smakyli/3033/2016-2017... · ® let o
TRANSCRIPT
fta( PrtC~~~ 1 -to 3 stlfs pe ~oup
0 j- leber wfw S aS~Jt
1 p- rne~~ wlo 1ries ulfh J-flk ~~ 1 2 ft yen11~ Who jefs ht~lf w~ middot
btAi vacJt middot Cobullbullyl~t fE 3 f-r f1 e~er lttlto Solves 4-d ~iibt~
~efey
-r A well cpoundooSe oJ~laquo pr~t~ -ftr-_p c~- fro4l4M (A J Dbulle ~- f tJSt~Wr 3--Js -or fiA-t ft-1bull
GverJ ttteMber w~o Is VUf ab~t) middot rvuty ~et ct(ful-J1t ~tk
middot--middotmiddotmiddotmiddot-- middot~-~- ~middot--middotmiddot -
l I
I I I
I
I
I bull
I
0i0 middot-middotmiddotmiddot---- bull Mbull-
( v~fof-- V-fcpound fw~tc-f~ - ---
rmiddot re ~W F ~ I CW) ~ (yJ J J )
tt ~ (p_~Nt~middott~
Prffer~~~~dYL ()Jeurorivfl-ivJl tJf F) cIt~ 1J e -
~verse ~~ -rkof~ l orftci F~amp -1--r-- [ may be ttltd in Uaft 5o3 O])E
0 Y Haflt S 2 ( 7)fGeo~
s ~ Cl tk~~~ fC r t 7( ~ tlh t + ~ s t + e -== 3
ros(~j) + ~Q)( + fe d =_7 ~ e + ~ s ~ t- -s middotJ = C
W~4 s ~ ot fot 4VI ~ ~-+ 1L f-e~ ~
l t t 1-t~+X+W (~l~
Co(~~Hmiddot Si (~~)+ -famphW)bull etJ~
w h_- ~- ~ rs -rL-s ~~ ~fredj foSed ~
I I I middot _ middot
J r i
I
-I f E
middotmiddotmiddotmiddot-middot---middot ---------------____ _ll
--middotmiddotmiddotmiddotmiddotr middot---
cew WeW w~t
~ ( ~~ltGJ +f)x) 4- bull bullbull ) c
-== J -fcJ(l+ ~f~CJt AffUtmiddotmiddotmiddot 1(~ ~~
~e f ~ 5 t~~ wlaeA wbullH i J_b(f(J()t-amp(~tl- ~ht)+ bullbullbull ) J ~
-= J f Gr) t s fttJJ~C f s f (ClJx + middot middot middot
middot middotmiddot- -- - -- -----------middot---------~
LlLfSJ4 ~fe (JJ JfrofW1~ ~ I I
L~ t S S [ tJ f l middot 1c lc X E [ o 1 f J I
w~ f ~ - ftDbal~fJ of ( E s l
s = [J J_ 1 t() f I -rmiddotL ~ - l middot ~ 8 rfb~j = I 3 f
3 1-o I
0 i i L ~~ ~t4 I w~ ~r s = a totl ~ 1
w ~-~ s bull k~-1 of s- ~ I w~ ~ S = 1 (E [o1 fl~~~~
of C hbulls CMj oJJ ~ifs ~ wks lt s ~1( 1- s ~
S ~ ~ ~ s S fitgtJc A-~3cbull~f ~ ~fS-
s [ tSf j
I
middotmiddotmiddot-- cmiddot __ middot middotmiddot- __~ -===~
t t ( tl ( If 11 middot middot +(~ai~) ~ t ~tt~t) ~~) t-t - _
1raquoNbull~1 ~ 4 tAWIJ Aktj s~-rt (cJs 6
icegt~ Sodt~ 1 Wt ~t-f
f~middotbt I ~ ~~ ct~ J i~i ( Cast 2 All a~ s tMtt -z e~os) tctl Si~s tAJt UfiS
middot ----~-- -middot -~--bull -- middotmiddotmiddot- middotmiddot -middotmiddot
bullbull Ill tmiddotmiddotmiddotmiddot--~ --~
middot-middot-middot-middot middot ~-- -middotmiddot middot~middot-middotmiddot -middotmiddot-middot-middotmiddotmiddot
~4~e fttltL-7lf23 f[c~l=-6ccs~~XS~J c) l S ~f~ (f 1-lut~- ~aL ~Ccuct
middot middot tl t gto 3 6 gto -d illtt D lt Ul- pt lt S iffes 1 f(~ )- L l lt ~ ii
reg F Is ~-L tk re IR 1f 1 fir) 0 F4gtl F Is cfc~ ogt 11 st- S off ~ ~ a-ot~ ~ ~ery fE- s
Ji1f1ktotl- 4t l-==(f 1 Q~-1 1Q)Gfe~ pE-JC~ fiv-a_~ F If~ oc~ we luw-e-
0 f(b)~l 4f ~ f~()~ ~ ot-Jl ~=ll-middoti~ b~f 1P ~-tt~ l-= Rp) ~k F i4gt c~s -tP_ de f s ar~ ~~s ttt-p
