',1,.,

+ -,,

t41

'! INp mxCX ,/oz./

=+ l,'l* J^

cfl

r+1,'J*'.

il: I*coD ,*Ji,a 9 = 7 )o {*l coD mx dxr/)*el-

ILr.q ,(D2./I -:r-

r+-

- f"'';*Jr,/o

Page 2: AM II Cursuri

m"2

-/" 6'trd .

I

=) *,2 ? .r(o-' 7,,, ,*(,* oin*4 =J* E;&:Ylo =l

Jh;\a.a x."do s7,o"( oL "*{-;{{- o{ J +

;-k n^=#f ; h** ;&4 + t- =ry' .fie,ca*.,x &r,,4

l$,^l = 5ro) =

gs&,tC o';J,e-"t{..f;* &"* l*-'{t o;*J6,'60"a;o6

4r . lL, {: ,-T:*o u

[x )o<K<( i- |('- "L J^^.a Ouf?x f:orzr'e,' t, 6ff€.l3 t-)o

.llg-,ilr'2.. -A2=*f^u r d^ '=*a:n -{ (. lo' lo

fl(Jlo

Page 3: AM II Cursuri

JJ-a'.d* =J, Jti, t^

/e,oDrDn =(()'

-

&*: ,,

fq"zii - ft

,ry. * I: Jtv eob -x Jx =* lou

r eobox&

J =," ) 3 '= aon rryx

J'= | , Z=* w,rynx

r #W ui,,;lf- *l;nr",.J.).r* * *C

=#'h[*^rntr )=+ A(n,,'-)(u, n-- (a?

qD

7-t '*,k I o; io,o,au.

f, = + I : Jcur *1.,, * J* = + f: .)r urt * * J*

l(c-oD n* l --n

J,=', ; l'=j,f;'=

f}trarnx , $=F Cour}X

.+(_+

I n L ,|'nl

Page 4: AM II Cursuri

q/n--rR'I

/ tq ** u'ofaV '

Lr-1 n

(+{b.o

r? - Lp, coD/r2x +fi, *b "* ) =

&sl

=+ * E_*, c,a\o)< *I 6rrr'nru* =' *., tvt-f

-4 {' (*- e,obx + S eos,s* + *.* €xt J -F, x_!o;,exr-q *zr

+ t ,>lclr /

'rf- e rr(; KJ ,A 'o#^*E , \ P 2m,

;Jo, =+ +L#r. e.a {zo-)'< o L(* aianx

X=o" - {co,=fl.xl*) o=t- -k L,@t'tr t -L .rc --rc:=+ p-:,f 4 a I

{hr I }

l*t. 3 : tv rR) -',o'..,

5e' cr..to . uc, b€ eto ? W(o r'9 *'? & n'!' '

C& {-o* #,,.f" l. L ,t"fn *Clf n; nJ q.?, *

d'*r.rrE ' fl6) tk€ (o,re)

,{.-r, =/-"1,'*r )< e?rr.o)

Page 5: AM II Cursuri

c

.ut*, n x J^ xL n,x J*=* {onJu,

'0,, b 2.o

=* IuuJ,,,

) ct,

L,

ilfl'- J ,(c,re) -s ASe c4 reo . t)d ba .t t ""(6 f* ne lute .t eo\ : ,

fr*(.* U, ^fu"{

" ,J f ,L{ on(( y v; r]'.-i, ,;!,apwP JJc"l , kelo:'n1

Je(*'' =)lrlt,nn (n,u)

t o ., ,k e[- 4, o,rr ]

$r, =Otr2>1" * a

*ry i + I: J.,., e" ,* J* =* ff l* cou ,..J*

l- xe". ",*i'ELr.r

ffi*Z* {o,r$o l*l-b{" K, \c(o,9) tin D(,,e *L *o

q*L*{Tto{lg ;"!;*h' H;:' ,o,*-ra

Lo /i-lnt-q,o,o\. 0., kefn.Edl

ld-'>ut'

Page 6: AM II Cursuri

6"= d

;;'' *!rn $c,, J.:* trrv 'r' J^ gn

0' =*l: J"n,qoo,ryk&

J,ntu,V* *r D't( -d4e =

=5kI

q@-tI

2eP

,"t'*, X CoU n, J*

{

/-*o l;) "*f t").{

g. lfr..-..I 1-n e,be (n

=n)o

nEF\Lft=

2q:-- _n/( a6s (e,k^)

Page 7: AM II Cursuri

fte p;,ro 71lo)*,.t

tt,r,.*t, -u'* *t,f fri& &=rt r\

,.61-

t:(, .t

[(fe,-7

,l-(

{,rl<

=+ [{,:, &

!e(

)

tr,trir,? ^C,C:

L;

*-(*,t *L-)

J&z J.

8

t/il.

)praa Cora U.

t6rff"J-, C";

t* pnru, fat'zi"r.

