cltfPrER. +

E LECTgOST4TtrC FTETD S

i t irne - thvov viarln^ar.

gtah'c

E lect"os{".h'c Fi:at d '.

Applical4 Ltn 5 Dr l . o

a

e

q

Tlod^rced, bf q s{z+?b- cl'r^,It

d'{ stvibt^trb q"

E I eot- i e ?o

w e,'r trt'ne "' iss tb u

X- r-Y ma.&uhes

Lf fh'n7 pp'kaltiw

go( id, - s+aJr Elentnnt o- De'uf ce-g

,i + &s[s+nr s) lI | ,nr"c f{o rs

| + br g"towt tV

I ti-td e4<* tr^nsis{r,rs

6npa{<'v f*i phe.^! d,pvfce-r

If

nqln eh^e rnerno.y

If touc:t^ padslT

*r"ctknca keyboao4"s

Co$trod,e - ,4,1 t.lbes

LiX.^^"t e ryst*} atsglay s

I aN.L 6w

cont,o I o (

okp(*w hoh'ow

hy Epz{ws4o&Lfir,tJ

ETC,

r : i2 L*w s 1- r E lecf*sfa.rrc. Clda

Co,^lo- b

" frnr/

r5 Aaw

o Fott ,,, Id"Fe{-

' 4c =

o e' dort-+

atn

6x

=

dis*tibutrbw

F: kdbc.(I--

pa

ol"a.vfr^e. an€i 2w

rahbn.

@ G^tt !5 l-a-nt

' 9ymmr'Frf col CkarV

or frce* Aqil*linS t'n va"oi^.vnh s Fq.( e

e 0U Lo tt4B 's L+vl anA, FDETD I/v rE^' grrY

tV s T by Cl*av I e s ft. de Cad o*b (fi*"rt-)

18 e. to e

-1-oo?q x , i ' r c

\

a\

Foxc ,t)

L,

?)

F '

bc{uecn Z pcirf drcv1cs @r erd Or rs I

^loql +hc .|ivrc. joi.fg {4crrr

Dirl+t7 ?rv7o*io'r.f +o {6c ?nhd &,OroI fe+ .hrr"t*S rrnrcrsl; ?E?ort br-l ft ez (4irfrncs i" m.g

=L4tL"

q: qr lo, */e

F= k&r@zp>

*rt_vC go= g.gr+t tJ ' ' " , i? t /^v6tt_

( pe'rm,^11-,tni4 o# free 5foce)

5

&gtz_ =-\

.&t z.

I eel

a\

Pp=)

"\ ->hz- Tt

^.))ot Fp

+TL" l"i -i,1.

w - .S -,\

V) Flr = - 'F '>

GJ +-4 I

.H a--t

R. - tnv tf $" -8.o rSzr ,l6on At a,^d & z

€o, Or qu{ &- nvsf be \\ po/v* el'tarpes

Qr and &"u musl- be- r+qfib - Ca/- re*)

TAe- st;a s o{ &r q\4 &.1 a}c eo n:iat-6Q.

l"lon thrn

+

*rno pothl &taY6zs

fr{n c,if e. a€ swpu/po€ihto w

:

F- _g4trg-o

NJA

2 &t c7- hp)F=l .5

17 - rcf "

OY

F lec{rfc Fi e(4 Tnrenyfi

( El<-ct-ie fiot{ 9fren6+t*7

el J . l{aT

ot.

al '

sE dveto @r@

(f,fu^s*yibwtrbws

61f r

pcir}6,l.rviG

c

Li". ctl'^*

?hn)""fuce A""S+

vrb-" ^"Vg

l.-.?/aD

-- . t, - f -L. ta-

- - -r 'Z

Y'

?ta--

t

I jacohrrtc

Cfm

VolornlCllrivge

Cln'

5

v6L

t \aAlI \-v. ,

+wdt

.S

E

\A.p

\O.R

\F

r+Wvn

9o, -5

Z= -s,a.p

ffirrrr'3.aachar3e

c/-'

C L" 0,. "J.

ele,ne.'nt d CI' 4 totc"/ che"Xe &

'it*' f{$rj'rrrt

dc. = p,dl ----zF= f p"oo

da- : p, ds +trt f r, ass

dg : fvd,V

r t@v *rE-. PL

r@+vg. (z

f L6E"/ FlrLo k'

I Li'^e W

S,,,*7;g. &^W

2o,\

- \^^,^

I

l:;,j':.f f1..,.)

I Wlr*e- &^2L

Apdy {4{- fsrrntllas {- some. speciG'c-

"tfs{ri bwbt'o

G) Line char;q-\-=r- v -

(ororz)

(orar/1

d&=

0=

dEr.