a- p 1f ~ d1 i-==- J 111 -
fl(j)-==~01 ) ~(cJ)-~J -(j6tJ)~ pot~ ~- P~middot ~~ tr~t
tltf- CJJy1-~s
ltMM- ( ~ IMer-J~) fo ~ ~ t 12 _ 1
l~ [ t ~ y~-tY+middotY~ ~ l~r-t (y~l+ -+fJ- 1 ~ S~t~ ttll-t-11G~rts tve ~ ~
1J l lt 1J _ 1 t t fo]bull - u-t-~z +middotmiddotmiddot1-V~ ~ 21~ + 2 2f~jmiddot t
J a-1 ~ltjfol l ~
fqll ~ tw~ - IJt ~ 0
- _ bull middot -=---
----middot middot~ --middot middot--middot middot-middot-middot --middot~middot--- ---middot middot-------middot-middot --middot-- ----
-fO Jf~ -Ike Jent~--f~ of F ~ ~- 1C M I ~ w~J lb -to kffamp it J a ~t urfe~s~lfll +l-o~ell~r we CA~ u~ ~ Sa~ ~~ss iCM
~ r(1-)- F(p) +-- vt-cfcr t~ ~ 1-stp o----f ~Vecfc-r f lR
~ JRx4v~vt__ ~J 1~J-k_ 4( -fk middot~ +~ middot To k~ri h~ ~ ft0~ o~t-cf 11 +o middot -flt_ ~n-ph c(- T4
middot~ ~~ ([ -k fo~ One V4lr ~l ecse ftg~f ~~~at-a ~ t Ffl()- F(A) L- cflt~) -~ u = M Ut51~ ~ 1
~~~ ~-~ r
IJ rt~~
~7 kM l rcl-)- f~) - lt I 0 fr gt~ JCTR 1 ~A I -f)
~) 1 famp)-ft )-twt~~l =O 1rgt71 be-a fr ~ 11 E-R
gtiv~~_ )efwee- fbullibullt t7V--h3nf-cf-~ W foC tm ~ hmiddot~~ d-ec+fj ovev- -fhrz Saflpound- ~
-middot-middot--middotmiddot
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
0i0 middot-middotmiddotmiddot---- bull Mbull-
( v~fof-- V-fcpound fw~tc-f~ - ---
rmiddot re ~W F ~ I CW) ~ (yJ J J )
tt ~ (p_~Nt~middott~
Prffer~~~~dYL ()Jeurorivfl-ivJl tJf F) cIt~ 1J e -
~verse ~~ -rkof~ l orftci F~amp -1--r-- [ may be ttltd in Uaft 5o3 O])E
0 Y Haflt S 2 ( 7)fGeo~
s ~ Cl tk~~~ fC r t 7( ~ tlh t + ~ s t + e -== 3
ros(~j) + ~Q)( + fe d =_7 ~ e + ~ s ~ t- -s middotJ = C
W~4 s ~ ot fot 4VI ~ ~-+ 1L f-e~ ~
l t t 1-t~+X+W (~l~
Co(~~Hmiddot Si (~~)+ -famphW)bull etJ~
w h_- ~- ~ rs -rL-s ~~ ~fredj foSed ~
I I I middot _ middot
J r i
I
-I f E
middotmiddotmiddotmiddot-middot---middot ---------------____ _ll
--middotmiddotmiddotmiddotmiddotr middot---
cew WeW w~t
~ ( ~~ltGJ +f)x) 4- bull bullbull ) c
-== J -fcJ(l+ ~f~CJt AffUtmiddotmiddotmiddot 1(~ ~~
~e f ~ 5 t~~ wlaeA wbullH i J_b(f(J()t-amp(~tl- ~ht)+ bullbullbull ) J ~
-= J f Gr) t s fttJJ~C f s f (ClJx + middot middot middot
middot middotmiddot- -- - -- -----------middot---------~
LlLfSJ4 ~fe (JJ JfrofW1~ ~ I I
L~ t S S [ tJ f l middot 1c lc X E [ o 1 f J I
w~ f ~ - ftDbal~fJ of ( E s l
s = [J J_ 1 t() f I -rmiddotL ~ - l middot ~ 8 rfb~j = I 3 f
3 1-o I
0 i i L ~~ ~t4 I w~ ~r s = a totl ~ 1
w ~-~ s bull k~-1 of s- ~ I w~ ~ S = 1 (E [o1 fl~~~~
of C hbulls CMj oJJ ~ifs ~ wks lt s ~1( 1- s ~
S ~ ~ ~ s S fitgtJc A-~3cbull~f ~ ~fS-
s [ tSf j
I
middotmiddotmiddot-- cmiddot __ middot middotmiddot- __~ -===~
t t ( tl ( If 11 middot middot +(~ai~) ~ t ~tt~t) ~~) t-t - _
1raquoNbull~1 ~ 4 tAWIJ Aktj s~-rt (cJs 6
icegt~ Sodt~ 1 Wt ~t-f
f~middotbt I ~ ~~ ct~ J i~i ( Cast 2 All a~ s tMtt -z e~os) tctl Si~s tAJt UfiS