*.te,* oL-)u=l

FAes&/+2 :

.r{u ,aftrn, r vn'Ytrs. *{u'o' '

Co"r* otJo.^--- -,r

^?y {:r',6il= fl :,fu*q"? =o) k"L"oh )v \'.

hJ*(./ ,5:t, pon'bJqr or ry'"*aJa ? 'i,v*L't so

Sez,o Q'upB , ? ,8,(d' ea ffx *6* o,L ? *)urJn rr,,.|!:Jo,edrf x J* ,b2-d

L* =+ f L*t ,i'# i>) er€loqoi"fxJ*,b>t/

Page 8: AM II Cursuri

3

^-l- [' *, o{,6a +,) r l: - J€_.*t(* -d-[y ]--^ L a

= * l*, *r, [o {n)n r *- *.1 F -coJ=

=-l-lJ 1^\.=l l- *lrqeeosrn)l==[ /;, {tto er?,?;\ r d o

?tt

=*(-,), #, o( (*, r *.)

ce> cL,x '4 ui,r a n -L * r, f ,x'o r,n(*r* *-) e cd)ryrra ( h=l

SeL\- =* nt, cit r * vccr o f=,t-,f (*r+ *,!eos mk

mTuaaie (\

l;a*o) r lf -.,.=\3x:(cbqqE) k=r ,5@) = t.F/-) e<s\o,r=# y'n,,u** nLon f (t)^trr 4 *)q*d,

rs)-*n -i + *L*, + Il ( "'li'

csiqa( =o'T n-:," 1

&k&.* o{ =$

I L t'to. J = s )

L{aA-,n

J-- \\-oR/

"Ytt*+,{_.*

ift

l!- II I + nltc"{ Er=*

Page 9: AM II Cursuri

=r(,9 t - 8rx

go

=r*/ *€ tn,ilc{o? .,JJ"-, b nnqne $*' qle} -

Ct,,

p(7,- 4X7x riLe${er= *'; ,:,tp,*ilan sd. (,%.Y6* =?.

Page 10: AM II Cursuri

J*L-**L iv,taffii '

&'".f,il1;il#.'fdf:n'k:ifuf-

ol ,ffiffibef " rL* {b,o,fulS"n): [* Jr cdMV

tt,xn, , I*!*J. =fg f {*r.Ac,.a G'* S6 [ t ] q

iir t b+rc )u l* *- ,{ zb*u nu'l," N[H rrnt6q :

T'F,d, =k*j,^ln,J*

i$y, J,o*R, ,%*J l*{o6,o,*a i

J;Joi,. coNv, <*> tn etl .

J:Jr d* ," f {*, d. *qan{ c**fty,{-

H, I'0, J,&. -r,Q-r%.,/ oa{eVae'k

) * d',".t *#i i*{ug=,};6 k*u,**/ rrfuo;' trw^6# d.";8,* r'q ,i I 7 t t. l! te$Bo "l ;JolQI',{,g,' -r"6 #*&

Aoer, : tA f* {,,., J. ^./,C fi,"u, / q fi t

t r'q, il t,e"lq{t4'1 'L $,1*i*ra er{., 6, H

oi t c-'rlr.c1bi{eunul

/t6,' txYr,,aq' :

Page 11: AM II Cursuri

i-'ai,,1,,I rl -, a"J

't *,

/"

i" f ).:,{;;'qr',-Z'xrtl 'Y7t.

ta'' i'

Iti. I*"1

i!'/ tit1,f

{.

lu{1,-,-) r)i + )tt' ,..1i,;Li

.rlf*i/_ I {lni' J . l'*,t ,/- *X, 1, j

! *u,,,,7'1(,L l

r ilrll& lir:,,1.+n.r'i '

d"* :

Page 12: AM II Cursuri

,+fr Cl>orl .t, . ra J#f,(- 1rn',P,oP,!r'

-&,/'

=r{"(l; {fim *.{uye,* r*., rqot,il.fr

er' k ;J,;d",i J*l i,u(^,j,t os6

,'r-{ €qrcL;G'J, +,# oo *&u,*( r,,,^Jrg'z{.

u,n i ,"rrr,1->,p. t";{ ,a,{n7*'LG

Ad.,uA,e { 5 =* , *;1,^ {t"t Jo ,J,&'*\6.

",'{,"o 5: Jw J^ ,:.oJ.

Aoo*, , J: lr,,.t =6*{rn !w, d*

r}aez rgil.'$,"{"A':. *o-[" D'c q{-q' ]

I

5Y {u' J. o''{ u t:; v

der

p&sru&6

=Ct*e:> *r

rA;A,

{** {*,

{a*lr'F n

J- * {,*'^J *€<rta-.<+ {+6r&

Page 13: AM II Cursuri

6oJ ,

(V)* y'

/' .r

da ea

G> -r

: .fl, +A fu 'u( ;'4'rL* ur n

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{{*J, r'{i' '!'"{og*{,6 14 rv'w/ *futc""'*7=$

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I" U I t f

cc?*trvYoh r:i l'' Y''

, r f*oq ra\,t u2 'arr'? fli o Va

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tbl: {*J,.=r {* dn,

f*#'Nod,*

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t)Ll,v

b ->v

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frl-J t

(LL

l- ot

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d

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alC./ n.\,td " l^J t /I -,., llI Gxl: {= !.')

