L1 b^?[ f]5 i/sor P/.y; 4 or, Pa ODF /r'', arr - Mb ta\e..r - - PDF document

(

b^?[ f]5

L1

P/.y;

4 or, Pa i/sor /r'', arr - Mb ta\e..r

ODF

*

Revr'!u/ J /r'r l{r ObE /orr- /r',ert ObF Prciar l aJ

• f

Jo/u f,.cr.J f,o uorr- & r.lrr e0 F

I Bg.ry ' Ltueq 6E

6lven zc'li',,/o4i f"v'c f, o-r q"b ' (t,,r.) * R , wtt tL eiJ 1iv?r' corrlllr t" e (h, trl t lle fVP rr flr. qlrhrcwu l:1t,, t1)+R 1tvr+ , tcy

ar)

Po"{ .

>a ,

hc&,

Y(t") ' Y.

hrr

lha

tlvt'' ? tr e Jc,t f'.ort

(r)

w,lh

It*\ . e

Atrl/

li

I

lnr,

(r.3) r'J .

brse

3.rc 6cr

It" e

wlrth.{. t'

il I

f,rll .fl I

Ir"

Y(f) s

I

/(1,

/tt,

f '. J'e 5

r,rf . '.9

.3

{

* |tf.* !

• .sq\,.J

f,t,rI tl. .oefi.,'a,frJ

[ ",U dr. .orf,ih4cer .'h (t,, tt) C R I

(r) Thare .t an arplr..f arprall.'ch foi- th? solu a,or, yu, ( ii Ut),

r Thr",, ! 3'!', F/r es th..t ttra (e/r. C,

• r.

r

to ,.r prr OPE sc, /r'5 fy r (e) Fo" evety rr.r'li'*f ecro4't|.or. lo C tR

thFrc r't ,L i^!rt'!lu,4 lcfut'ov .

(C) For evc.y rvr'f,'*/ acv.Jr'fiuu h a f?

fhe zod-etFr\el{rl i,r/*F'ou I tS

• .l.&'veor l"-
• J(

t c C t" t.\,

l6u e

f.t "( lt ase pcopcrf,r'it holy's

so/q tt o,"J t" Noq- kw e qr ObF

t

..(

* rVor.- /rr.eqr 06E De{ r

.{,.1f er er f.4 (

Yrrtr, 3(t,

r'l

is

r]:.tgr4J

{')

l'.

tr y3 (t\

Y, ,

,t Y f h0) (r)

lee

s". t. 2,2..

e$. Ittt )

• e r'at

c-lled beh

t?l ?tt,"1

.l eror J ,rt i ,.r

• r. a!' f.

.€

r Rec */1 the u"to.(;o',

• f,

Yl(l res.,-vt'J fo. sol,rho-5 c'l

• \.

ADF. a C ,R

• /e

t,"fet at r'r.

• /epe.r

y'd.' t

Yo. c'' r b' (f .

Er.o.-,Pl?

(r| 1,fi.r-'ft , (ft,a).

(21 | (t, y(il) ' dvq(rcA'ot "f ( *f I .r'.*r/ ftae soi. tl?r / cf $re

• OF

Ittt\ = € (t, Y(tt\ ,

{

T.!lr..r

(tr)

F,x ,2. re.far,il/e R -- (t,,tr\ t tu,,rt\cR", a.J let f .R-'lR be o- ("."c l,'ou ( f, 'r t r-o | ( t. ut . I{ f, !g

• .d .otA'rrrrs aw R.

,

, ),.

/r", 1") dR ,

th*t errr(s

6 R sucl tb rt

f,hrvr

a t., y.)

Ra R ,utth

tbe tVP

l-v,t.r, y, I

hns o. qhal-(c

i o/e l', ou

• u

(.

Pe.r( ,

tUot

l'(t) . €lt, ys711

{

t ao'p( ct so\. z? Th.-r f r"Y [ .

(') Nc cxpkctt ex p?essLcb {"r the

Solqt, cv y ,'v. r,

(") riloq

• u.v,'1,ue'net5 oI

solult'cr,5 iAo T Y P h*) he I'p rl a f por'rr fr (t, u1 \rhrt.e I! t t..t Cs hol .cb fr'r'!.csl.

lq

(!) A chrvl a .'e th. t:'','h,*t .uu,oltftcv lo v*l eharl P tha "/or*r,r' vr whlre ltne Gl"f,,)" ylt, rt c'lPl'wr,!'

rg

I iro.r^p/P. (')

(r + y't1 ,' . t' Jt&lq)y'ott, Jt',tt tc \6*ur1 au . \ t.Jt +.

tJ

,*C = t ?.

c

y'(t) + yft\ ,

t

tt

?c

t + Y lts1

,or.,.r.eqf a0

Ftud,zll

'. Y'ft\ . (se p*..1ro

So/q t,o! t

t"

"fl

I

j

• -)

s

• (.

I

iqV [c ct t eXpr.8,.'o'1 eu ly.

e

\

r Fr,r'"A (r)

Fiio/ r(f

y'lt) .

I(o) = o

s"&. I vP

fQ)

l/olic I .'

u.

lu

So/,. f r'e r

• {

IvP

l/ot

ccw h\4ou,

at u= o,

r.f

r's r.re t qtfr.t

te tR

( J.p.'r,r b/'.

( k,"s '

tfl

IJ,

I

• Dr \
• t
• 5

Arr'l fr

rl

Frrr t lrl'

Se.o\d 3o(.

• r Y

(ot

/'

y-'" y'

,''4,r/q

1rl

Y{i\ =

/"

t

y- " y' olt

Jut

+c

Jrt

t

ta

2

t

2

r rll3

LYtt I

t +e

j

| f, ttre) [

15 |

i

• t \/z

= Lt " i

• '

l+ *l

13 .l

l,(t1 =

{

lhe r vP

hrt

two

t o /re Fr oral

* fi=f.1s

6)

lo( . Fi'rcl

y'lt\

f to)

( see.^.,*lre

tc/, of

y2(tl

)/o

tvP

• Dt'

)

yl

y"

I ,,rl

y2

,!tl

u1

J*

+c

• b

t

=J

• l

0t,

ta l- Yfr)

t +e

J_

t+c

Y (tl

{

lu. Y(o\

• I c

//tt -- - -l_

(t- i")

l).!.c.h r (-e, CPhyt/. i)

i)

a<Y<t

Do-rr'.7

ce,i) vtr)s,rv)

),/ ^ S e,

t't

/(t) =

/J- - rl

(v. .t

T FJ:IP3 j

5o(.

vot

Y'tt\.

{1r,n}.

(tt) lt*r) (,'^'zl ,,1s fr - a,/ ae tL

trr l r S.-l t 9--1, q-- -3

fb dr rar- /. t'c.f

• D

e-

(t u) (t*,'t ( yttt

• z) (yru+t)

r? l lohl

• \n iR.t

where ,y'cas rcf L

• /ol

. (u +!)

p /r'w ?f

arvr L'v(a cq! t,h tk aJ<.

F,'hd lt t

So ,

,(! PJ .

ft vro f

• e.

ll

Yb)=2

.-L&,,)

Y(,,)- I

• L
• +-----.

For fh? c'ui fu*( ecuclc (roq

Yto) s 2 ftea h2po*hacar .f ll.e* .tr

• i e ,Yc

t s.-A: P'a"f.

(b)

ax..\.rpt|,'

l-l

(e! e-41rp..! r

Foc the t\t ft*(

Yto\ - |

T\rv.a If h ohtt roafu-u1/a

thP

(: (-r,r) r

/-z

z)