middot ----~-- -middot -~--bull -- middotmiddotmiddot- middotmiddot -middotmiddot
bullbull Ill tmiddotmiddotmiddotmiddot--~ --~
middot-middot-middot-middot middot ~-- -middotmiddot middot~middot-middotmiddot -middotmiddot-middot-middotmiddotmiddot
~4~e fttltL-7lf23 f[c~l=-6ccs~~XS~J c) l S ~f~ (f 1-lut~- ~aL ~Ccuct
middot middot tl t gto 3 6 gto -d illtt D lt Ul- pt lt S iffes 1 f(~ )- L l lt ~ ii
reg F Is ~-L tk re IR 1f 1 fir) 0 F4gtl F Is cfc~ ogt 11 st- S off ~ ~ a-ot~ ~ ~ery fE- s
Ji1f1ktotl- 4t l-==(f 1 Q~-1 1Q)Gfe~ pE-JC~ fiv-a_~ F If~ oc~ we luw-e-
0 f(b)~l 4f ~ f~()~ ~ ot-Jl ~=ll-middoti~ b~f 1P ~-tt~ l-= Rp) ~k F i4gt c~s -tP_ de f s ar~ ~~s ttt-p
a- p 1f ~ d1 i-==- J 111 -
fl(j)-==~01 ) ~(cJ)-~J -(j6tJ)~ pot~ ~- P~middot ~~ tr~t
tltf- CJJy1-~s
ltMM- ( ~ IMer-J~) fo ~ ~ t 12 _ 1
l~ [ t ~ y~-tY+middotY~ ~ l~r-t (y~l+ -+fJ- 1 ~ S~t~ ttll-t-11G~rts tve ~ ~
1J l lt 1J _ 1 t t fo]bull - u-t-~z +middotmiddotmiddot1-V~ ~ 21~ + 2 2f~jmiddot t
J a-1 ~ltjfol l ~
fqll ~ tw~ - IJt ~ 0
- _ bull middot -=---
----middot middot~ --middot middot--middot middot-middot-middot --middot~middot--- ---middot middot-------middot-middot --middot-- ----
-fO Jf~ -Ike Jent~--f~ of F ~ ~- 1C M I ~ w~J lb -to kffamp it J a ~t urfe~s~lfll +l-o~ell~r we CA~ u~ ~ Sa~ ~~ss iCM
~ r(1-)- F(p) +-- vt-cfcr t~ ~ 1-stp o----f ~Vecfc-r f lR
~ JRx4v~vt__ ~J 1~J-k_ 4( -fk middot~ +~ middot To k~ri h~ ~ ft0~ o~t-cf 11 +o middot -flt_ ~n-ph c(- T4
middot~ ~~ ([ -k fo~ One V4lr ~l ecse ftg~f ~~~at-a ~ t Ffl()- F(A) L- cflt~) -~ u = M Ut51~ ~ 1
~~~ ~-~ r
IJ rt~~
~7 kM l rcl-)- f~) - lt I 0 fr gt~ JCTR 1 ~A I -f)
~) 1 famp)-ft )-twt~~l =O 1rgt71 be-a fr ~ 11 E-R
gtiv~~_ )efwee- fbullibullt t7V--h3nf-cf-~ W foC tm ~ hmiddot~~ d-ec+fj ovev- -fhrz Saflpound- ~
-middot-middot--middotmiddot
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
--middotmiddotmiddotmiddotmiddotr middot---
cew WeW w~t
~ ( ~~ltGJ +f)x) 4- bull bullbull ) c
-== J -fcJ(l+ ~f~CJt AffUtmiddotmiddotmiddot 1(~ ~~
~e f ~ 5 t~~ wlaeA wbullH i J_b(f(J()t-amp(~tl- ~ht)+ bullbullbull ) J ~
-= J f Gr) t s fttJJ~C f s f (ClJx + middot middot middot
middot middotmiddot- -- - -- -----------middot---------~
LlLfSJ4 ~fe (JJ JfrofW1~ ~ I I
L~ t S S [ tJ f l middot 1c lc X E [ o 1 f J I
w~ f ~ - ftDbal~fJ of ( E s l
s = [J J_ 1 t() f I -rmiddotL ~ - l middot ~ 8 rfb~j = I 3 f
3 1-o I
0 i i L ~~ ~t4 I w~ ~r s = a totl ~ 1
w ~-~ s bull k~-1 of s- ~ I w~ ~ S = 1 (E [o1 fl~~~~
of C hbulls CMj oJJ ~ifs ~ wks lt s ~1( 1- s ~
S ~ ~ ~ s S fitgtJc A-~3cbull~f ~ ~fS-
s [ tSf j
I
middotmiddotmiddot-- cmiddot __ middot middotmiddot- __~ -===~
t t ( tl ( If 11 middot middot +(~ai~) ~ t ~tt~t) ~~) t-t - _
1raquoNbull~1 ~ 4 tAWIJ Aktj s~-rt (cJs 6
icegt~ Sodt~ 1 Wt ~t-f