,*/ /

J:1,

a

Lc(-;

/),"rd / /

-"(tt<O=l

/eb D( -r t )A

Page 14: AM II Cursuri

.- ,i

+ (r + e/ * qsDa CIJd>/Jo k*

,JMJ*". (- rvt*J^)-.n

* ic $ G &\ 6ct,,<'atB -

{ ubx Jx = C'n [6rL*.e =5seo Jn

= P:* r u,c,* lor ) = S;F *,a +ecN q-r

r+ f ^krkJ'.r,d'*.

-Jr-(f

% )--xo ts J^ : 9'3- f: D''e * J". =

.(, tc@\xl?=-(Ii WJq5>-i {.-a! as}-t :O.

+ tt' :o?ie (: oi,o lx :o

t)i,t,3-

,i\--/i ,/ -'1i \,tx.

*"d

Page 15: AM II Cursuri

Psq

q,;J"3*6 fre t-d"n*"/ oe^^'dn g^& 0(l 0*,,-'# @*,r'-1, ^ o oed0 ,n"*rn+p4lu'ci- :

r r<r

)^ l,*,ni *'[r' {o, d, *fo*,*u{u/* (. oLrr.:-/*r*r.

,(f'+t .' f a'1 $)rt

I Jo, o/^ = h,r.lqtn

=) ('{*,.t: dar(4t +br){.-l), dt}/\!21

\ "Urv1 -r r"qt

F{ *ri .[ p-P. *oG ewrn>. erarn {*'of ff**f & o*,*.ry',$ef Q'' G*"[3 ; I ue r,o,,t*. ($ 'rt*, + w r*-e bt *.1

{ ",t d r;:: eb(n . I urr, * hu*r,.-.€ 4.r l.eAV*:Lunt* u,*u t . .rt)ry+F =l^Tji\..F .. r l:r.#i.L

:-

fetr!.pnl. . A-\ #p.ra". (hS-:ft4.t1!="rtqlntt (atn+|r(=F

A*rJo* C*,{uauf & +a+*rn6nfi *{ (,' G,, "eff'fo, Jo *qadl e fs ?0 .ff2r@, oi ffa fr>t,

a?>45' ll,P$xt J^ I q

Page 16: AM II Cursuri

fa{/f 's.

d&0,'."--- rb8', t' Io,

J >y,b{b )rA, t : No..E

t rr'd or,, cn' \' JCI

E *{.rk

*f- =Q .

('*/ i* 1J^Ja

J*, J ^ n"{o

nJn e4rz ef" t

o{*C{ ceI

*[-*C.( ad,t . nJn .s,D

I J."J*,J^ l< 5l t k, { dn

(t- ^ L cra Ju*l ^ l, wat- M'\o 7n*fo

cF {--"!"d.o,'-'lrovrJ r{..,r,4/*

6..":- ^:,*-';'&;"5,tia*;

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,l 8""; 5{ J*, ri " (brar, + _{*^ g t+ .{* oc'p e,.

9 o* L*rE1

*t * J'r, :) J: {,*, J*' J'a,

F,

'vI € OT& t.-a

-

G)-, Rtcoql 1,foa*q ib-e f* c&,hJ

rre 41fu *!*

Page 17: AM II Cursuri

-deca +€ J9*)PJ.4s/ -e4

|:\ *l* J, l.-

!*

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I

rbA{+rl

f'P u

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), {mo\ x co,,rbr

IU,.a /I / r, f'J #s

u.l

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q.$'*{' :

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,|

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^_ *u o*i,*ry; f"{t ,* )

+ y, w-7!i o"t*b-* ** fo t 4*Aro-:

)C,,X'r>"

L,n kd .W ru. c=Y ') /* kt^)

1

l_,xt 1

Rtz4try

:fl ,,=/=d :/ +[^#, ** adpen

Page 18: AM II Cursuri

,\Sx

I N "du'&

r-t dx

Fof$.r

t*w

(lo

= /gdu,,

J,

..f e

t+rff,

: Qr',, ',k dk j,r

w

(';

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lJ"{-o

k

:)

,

d,V

al xi.rl-.-

/-tUklr

tl"l=,% x1(*a -A4{

iv.,J.,"o , f *=J--

.t4 tffigQ-r '

{rr* xJ I : C, xJ,kD,- ,5{*h*) r$p.,

e(:q>l, rJ* L_t "ffir;

a_soa_

1}^t=, J_ I lw l*l * eaPD;. =\ j,* k *L uLo. wya=)

.-\*-> WZ_.

Page 19: AM II Cursuri

['e.f

il

I

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o

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k

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?)$rq I Julr*J

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h, aa ' J (vl >o o,? {a P}o) J*q

^&,"S o fl :[*,*) )/R

J oo C rrau.a doaf.p M Q,-, ,k.)p- ]fry = O'

:) i: {roov J^ =@a*}

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/ffJ*r^/:/j: Mry^t./=l-

: h *.p (- qo\ J

l-<J

e ', n -,r,k 5x ew = f:-{" so \

Page 20: AM II Cursuri

f,-. {t"tf --*J-+,=.Lflr'* J ,!CI,x)*>Jo,y)

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fi_v ca o/*,C,1,',-(oo *[ ( [* w) e-, .ro , n)1, , ro6; ea Np *(,$,+* ,-{ru &rr,b :

l_A =*Q,:,* + {r',Ll-L$,r!-*f:

Page 21: AM II Cursuri

./-Jq))fxIL

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+{* Ju

I*J <'C.