?Tg

ft-Z1

t7*

I ,5

d!. = f rdz

/

f rd 'z

.J

-ct'P- = E =- Re tEta

Pi, + cz*y'

f pt* c z- 15'73/ '

Por * Cz

oY s f *+ (3-:1 i:

f= ;irt= ,.'+ yl+cz -Jr'

.5

)qz

AE- /=\

-z )Qz d:

L P'+/,z- z' )2121'

L+.t !)

lere xr Yrz)

-I-r2

loirl o{ frle rr.rf'

.t .l4r3 t

Fff i rJr,

R 3 (rr l r : ) - (orort t

- . laf3 rr' + tat o (z'z )r3

PtCnF- J

G f '+(?-Jt '

A= reLP +

P@Se{

(z- / l 'L" t

= Psecc4;

/

td.z =

OT ̂ ffa" "c

*PSeeZa d ou

t*m [+' tt1rdr

-s -L+lTLb

= -L€ttfo p

I

5ot .t

oL

t-t

tt

Fov di^ iJ< ,9t -< :A""I,L

ir,r$inr'l< htne ne-Far

(0rora) dz= -Irz

o$.ta-n

a

III

?

o(l = -fl-

-2-

vsrZa-f cos * ir+ sihdt- l otoL

Pl te/a

2.

L Cos &af T Sr 'n* i . ) A"L

(oror-q {*

and doegrn'f hq'tte Z

Su r$a;c< C0'ra4e

A+ PCeo,h)

.1,Ps ds

S r'a" b@ff+ve''F._'

R,:

.- rl

ae:- F

tt,t. l -c

F = pl 'aal t hal

rit = ( ft r h?l t/' '

d& a Psds= PQ^ear)

de?

CI,

:\de

J

dE=

tEf = O

J- le h.a.S

p, pd 6d7 L-f ir * hel4fi-Lo L r'* 6z-1zlz

C u^V d,Gfutb.,+rbr^ {w,- Q

ohlT 2- - cow?o^..* )r

'?caro rh)

^^4 @ e7 ce^r&it o**f )

Ae pfacinS

2-n-o,n4,

f. Co,I'{TJ

-[-Jnere [az t

Fo, t ".Fia r'te

P! err-4tl-Lo

f 'h l- l?to

v

:Ps r*.

zL<r

She*t

lr f,t:pcr.(c.* oI

{tg Eleef .d f(c

uilh a' f i* rzrren4 t s,",n+d+

o

-iraf

dQ

r r . lsrnQ ay

=O

.>

lo iZ?t-

P2f4trto t =o

.\4.2

ct>

()

P= o

to

I ' re

_ z JL4(P) qzz

sO

1's

lq.o

hp aoaq

f'* hzlarz

L F'* ^z

3\ tz

t f '+ h" l "J

J

E:

*e

E it ncrrrrJ

{t {Gc s[ce*.

ltt.a oliiltbc? Act\recr

pffrl * o0trHtrbr.

7^yd,U&1 pfc.te Cr4?a,c^i{or'

-&- r-e )2-Lo

P' i +22o

P' i"t

.sE=

.Vo Iv rne *"6?d,E

z-d, Ez

oLPb,aJ dv al, ( Y>9t +'t

f\t

4f P ( 0, o,z)

dg, = pndn

e"=

-.sdE=

,dv = Prfao

3g3

4lrto P-

lefv

P, &v fo tr (,osaf: + ri"e i,

l

E r- 2 G7 = o t sy mme.*7 o€ +h"e- c-L....ary &isfuih,*rbu^)

. \sE. a,z

C

J d,Ecos

Pv ("Gto J

{ \ja

"

E==

* otu =

Ag ply f"3 {,fn e @sir,s rule

(

Y'2gln{ ar 'de'abl-

5

I

Cos 0 ='+ ,^"- Rt

22 rr

, '+ R2'r t2

zz?

tz - 2zrtgs5gt

2R- - zzq Cosot

sinl'd e

z +"t

'L*-

R"=

FtL =

zz+

?.z+

Cos "{ =

h (*"') ) Rd R.

ZY

ztf

Ez = pv t df,J

4tr9" Q, = o

= P" LIft

t

t tTCoz-

f r f-- .'