f~middotbt I ~ ~~ ct~ J i~i ( Cast 2 All a~ s tMtt -z e~os) tctl Si~s tAJt UfiS
middot ----~-- -middot -~--bull -- middotmiddotmiddot- middotmiddot -middotmiddot
bullbull Ill tmiddotmiddotmiddotmiddot--~ --~
middot-middot-middot-middot middot ~-- -middotmiddot middot~middot-middotmiddot -middotmiddot-middot-middotmiddotmiddot
~4~e fttltL-7lf23 f[c~l=-6ccs~~XS~J c) l S ~f~ (f 1-lut~- ~aL ~Ccuct
middot middot tl t gto 3 6 gto -d illtt D lt Ul- pt lt S iffes 1 f(~ )- L l lt ~ ii
reg F Is ~-L tk re IR 1f 1 fir) 0 F4gtl F Is cfc~ ogt 11 st- S off ~ ~ a-ot~ ~ ~ery fE- s
Ji1f1ktotl- 4t l-==(f 1 Q~-1 1Q)Gfe~ pE-JC~ fiv-a_~ F If~ oc~ we luw-e-
0 f(b)~l 4f ~ f~()~ ~ ot-Jl ~=ll-middoti~ b~f 1P ~-tt~ l-= Rp) ~k F i4gt c~s -tP_ de f s ar~ ~~s ttt-p
a- p 1f ~ d1 i-==- J 111 -
fl(j)-==~01 ) ~(cJ)-~J -(j6tJ)~ pot~ ~- P~middot ~~ tr~t
tltf- CJJy1-~s
ltMM- ( ~ IMer-J~) fo ~ ~ t 12 _ 1
l~ [ t ~ y~-tY+middotY~ ~ l~r-t (y~l+ -+fJ- 1 ~ S~t~ ttll-t-11G~rts tve ~ ~
1J l lt 1J _ 1 t t fo]bull - u-t-~z +middotmiddotmiddot1-V~ ~ 21~ + 2 2f~jmiddot t
J a-1 ~ltjfol l ~
fqll ~ tw~ - IJt ~ 0
- _ bull middot -=---
----middot middot~ --middot middot--middot middot-middot-middot --middot~middot--- ---middot middot-------middot-middot --middot-- ----
-fO Jf~ -Ike Jent~--f~ of F ~ ~- 1C M I ~ w~J lb -to kffamp it J a ~t urfe~s~lfll +l-o~ell~r we CA~ u~ ~ Sa~ ~~ss iCM
~ r(1-)- F(p) +-- vt-cfcr t~ ~ 1-stp o----f ~Vecfc-r f lR
~ JRx4v~vt__ ~J 1~J-k_ 4( -fk middot~ +~ middot To k~ri h~ ~ ft0~ o~t-cf 11 +o middot -flt_ ~n-ph c(- T4
middot~ ~~ ([ -k fo~ One V4lr ~l ecse ftg~f ~~~at-a ~ t Ffl()- F(A) L- cflt~) -~ u = M Ut51~ ~ 1
~~~ ~-~ r
IJ rt~~
~7 kM l rcl-)- f~) - lt I 0 fr gt~ JCTR 1 ~A I -f)
~) 1 famp)-ft )-twt~~l =O 1rgt71 be-a fr ~ 11 E-R
gtiv~~_ )efwee- fbullibullt t7V--h3nf-cf-~ W foC tm ~ hmiddot~~ d-ec+fj ovev- -fhrz Saflpound- ~
-middot-middot--middotmiddot
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
cew WeW w~t
~ ( ~~ltGJ +f)x) 4- bull bullbull ) c
-== J -fcJ(l+ ~f~CJt AffUtmiddotmiddotmiddot 1(~ ~~
~e f ~ 5 t~~ wlaeA wbullH i J_b(f(J()t-amp(~tl- ~ht)+ bullbullbull ) J ~
-= J f Gr) t s fttJJ~C f s f (ClJx + middot middot middot
middot middotmiddot- -- - -- -----------middot---------~
LlLfSJ4 ~fe (JJ JfrofW1~ ~ I I
L~ t S S [ tJ f l middot 1c lc X E [ o 1 f J I
w~ f ~ - ftDbal~fJ of ( E s l
s = [J J_ 1 t() f I -rmiddotL ~ - l middot ~ 8 rfb~j = I 3 f
3 1-o I
0 i i L ~~ ~t4 I w~ ~r s = a totl ~ 1
w ~-~ s bull k~-1 of s- ~ I w~ ~ S = 1 (E [o1 fl~~~~
of C hbulls CMj oJJ ~ifs ~ wks lt s ~1( 1- s ~
S ~ ~ ~ s S fitgtJc A-~3cbull~f ~ ~fS-
s [ tSf j
I
middotmiddotmiddot-- cmiddot __ middot middotmiddot- __~ -===~
t t ( tl ( If 11 middot middot +(~ai~) ~ t ~tt~t) ~~) t-t - _
1raquoNbull~1 ~ 4 tAWIJ Aktj s~-rt (cJs 6
icegt~ Sodt~ 1 Wt ~t-f