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{ "x,jJ #n{r[n* = tt .) *

)i+= hpt

= Q,o6 +P"

Jn =J*

f b d,.

,

-: ,P=t

Page 22: AM II Cursuri

3" ^ til.,

rH iI q\x'l*-lCI XcrQx,rl

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t:=ry= Q|n I,u *"-[*q5*-Pa t o

^r--t i'- 1 l-+/ *f

of

(k*

{,qt(-- Q,*Q5*p-

.r"{, | =

Page 23: AM II Cursuri

rf--- \ t1L/tnJ | / f, '| ar J '+ in i/ '4/\.

)o.

flg.. 1e,-

,

D

q== F:r(, {;r I,,# Ib _)_D" / 6.

=U trt+t,(, rg_- LUrry

Page 24: AM II Cursuri

+ i=l.t ,

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t,ri'ton nduf o"q__,:" :ogfty",

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ojur" ; L

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/c., J^ =3; l*'r, l*,Jr d l!, {*,d-*ui#*.l z >o L

ffi; pJ, p*.r*f o,rg,{*,t ':}J' J; ={'i#: ,!;:,

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Page 25: AM II Cursuri

{,

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U,n (.v-5:, 15 n ,:e,u,{:; TiLnr,{r'r:,yi

Page 26: AM II Cursuri

fr'p ,4 =^o;[ 6-uul*J A*"a AeJO,N) g{. l<-t. {q.,a L>o p,{ D{ ) r d

&.rI9y- rr, -x)r lu, =.7i

8r, lx'J(*8

/ *'}[^ {,n d* eeoa-

l'6 tt

Jo" Jur r/" J*

a-ot{ -/\ // (,.*)rD lio =

l/=.- gY d=!</;7-t0 -l

1'{I

t-)6ol* 'eon?r

Page 27: AM II Cursuri

*r{{J*dqrotf -.?"* G

I14

t",Cli?A 1'1Pr\ ]LL{

#ic H*k ,Hr d Y {o,6s c'rQ

t*ni*il r'ti ryt t ,p 61ng + A.^^ f*d,*{o'fu. Jc gJ ns t'd*f**'* ff( p'e: #t

fa"J N rL

r,nL, f€ c''q foc*-*'*urx, f,* ),ulu' *b{kt/& =-i"*-(.JJ lnn' #(;'t --l .

Page 28: AM II Cursuri

fl p I.f "|Jxp.J5 -,r&T,gr =II'j {t,{ J* , r,i, - it;'jTu:('"?:Jff ;;r:ud J3 r,{ ^J,, fr,t,t: + F,L\ ,r*t ,l*'n {,{

=lff' t,Y,'!J. e'to l.*(t Ytl, \

i il-'$t ) I?rJ, Jqu" 5f(,,,s/ cL * f',E, I(rt/,1)

ri

o zro,>g,' I f-- I dfr,s)-

Ib { rI E-

J" i; Q'.* =

{$,wl'*t o,'{ lz t.1.6

" Trgt *

-iykv,D-%==-<__

fY,ffYryrb,E).k + ,*, =I,r#{*! J,w = J.:;,' lo, *t * :)

't4{w " I fr{s, 'Jtt, o',J, Jf*)

Page 29: AM II Cursuri

rE ,;fi:r, ' {'"- iv*!,!:*d J-v Jt x )

i (5\, I7g) --J, _* "re-r

=t i, {., *.il|Ir

h,-.r#*i@

l^ >{1u

x ,2JJ,:.J

+

,il-0 ?

JSBh M=b4

: i (tf *!r/ {,1i .il)oa Jy@sx '-- r$ i a

Qrrn Jo- eor *J J* p

l^ _i. t i

"Q.=q1,.lil- (,; Lg"r-cdc) c^r 0r* -*{li* 1

IJ* ,t,.s +ft "6,**a

Ab#,ry, 1[ iJ"r J*, dilJ* -Irf f: loo, d.)ltJdf\(1b5.: r ( /

tr-6..? nX J. ...i o^Q ?.so ctnn^{ &d a * d*t +

*]rJn# " *r{q d,,{.#. + l,[* f, ,ii*g{,7i,r

:ry, bJx&,J:

.&: 5* r.*

Page 30: AM II Cursuri

q

' { Jrlr

Jd-

{t Y*

kr l") 4ol5 --

=[' {

t6ir! /d* "a/Js )l-

I 16', {lrol lo }

v{l{-t

rl:){

)o,b*q td'=tUt",x t' atl

= t6|d 'lt l

)o ( r- l, lJl:{,/*{

Page 31: AM II Cursuri

*L,r) Uo*,*/ ,,*lrffu{'ffi

ct(x)'Jn^ -on nl , A >o

5 ) j"{ ,,ru )*, { , r4o*r ,/oal.o.1

5*i ..8 j: -,o / 2J/ )n e A,

{l %btnu,,r*,[ ,-#rl ,rtu'*{

Q") --rH ju- y,/? J{ .,xe-,Q

{) I-t,1-{" Jo o*hkhJ"do" ./

i,, =# 1,.J'k,reriej Irgo*'J',L

"uj"rG-t t;*,:J *+Jl )x{o

5) {,Tdl-a=,;ol n'd ,'

&'8) =!: # Jt t:*''r) {*,rh'u 6,.a-w c? {,, tr$o

;FI

fr-. 1 : )u €-r , -v q -t o/k, qla

Page 32: AM II Cursuri

&,t*-, ft, 'l r'l k o6 L,.