4tfLo z'

P"r._

*[ toz

utz RARr r

_rT= Z-Y

/ 7 .L- v '2f t r = IL' gz J

E* r '! l r r 4

( z ' - Y' ' ) | ,"__-- ) Z_f

R

tJ^1;L" 22

dr' =l* t -i^ {zzR_ RLJ

&

I

a.

tJr t =o

z+(

I iK= 7-Y

q,

Crl\ 4rdv =

>to

q,

tJ/=o

d,Ld r l

N

lFJo

dr

( r ) \Iraf v )

pCorarz)

erl* O F-

PCr)€rt)--

6e-.n^l Org

{A- "m'd" o{

-s-- \ TAP=b(Q7v-

4ff Zu vL

* @ .!,uc,'k{ o,f

{4,*- e pLetre

IIv

Go',r"s ( s- +-r)I t Lc''l

&Qz

Gut'

, / '

E" +"+

^ circwla.r

O- Vr',i{e6ryt Pt

ori{4t ax& */t

q) sho,,.t

\to1 radius q

Al

an& ts place4.I

^a z-- Qxt's.

t l

Cqvrf e-S

OtA .l,f^L y- I

r ir,gJ

C fr"

&.,.'r\L

lE- a

plan g

{CrtOrorh)

-\R

v

Eco,olh ) = tohzzolhz* ,z1\/L

5Q.z-

€ul5

E=

dT

.SR

k

a"dbI

A

&(-ae

.sle l

JPR

J

g=le l3

r -5

) + l \a"z

= Caz+ h")1"

sr.>-Aa, * haz

.\tap

-5

3R2

*haf

t ai gra , 312

sc-

2n-

tf=o

@ od+Loto 6z3rrz

Pt

lfirg-o

0y sfmtn.,try dEf = o I

Eve"y olemen | , d.t ,i a- eorres pondinl e)tm enrl

dJs"metri caWy oPp"si#e f+.

J

E = ft.5

a"h az

z(n\d+

)o4trLo t h t+ a'7 >t

'

*k

b) [^./hot v^{ ues o€

s€t. a rErF:t"

rhA/c - Val,vg ,+ i )\rh 1/

=O ; h= ?

ffives 'll'v-

J

d le l _-

^h

PLq

zra tt nl o"J'/"c,> - Zcn zh th"+o', t/a

[$nt + ae1 3

17 ) . t 2-rh+a.-zh J :

la Azn = \,,

t h1+ az1ttz t2

Ar-

o

ra= p-a-h az

zLoth"+ t J "t

* Vr,h=+

c) rs 4-l*

/ \ r t4lh6L

&"7

e-4

04 {4.{

o"

#"J.s€Qs

rinS [s 6-)

d!. = p,l+

= p, zrrtu

9oldO. = Pt d!

nne = Jp.a-t .

t_ zlf_

= P" [a"A*

l '

2

%r (P. l : oY--/ ztA/

6rc"n (o.,) d :\Qz

zt Ltnt* &) 3tz

Ae:

5

6f G.7

+Ft E h'* *)3t ,

e4rrz-oh'

o-+IfLb V

lrs q+o

Ion Sonera'9,V€

JQz-sF

E.=

-\Q.p-

Jtr

6'2gaua p [e 4.0-

P|,."..t x= 2

anA qq nC/m7,

1 ca\-Yvy oL\q?l-s 1o ^c/t^-

Z=L Cawies &ord^ 4otl ^Qu .

a^ d{

Lir"e

)/= -3

X=O )

C.J.. E at C{rr,-t) d,eb{ra{- {4.rce_ d^"-7* d4bfuib"+frovS.

lcoi :s:

t ; ' l

v

J

. " +€J'. ;) E

g.S.S

EttEz

.,s

Ez

.s€.:

C sheet )

C .?-{ne)

E9

.SJ

Er+ E> +Eg

A:

re ccn2ro

-sPt- af

zrf->.P

J., ,

t t= I 's ,E

( -ax) -sIo- lo '

-2. lo

I

in

-g1T- 10

-?2. lo

Tr

.\-/ to fri\r.

a\./\.-l'J'

..\

"r70 rq!4ra.rg.-

.\

t-L -

Aqx=

Ja-Y =

Ja'y =( ' " .

?-Lo

C"rstrron ptaa ex

I

Y= |T

PCr)_r)

5tl

:

Eg=Aa"PPt.

zTTtof

->p= +-34'z {-

-.\lp l

Jf=

J

lP I

-\Q,7

Jro

\ - \f , r - 3az

f=..>

ot'P =

-9lofl-. fo .

-?zff-. ta

ITo

3')L (a^-3ez)p

t - ) '

b*

36(

'1&tT-( e - ta^.,1

. - \ r r

- l62t l -ax + z lof idyA

* f+ lTaz v/,

Tb 4iqd*5

F

fr heed to Gqd*S

@r A,v. F

-+l,.< {i.la Boi.tJ-

Cr)

q,JA

F

+Jqr) ep

do lwn

e{r"e &v"6x

c i')To

.\Y

6 rr ; r \

4*J

Qyj \ . \ r , . t 1r , -a -L/

t aLp @v- a d.W. "141e Unr* Ve<j+v &oo4- |.-k *:e

rh ?o3?4r,r