f~middotbt I ~ ~~ ct~ J i~i ( Cast 2 All a~ s tMtt -z e~os) tctl Si~s tAJt UfiS
middot ----~-- -middot -~--bull -- middotmiddotmiddot- middotmiddot -middotmiddot
bullbull Ill tmiddotmiddotmiddotmiddot--~ --~
middot-middot-middot-middot middot ~-- -middotmiddot middot~middot-middotmiddot -middotmiddot-middot-middotmiddotmiddot
~4~e fttltL-7lf23 f[c~l=-6ccs~~XS~J c) l S ~f~ (f 1-lut~- ~aL ~Ccuct
middot middot tl t gto 3 6 gto -d illtt D lt Ul- pt lt S iffes 1 f(~ )- L l lt ~ ii
reg F Is ~-L tk re IR 1f 1 fir) 0 F4gtl F Is cfc~ ogt 11 st- S off ~ ~ a-ot~ ~ ~ery fE- s
Ji1f1ktotl- 4t l-==(f 1 Q~-1 1Q)Gfe~ pE-JC~ fiv-a_~ F If~ oc~ we luw-e-
0 f(b)~l 4f ~ f~()~ ~ ot-Jl ~=ll-middoti~ b~f 1P ~-tt~ l-= Rp) ~k F i4gt c~s -tP_ de f s ar~ ~~s ttt-p
a- p 1f ~ d1 i-==- J 111 -
fl(j)-==~01 ) ~(cJ)-~J -(j6tJ)~ pot~ ~- P~middot ~~ tr~t
tltf- CJJy1-~s
ltMM- ( ~ IMer-J~) fo ~ ~ t 12 _ 1
l~ [ t ~ y~-tY+middotY~ ~ l~r-t (y~l+ -+fJ- 1 ~ S~t~ ttll-t-11G~rts tve ~ ~
1J l lt 1J _ 1 t t fo]bull - u-t-~z +middotmiddotmiddot1-V~ ~ 21~ + 2 2f~jmiddot t
J a-1 ~ltjfol l ~
fqll ~ tw~ - IJt ~ 0
- _ bull middot -=---
----middot middot~ --middot middot--middot middot-middot-middot --middot~middot--- ---middot middot-------middot-middot --middot-- ----
-fO Jf~ -Ike Jent~--f~ of F ~ ~- 1C M I ~ w~J lb -to kffamp it J a ~t urfe~s~lfll +l-o~ell~r we CA~ u~ ~ Sa~ ~~ss iCM
~ r(1-)- F(p) +-- vt-cfcr t~ ~ 1-stp o----f ~Vecfc-r f lR
~ JRx4v~vt__ ~J 1~J-k_ 4( -fk middot~ +~ middot To k~ri h~ ~ ft0~ o~t-cf 11 +o middot -flt_ ~n-ph c(- T4
middot~ ~~ ([ -k fo~ One V4lr ~l ecse ftg~f ~~~at-a ~ t Ffl()- F(A) L- cflt~) -~ u = M Ut51~ ~ 1
~~~ ~-~ r
IJ rt~~
~7 kM l rcl-)- f~) - lt I 0 fr gt~ JCTR 1 ~A I -f)
~) 1 famp)-ft )-twt~~l =O 1rgt71 be-a fr ~ 11 E-R
gtiv~~_ )efwee- fbullibullt t7V--h3nf-cf-~ W foC tm ~ hmiddot~~ d-ec+fj ovev- -fhrz Saflpound- ~
-middot-middot--middotmiddot
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
t t ( tl ( If 11 middot middot +(~ai~) ~ t ~tt~t) ~~) t-t - _
1raquoNbull~1 ~ 4 tAWIJ Aktj s~-rt (cJs 6
icegt~ Sodt~ 1 Wt ~t-f
f~middotbt I ~ ~~ ct~ J i~i ( Cast 2 All a~ s tMtt -z e~os) tctl Si~s tAJt UfiS
middot ----~-- -middot -~--bull -- middotmiddotmiddot- middotmiddot -middotmiddot
bullbull Ill tmiddotmiddotmiddotmiddot--~ --~
middot-middot-middot-middot middot ~-- -middotmiddot middot~middot-middotmiddot -middotmiddot-middot-middotmiddotmiddot
~4~e fttltL-7lf23 f[c~l=-6ccs~~XS~J c) l S ~f~ (f 1-lut~- ~aL ~Ccuct
middot middot tl t gto 3 6 gto -d illtt D lt Ul- pt lt S iffes 1 f(~ )- L l lt ~ ii
reg F Is ~-L tk re IR 1f 1 fir) 0 F4gtl F Is cfc~ ogt 11 st- S off ~ ~ a-ot~ ~ ~ery fE- s
Ji1f1ktotl- 4t l-==(f 1 Q~-1 1Q)Gfe~ pE-JC~ fiv-a_~ F If~ oc~ we luw-e-
0 f(b)~l 4f ~ f~()~ ~ ot-Jl ~=ll-middoti~ b~f 1P ~-tt~ l-= Rp) ~k F i4gt c~s -tP_ de f s ar~ ~~s ttt-p