P{" ,11 =lo' xq- , (, _'\)/r-, J*.

X ,= f) , k '=^ I fn,, "{n u*ff {.*Qrory tx.Dp1d.i , )

ftl*1,: fir.,- t, - ,)b ' J, rI' *u '{! -\)

g{ xe(o,cJ.' xa4 !(r-*)b't <x'a r

Jr"*a-/ l^ =lrt i J,

L" r tdk

IqnZ- tt*, (- o 1/u /-ffiJ

rl'q>dL -t

-x)

=,., (*kq-'(^- tb"-'J* %,)bfroT. Jo

fJ xe/c',A) :ko-t tt- *)L-tz tt

(' {t -r)L-'J* =l"t t

), '|' *>) d'* = ), W l*

+J.' fi^,-n)b''J* qrnzr fl'*,>o

Page 33: AM II Cursuri

l$

ff''r,'€l-[-ere") -'

F"t rl^4 {* x"-l =o,6'{'tn xr 1",

* o(J,n

\* e-' f&-'J^Jc

+ Q.t.J; e-Y

=)

Page 34: AM II Cursuri

E\f,{.; Gox( q-

l,5e'

-, (,

e

F (",

[r,*,,

fl-.6,^6/. r(bl: { xo

Jo

tr),y (= c, {y{\${6', 'e Po( *[;{o

.* E_'

-9b*1 J y cz) o, La,

' d" F>o

{ '-'( Jtt i<+/ I tr d{' = F@.,

-

J{

ff.ra0",>f"1-_ I

-r p;b. fd6 ",tl /tf*b =

J r' *o -' t r -',)o

-' J-

t*y={ l-, {o, @-1r.o=)/=/ {'J, fi {1 t

l : I $ {-t J "_lu' {r,(, ilt)d

P(,fi- {* / q-' 'i ^

be, 'Jo -,fut J{

r,',#r J{ ffi, J#

Page 35: AM II Cursuri

s. pbr,*) >7r

Pr t , rl I i *_I ll-)u# et -)rffi. J*= Gac*t f l'=-/a

.,..tc.",rj, 1a*-l{ =*-(-fl: n

tt) l,,t: t"

5- n ffrD = a [-s)'t YrY (rsra) ,^-_1- ir.1c

l: *o-,?+ l=a*'-l3'=e ) A =-dt

= q V"lq

6. Pl**g *- n{ ) n erY

['r,.) 6

n ttu) =h P{r*, *r) @'(r- il{t - 0 =9,=,!*u(o-,) ,r," t,fi6il1"p.1

nrf j; x*-t €*J J^ = f% ; g>o.& q / d -t'r'd

Page 36: AM II Cursuri

- fiv-t o*t)o A' eug d

X fr=/,

rc r=\

L$k=#*r*dtL'U "F

d= ('"*{ ../ a-1Ja qZl-1

-"f I

__ (",

3'8' P*,bt

[*,:J* @

+ do-gr{ =;

{,1 , a t--/ #,.

Pto.s i>,b,=;---_,

f (o *b)

:fg=$+t:

[* -- , *6,f 9- ar6*t _x{g *t) J , : la r!)

^ l, (4o_, j?+)u x-- e d*:ffir, l_

* fi@ rL) . a'-t c/ o_, ( \r- (rf U--'J o *n,6 rn*xr-a k Ju/fi

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3 Frlt

0P/l ,l)rc

Xlot

c6o ,

-,trrr?r -) r(: P?4) =) {'(t.,Gpt,)

w'op n)

Q*-,1 =

+ []r*l s

$.m */ $ q { t >o =sf tlprl) ){ fr"

$o., -a< @ 1-t + c: r? >o + j {r1,g { I Rp*p

*ts: F{e y eJ-{,'12t,

*lr] er5 -!io 1*o ) A rnr I ,e d f l'#* r,uil ++G;L q(*.(l "- F +u)

q

/q z C

G* *,-#, " An"-- ald&ooa 0 zo

D

fltor' ry

$ lTot -Ji r' xn-'

B 4 &fi*'/ *A

o frq

^rg*$- $h4*yi '

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8e,

^t J, =['d( l- Jt _-

$ * ,# +&" =#Jl"r ! /,- u / t-! J{ "/[n{ gttu

/o/& =.! =-*2,

ont*(r3=[ aJ6

xer{

1J/

t) * ,)e

)- x- /e Cx.