a- p 1f ~ d1 i-==- J 111 -
fl(j)-==~01 ) ~(cJ)-~J -(j6tJ)~ pot~ ~- P~middot ~~ tr~t
tltf- CJJy1-~s
ltMM- ( ~ IMer-J~) fo ~ ~ t 12 _ 1
l~ [ t ~ y~-tY+middotY~ ~ l~r-t (y~l+ -+fJ- 1 ~ S~t~ ttll-t-11G~rts tve ~ ~
1J l lt 1J _ 1 t t fo]bull - u-t-~z +middotmiddotmiddot1-V~ ~ 21~ + 2 2f~jmiddot t
J a-1 ~ltjfol l ~
fqll ~ tw~ - IJt ~ 0
- _ bull middot -=---
----middot middot~ --middot middot--middot middot-middot-middot --middot~middot--- ---middot middot-------middot-middot --middot-- ----
-fO Jf~ -Ike Jent~--f~ of F ~ ~- 1C M I ~ w~J lb -to kffamp it J a ~t urfe~s~lfll +l-o~ell~r we CA~ u~ ~ Sa~ ~~ss iCM
~ r(1-)- F(p) +-- vt-cfcr t~ ~ 1-stp o----f ~Vecfc-r f lR
~ JRx4v~vt__ ~J 1~J-k_ 4( -fk middot~ +~ middot To k~ri h~ ~ ft0~ o~t-cf 11 +o middot -flt_ ~n-ph c(- T4
middot~ ~~ ([ -k fo~ One V4lr ~l ecse ftg~f ~~~at-a ~ t Ffl()- F(A) L- cflt~) -~ u = M Ut51~ ~ 1
~~~ ~-~ r
IJ rt~~
~7 kM l rcl-)- f~) - lt I 0 fr gt~ JCTR 1 ~A I -f)
~) 1 famp)-ft )-twt~~l =O 1rgt71 be-a fr ~ 11 E-R
gtiv~~_ )efwee- fbullibullt t7V--h3nf-cf-~ W foC tm ~ hmiddot~~ d-ec+fj ovev- -fhrz Saflpound- ~
-middot-middot--middotmiddot
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
middot ----~-- -middot -~--bull -- middotmiddotmiddot- middotmiddot -middotmiddot
bullbull Ill tmiddotmiddotmiddotmiddot--~ --~
middot-middot-middot-middot middot ~-- -middotmiddot middot~middot-middotmiddot -middotmiddot-middot-middotmiddotmiddot
~4~e fttltL-7lf23 f[c~l=-6ccs~~XS~J c) l S ~f~ (f 1-lut~- ~aL ~Ccuct
middot middot tl t gto 3 6 gto -d illtt D lt Ul- pt lt S iffes 1 f(~ )- L l lt ~ ii
reg F Is ~-L tk re IR 1f 1 fir) 0 F4gtl F Is cfc~ ogt 11 st- S off ~ ~ a-ot~ ~ ~ery fE- s
Ji1f1ktotl- 4t l-==(f 1 Q~-1 1Q)Gfe~ pE-JC~ fiv-a_~ F If~ oc~ we luw-e-
0 f(b)~l 4f ~ f~()~ ~ ot-Jl ~=ll-middoti~ b~f 1P ~-tt~ l-= Rp) ~k F i4gt c~s -tP_ de f s ar~ ~~s ttt-p
a- p 1f ~ d1 i-==- J 111 -
fl(j)-==~01 ) ~(cJ)-~J -(j6tJ)~ pot~ ~- P~middot ~~ tr~t
tltf- CJJy1-~s
ltMM- ( ~ IMer-J~) fo ~ ~ t 12 _ 1
l~ [ t ~ y~-tY+middotY~ ~ l~r-t (y~l+ -+fJ- 1 ~ S~t~ ttll-t-11G~rts tve ~ ~
1J l lt 1J _ 1 t t fo]bull - u-t-~z +middotmiddotmiddot1-V~ ~ 21~ + 2 2f~jmiddot t
J a-1 ~ltjfol l ~
fqll ~ tw~ - IJt ~ 0
- _ bull middot -=---
----middot middot~ --middot middot--middot middot-middot-middot --middot~middot--- ---middot middot-------middot-middot --middot-- ----
-fO Jf~ -Ike Jent~--f~ of F ~ ~- 1C M I ~ w~J lb -to kffamp it J a ~t urfe~s~lfll +l-o~ell~r we CA~ u~ ~ Sa~ ~~ss iCM
~ r(1-)- F(p) +-- vt-cfcr t~ ~ 1-stp o----f ~Vecfc-r f lR
~ JRx4v~vt__ ~J 1~J-k_ 4( -fk middot~ +~ middot To k~ri h~ ~ ft0~ o~t-cf 11 +o middot -flt_ ~n-ph c(- T4
middot~ ~~ ([ -k fo~ One V4lr ~l ecse ftg~f ~~~at-a ~ t Ffl()- F(A) L- cflt~) -~ u = M Ut51~ ~ 1
~~~ ~-~ r
IJ rt~~