/" ? ,)-fL| _)o 14

-&,:

(')0

=12

,=j{

{7b =4,tr,\e, z

Page 39: AM II Cursuri

tt ol.-: I a)o I'(

t", t )a/

{

/ n lur'=e f i et\

FH =f {t,) =

T.)

<.

1t gl-

r--

-2Z

^rcIt)a

6- | ' -.1

#ui J,,:0

*t^)

ut {t tu-t. l" Lr e

/a

{, of" =! pft,

( -'n J"= f,r/ t

(r* g''-' #r=l_ ( I art_t

le-a Jo k

)

trEla rb)A Dtry x a{!}

q =S:6= 6

Pp, " r €,t

{)=

I- .J_

Z r{Et

trtx

rttt l'r(dx: l' *'*

)o

-c-r t) : ;a/n

@n1

=iPlY /

_.{d

t, . .@;1 J" =

rrg) ilffit.----*-F#***

[1 tt)=lretrt ?I

m

-

* 2 c,ob(f q)

IJ

\/ pd7

effo " *)

Page 40: AM II Cursuri

[o *'P-'roFfbl,6) {;

'-r') = b, F( ,-r) rih:-r (r) W,j

f5(r ,

Iu ,

{ o'.

/a *lf

--Q,{t

{, {* +z)

^ J{-- ry )o5: r-{)=(L:*//' ,=4, pIJ

(

o= F'q ; 6 =l -J

J"I + xr'i,

* 1*/

*=f t

, t6

h = /- a.b e / _ tr.

tr x*(o

I

tt+Jr. I

+7

at $lt.,"{,- #1ru

Page 41: AM II Cursuri

il'u J.,A rt/A*J : J .r. n!**, f:**{*eal f, A\ s YQ'*ofb.-*,Ji*a tf , r ; /2,

u , ),a{,.(J ,(), {utr, /*r{),

J,Jn r=[ tu(It &'t^wn.

A n" ,-u,tzt

{ 'y,LJ4"o> d6,

/-{E/

/rz>lftr*"{ta'ct

lJ'|

=n'&, L,| :?,-a L,'*-)

c-ry-"F"6,{,-c< ( *q'.

' = l,(t:Jrd, +€I /),h, ec

t

L . l t( I o1*,^, C,' o

{1 :d,fr::J*= {1(: + {t Iro{u {'^tt lJ t -*

CDn\o x'd '{rJ.LV

Nu((r'* o

-.'6o4 l-I

I!.o

qn

q

{

,

fiD{I

qtalt-

-'43 ,flr", ,frL, :- "# d ,{*,^-1,,".

, fiA,, -) o(*- ,',*{'"o

?fi,fi.{i,O;** ri-c {'\'

Page 42: AM II Cursuri

.5?- c *vao'{u{o ft >C}/-/

C.!ffi

Wl-(n ..0{ 2? uro$*)

€- l. r- R c-o*{6 =

JlJ: R *bd .)fi?,tP =c (? =

5 e

.--.P /.

C

]

{W'If ,n,?) / r'.3e=/P '*, P sc J

A /^ ^e ncrr,'e !u"f",T , {* * fZ, , _)

? n ('u,,n ,lJ Fo.z(* F a-. J'= oI 'r ",u % i o*'4

,d.' x -xo., :

? - lo -/t! a5.

{x: xo, o,/ .

?Ak: gu t' o,{ ,/ e Qv \P =?^ { -^J

Page 43: AM II Cursuri

J* *,.

n[s *rQ {r4,*}'FrA-9

'{*,'nn{u,

/).)

I

Jr

fr'* Ff*;6 3 -, lt 3

J"$ t 6* ,*l r*oJn a g<r>r,{ A;

.Y-cq ) .ff&)

{-& =ffot

tfi ,{)- o.u oeo6*.\ W4 - @ue&,D!

4' M fi;$ , i, oom*tw' d#*o4 , '/

[\o{ .-=d

fr- fi '&/l ->rfl )

d\:{1,"J $/a )

c.-, ff"o{il.o fr {41 . frdt.o* o,[ fr u {"*, &, s.} *dJ =

ff,u f")y "/H!, ,, 1:,r:

{a rrin^r\d* jr** fr*,Esq'Lr'' fi c*[r

Page 44: AM II Cursuri

qk atr(.#tu

'-- fl"

l'lu * I(,lk

,:r{E o "{ (," [*.t ja &*&u* &

.(, *6te ***l "; h

/tLs

-llt =qh

= k'({n )= 3l{o): t{tl

4

Ir

fr'

Page 45: AM II Cursuri

lrl {a{ n, t r ea-a)*"e6,q*, {r! ( fO t,/ ?r,, ,*d.'