~7 kM l rcl-)- f~) - lt I 0 fr gt~ JCTR 1 ~A I -f)
~) 1 famp)-ft )-twt~~l =O 1rgt71 be-a fr ~ 11 E-R
gtiv~~_ )efwee- fbullibullt t7V--h3nf-cf-~ W foC tm ~ hmiddot~~ d-ec+fj ovev- -fhrz Saflpound- ~
-middot-middot--middotmiddot
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
bullbull Ill tmiddotmiddotmiddotmiddot--~ --~
middot-middot-middot-middot middot ~-- -middotmiddot middot~middot-middotmiddot -middotmiddot-middot-middotmiddotmiddot
~4~e fttltL-7lf23 f[c~l=-6ccs~~XS~J c) l S ~f~ (f 1-lut~- ~aL ~Ccuct
middot middot tl t gto 3 6 gto -d illtt D lt Ul- pt lt S iffes 1 f(~ )- L l lt ~ ii
reg F Is ~-L tk re IR 1f 1 fir) 0 F4gtl F Is cfc~ ogt 11 st- S off ~ ~ a-ot~ ~ ~ery fE- s
Ji1f1ktotl- 4t l-==(f 1 Q~-1 1Q)Gfe~ pE-JC~ fiv-a_~ F If~ oc~ we luw-e-
0 f(b)~l 4f ~ f~()~ ~ ot-Jl ~=ll-middoti~ b~f 1P ~-tt~ l-= Rp) ~k F i4gt c~s -tP_ de f s ar~ ~~s ttt-p
a- p 1f ~ d1 i-==- J 111 -
fl(j)-==~01 ) ~(cJ)-~J -(j6tJ)~ pot~ ~- P~middot ~~ tr~t
tltf- CJJy1-~s
ltMM- ( ~ IMer-J~) fo ~ ~ t 12 _ 1
l~ [ t ~ y~-tY+middotY~ ~ l~r-t (y~l+ -+fJ- 1 ~ S~t~ ttll-t-11G~rts tve ~ ~
1J l lt 1J _ 1 t t fo]bull - u-t-~z +middotmiddotmiddot1-V~ ~ 21~ + 2 2f~jmiddot t
J a-1 ~ltjfol l ~
fqll ~ tw~ - IJt ~ 0
- _ bull middot -=---
----middot middot~ --middot middot--middot middot-middot-middot --middot~middot--- ---middot middot-------middot-middot --middot-- ----
-fO Jf~ -Ike Jent~--f~ of F ~ ~- 1C M I ~ w~J lb -to kffamp it J a ~t urfe~s~lfll +l-o~ell~r we CA~ u~ ~ Sa~ ~~ss iCM
~ r(1-)- F(p) +-- vt-cfcr t~ ~ 1-stp o----f ~Vecfc-r f lR
~ JRx4v~vt__ ~J 1~J-k_ 4( -fk middot~ +~ middot To k~ri h~ ~ ft0~ o~t-cf 11 +o middot -flt_ ~n-ph c(- T4
middot~ ~~ ([ -k fo~ One V4lr ~l ecse ftg~f ~~~at-a ~ t Ffl()- F(A) L- cflt~) -~ u = M Ut51~ ~ 1
~~~ ~-~ r
IJ rt~~
~7 kM l rcl-)- f~) - lt I 0 fr gt~ JCTR 1 ~A I -f)
~) 1 famp)-ft )-twt~~l =O 1rgt71 be-a fr ~ 11 E-R
gtiv~~_ )efwee- fbullibullt t7V--h3nf-cf-~ W foC tm ~ hmiddot~~ d-ec+fj ovev- -fhrz Saflpound- ~
-middot-middot--middotmiddot
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
----middot middot~ --middot middot--middot middot-middot-middot --middot~middot--- ---middot middot-------middot-middot --middot-- ----
-fO Jf~ -Ike Jent~--f~ of F ~ ~- 1C M I ~ w~J lb -to kffamp it J a ~t urfe~s~lfll +l-o~ell~r we CA~ u~ ~ Sa~ ~~ss iCM
~ r(1-)- F(p) +-- vt-cfcr t~ ~ 1-stp o----f ~Vecfc-r f lR
~ JRx4v~vt__ ~J 1~J-k_ 4( -fk middot~ +~ middot To k~ri h~ ~ ft0~ o~t-cf 11 +o middot -flt_ ~n-ph c(- T4
middot~ ~~ ([ -k fo~ One V4lr ~l ecse ftg~f ~~~at-a ~ t Ffl()- F(A) L- cflt~) -~ u = M Ut51~ ~ 1
~~~ ~-~ r
IJ rt~~
~7 kM l rcl-)- f~) - lt I 0 fr gt~ JCTR 1 ~A I -f)
~) 1 famp)-ft )-twt~~l =O 1rgt71 be-a fr ~ 11 E-R
gtiv~~_ )efwee- fbullibullt t7V--h3nf-cf-~ W foC tm ~ hmiddot~~ d-ec+fj ovev- -fhrz Saflpound- ~
-middot-middot--middotmiddot