:)h)= g t#,J 6''*^ r {on,

: ? ($ft)

tq .l/5or * ) \,u,J { t,r l,/,r ,, /l'*

,J\b/* Jtil 'Jnr((-) i .,nJ,t r\ I // t r

ffn'*Yr{,1 ,' "'l'' Q*, [*1,,, r ({o,{a+tt ) '

(-),,k

inl

IrrIA

f{,

nl

It

{,

=)

Page 46: AM II Cursuri

) 5r, ?,' ffr ro, 4pil, e rn,.l) .W "(4*,4-)

t"{. ' fin , P, ) u,, Ntr & {tapi,*; 6( uvu* f,' fA \ dryie4' l.[ J, lt +.0, o -\ p t' S.N. ,'* r{og*6 orrL;6*q" la*.# e,,{ crtaz [

^' d-.{b," { trr np*{ t- 8,*,& ,

,,9,r8,4J* / Joq J, Jr*'#,{J;,;r,r{r ,wt *{,6r*; #{ € *:fi/rn,

. M6#., {'6 ,1.,/- u:-(

J{?w'!ii r;/-s*6 -,*{,(i.o d

,rfld': Turr-

l,to{l Jr uG( ,

t ri- r tfiAz

l1r, J,il J^ * Jo"

T{3,,,xrt,,/o) /f -ii, , ,; : gI /

,%E:ic;*=:%*

do ' l/ r''r J'* , a'{ J+" D .fr, *6*r{ Jnepe

,4#*{,"

Page 47: AM II Cursuri

s) c<.,{, { J. flNu{"/; o,#n :

Ja) x f Jo

^c3s

f\*ra, $B)h-3 rd*

cc

./,,?rq ( *h;{to p f .tu

(tu/1t^'? \ A

-n( { -*'rl)=a(r- ro"Q

{ {t,, ! Jo

, .{ {E *oJ, o rn

.f .O .) k =O^

9,Ot't:rid(ftr7

9-{ r'If =d1i )x:rJ.nq: oJ

r'&* g'd= ,? ( /- l, .p*{ r *oC/ * *tz().n?(s .:e %ot).e r7* (, - ,*d.) o

]..-li!.*.',

E..---/d(', _"otl) .J{

Page 48: AM II Cursuri

"(E " o/)

=) ( rrt = f,"oo rt 6 *L! J{- rrlrn*,*{ d{:-{t4 F%o!il'o= -Lt 14;-o L #r1=En

&+@&, A.d* /o*, | -{? l-*{,un *#1tr* )=(

nta q*ffev'% d

,, p ) 4', d*, -'-, A, J F) oi&o&,u,v (n L,- d tu ,*o.nl *[ =,!, [' y' ,'"{ {A;)/t ,ad 1d j ) = /r 14/Aio,^..r,{*(' ,rau {dr *,r A, nr/u *(r*,ilf J,od*{r6 d,,,,hfr,r,r{q[ d;"-;

r-.r (J(

"A&660 '// A, tl

y 'o(' o *fd Nnila'{ufr*' Hi 9{r' s6r, &urw r,,.r,pTitd. /

t)€or u,.Ana, Su '[ Jwi J q?,q (i )

{g

Page 49: AM II Cursuri

A"J' ' ilrr.$* {,a -rrf} o*{n oL-{,y66

i f eA a-, C*fl-6d- "'{gtdt f 4A c4 tt A l/< € stl)vr) *' /Sn *f [.5

4*"**$ ('*',*- u,{n

"'"{*f( d^#^'-I

,r"Lfe, l! o

rT'=l

{}a

nQ i,

{^

f t l

r*i,il',A/-.tJ CY.e Ca,

{dn,'a,i,ro

fu*fo Jrb

lU,U dullP

W=, + {a 2 Q'rvrr (*)t)

n- f lJw,r{fi, ,'), d&., o/,

q €u, A oo{,^a.t b*^ tt,t fi,$?* €u, A udrro, --" $) . ((3) (,",{r,u(,t-

fr{"{ ul i{1'x^ . { xf d* il)'rr

'

(t.:et{ftT?or&"""a t:

rw-?qC$/

r$q ua- I *r&'\ a- fa d =J IE''fr.p

t'.A+/Q *wn'#1Io ..- .* ( 'l' (q e rurt tt

€*; t eo/+ 'A*=G'

4,o,ty,-.{... ! .l /"" .,," ,7.' ^ ^ /.'/-

_, l{r i)' )J dy *. qD{'n ($f ,

ff*niu* *ffc;'"#6 qru,4

f f,t) 4*,$-

/i,,f f6{

,#rr, "r{{ *d*/, sD cs * lt,

"c ,{, *r\)> n

0{,, {

Page 50: AM II Cursuri

) /?, tirdop*{,'("

4 {'r) d, 4 s

{{ r, rr p[f1{^Jt

,l (,t) )e ,#? t5J.o -s

{ *,{, d;{ 2o

(,il>fl&,J) ft+Jkd =.i.o'r u{ flest J.4

',6; / ro,.{ {dJ 4 i,/ 1ad.g ., ,,{,1,*k[ fa d; ],'o r] o{o,c

""

ot * Jt ;f { l&',) l* dr

')o/^,* l' /f / ft.,ult* {JG'e n"-r d qz t

*#* b- .=> ; ( I,y srJ '?"fl

' 4 - n= {{f ,ryJ " e(h'a (A I

tp ft('^o(; od, ,** { O ,

r.**i i p ir{*g,o{6 y' ,u&-{*-=>

[+rn'uG$';fi'o.'J,$; A)

f), : -i/ C, p

$^{r {rPu, Aq.?

l,pr r do* k," { ,! .,r).1,n

P',,^ f,'c ,i. d A

do*a, I t {:tr*,)Jt {ot) ei

P'' l{ {f,r),Fe , Ear-ro*o

$e "a t e-cn

f''k Tbu*, o--=' ff'"go c:o I on,{"*

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Page 52: AM II Cursuri

: { ,lffi 1t)&; Ji J , Ti ,#j-,,3,)f*n*l[in, c*,t (Xr'-- y,,,-, ) y, Caro,*4. -Lfi- tt E

+ #,

.rtr, )ri x,_),[{ 1f,,,?t){,;:|;fi{

<i--j-/* ) l{F, ,r) i , ra ,l_{,,a, | llv,{/;,;--- -\ rl ll , n'[- I *f?t.tlAt L''tl_j',

5".2 N*-,n fir/ a

*^lhi -xr.-t)i, J,/ ,l_o

t/ {J*15r'-,,1iJ"-05,

l.l;t_--J-lrm

r(,

*7, !:-'rt * {t tu'il dn{s

-Jt: / [rlu'x)tt) l* '[t^,s) rt *{JI

tu,o;.r t lr {,r, J rr, J*6d ;t

(t) /:X: :l';,- J,d.fu/r,t)/,(\ lr7,{'^*tr ff{d, (; . {r,{}*-) ";t (Ir i*);,; i:'=i r{j.n

{r,e),l*

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"4

/ A^ '

c6rfc,r,ot'F'

f "

s) J*

&. I.tt*

-oC,

JII

h0

: lar l:1r "/$ =

>+

-lJy'.

,dJ =lo'rnff LeJr rf_*tlilr

**r {i=

.fo' ,^ftn, *, *1/-)==lu'J* (t, + i):=fo'{r*', i/J, I

Page 54: AM II Cursuri

{s#

. ,,a,,f'.-..;*l'''i4{f;r:'tii.ts

F*.'

C,ou,,f" I t

g* B€ *{*louo /tf" { *e* d',* (,' ,

tr rr"i'=*J,ltn /+d:0*1, #{, u*kl'ec.ti, ,& ga#**,l'.t *{*#{,

c"al'c] : f . t/HF -t *tr$ oA ,.fF{ *.(,_{*d,uC , Pr: e);

->rn

I, ff) =11 ;?? IVr ' fY) dG-"

x -l au AF**&*€rop.

.i)rt/ p^,

,(,iF d] i*.i

:- 'J

, f .2:2 =f'

d

f.r* Jo= ?

\( i ;rt loJq _v €l'

:I:)i',)?.

r{r)tx.K

iI

x

,I?;

;:)

,,P,

-t

-<t7,

-)Pr,0{l.'

i)lf

)6e* _$ n --

*_*.40 {a CI

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4=

:?'. kJt-r 3f'" eUilF+.-(f le q 4 trr^l( o p lJ* o/J <l0 t I t

P= P{, ?= €a

.rola t F/J.tm, l

: {l^ t,

: !f^

J

=.r_fl'= tf *rfl f t f _-r wt2 c*Y.

/,^

x?r 3n=.*

*.&- --- b -- ,tri

*r:f J* 4 s(x?*grJ

tq,) J. Je

6 , xz*$z -Jx =o.

fx =J:wf-+

(g =J tn;f

(t* 3y -

{,"7Jr

f'IW

Page 56: AM II Cursuri

:) /,.o,'',)& 4 (f,* f), : Jr J 7 =

& , Jqot/: {Fl[ ]' r'Jr)Jr

-JD2

@*d*o*te 0 cRt,'m

u./ : o &".f" p,, q,-) A b,rv, c&p

ffo rf?,3,?)fl'p No €0

$.^,*{*n! ,..5. n, y"f{-fi 1* nt*a{ -d"*#

o*Cuo f , r-u^(('"*o..

lsaGo

*$vn(,^

S=frr€,, I?ga)=PrtUI9s' (kr|,€) -- .wo#-{"fl"ao*,,,d*#, ,

{

I tr Yb ca'zu ,*n*d J'' u 4ru ****A#'Ju *.,*r7v

i j J*,u *G-{"/r J n;*[ (vw

e-6 ('.\U t/t0 .

c) **ff*-

rqU rVa me Vdl,/

Page 57: AM II Cursuri

$"J ' 5,, .*i*ryo "re"d,a'u{ o *1fr'"*{;r t., w*ru# or ,lofr.*',r r.,-,y .*fr,n@n#* 'of .*N'p k o, C{*''

: -**f> no^,G* q. QurA .' tt -) R w*'{ %-fu**4{Drn4'%,*L,' -B

#*.'#=fl'nnJ'*Rfg[: s,,'- Q,*'t J. .)* *&*.*Je (+; F' o zu*c+=

L.qtr, qtzo Fg*L{k t'a n

.'!* c/}' u f-.{ "/' Po' *d#h I

Pf r-r) u,,!{* r|*p''{ 6 q"P A;+al \s

&:G/,

V,*fV*(':l.) 6r; q'&*-

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t) J'u [il - f; ^ J,u ,,> n

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