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
-----
I I I
I
i i I
I f i I
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
middot-----middot--------middot --middot --middot-middotmiddotmiddot middotmiddot-- - middot-middotmiddot
i t middot I I I
l ----==
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
_ f dff ~ a I
middotmiddot
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
middot middot-middot middotmiddotmiddotmiddot-middot middotmiddot-middotmiddot middotmiddotmiddotmiddot---- ---------middot-middot ---
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
~ bull ~WtCt fto-s-f0t1CfltS d pound ckA~ Rdt lei 4 s~ Jgtf=(laquo)
b f(laquo) I R~l- fo) ~(Jlt)-b T~ PE(f(Cl))
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
Let fJ~mlt(fboJ fo- ~=(~~~b~)Etgt(pX) ~ et ~
b uCc)-= fl-i~it~) -ffx ~) v-(~) ~o~b~~
Dgt tJ
d~~J(~tt~tk)-(o+(~b)- (ob+~)+fClaquob) U(~4middot-h)- u_(a) 4( ~ 1
= u (an h Gii ~oer ~ a-ct a~E) ~ M etl- 1 ~( AJl cu~~ -
-==(~cabtk)- ~cch))-t J _middot _- (v(btb)-~b~~)i~
__ _~~~== ~~9- _ff~- -~4bgt5 ( ~ 1 b ) - I(
p ~( 01 fo) pound-15( p ~ I~ fgt(f ~ o)
-- -(6 ~ bln) Up-pU40
b)
~p-tt~gt l~-w ~ ft(ob)- l1 ~) - ~- t
_ -- ( A - f 1 J b) if( ) t~laquogt4~lt~ ~~ T ~~ llY -a~ 4 bull
lt ~~ il -av~~(D+~~ ~~(~b)- w l~ ~0 u --wl ~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
middotmiddotmiddotmiddot-middot--middot-middot-middotmiddot- middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddot---middotmiddotmiddotmiddotmiddot ---middot----middot----middotmiddot-middot--- middotmiddot-middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot-middotmiddot-middot
-------middot ----middotmiddotmiddot
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
rptct 1gt1(eat~trt Let f te~- ~~
1 f lfJf~middotmiddotf_)
ecfot ~r~-t~ s~sfe~ 4- e~fs F tt) 0 lt~ f (~~ I c) = 0 ~Yj-i
fJJt_ C) c~ bull H-ere ~ ~ V bullrJ5 x~ (~middot middotmiddot Jc)euro ~ ffl(JCJ bull 1 ~) ~a o
lf gt M 1 tle~ ~~Je PttAJ e 4 e +o s~~ r
W of -fke (~41-as i~ -f4Y~ cf ~~ c~et )t-M
~~~o~fe~ 5pec~G( cAS~ LineAt ~5--~
tlu Xt + bull bull i-lct~K=O tt~ x t- middot+a~~~ =o ~ e_~~s)
V~ middottgt ltove ~v 11- middotmiddot J XW a1 )( + middot +teW llt-=o 11 te-(1-s M-t XV
a c -t- bullbullbull + aIW)(JW = -(a Ptl )(tft~ ho +a~~) ==-gt 4z )(-+ 1 a~ x-= -(a~ bull ~+ middotf42~)
9
bull
~1X+middotmiddot i- 4~-= - (4 ~ t~ c IWt Mf f)j
Clu - (( 1 -~yen- ~ft+bull tQw a~ (l~M Jl -(A~ 11~-- ~~f) bull -
bull - - bull bull bull bull bull
Q - bullbull lW 11 -poundq~-1~ttmiddot--tll~)
M ~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
E)CA~s () ~wen (i )sA ScLiWW~ ltf4l2~)
--e~ -l+xV+=61 nNA~td(frJ Stt-t~-M (~tf 0 Skow ~ ~ laquo Jfff-ct j 1(
tQAt p-=lbullagt - i 6 2Z Q UObullfl~ f IR ~ IR ~ ((1 = ( TX 1 + ~ - I
=6x5+zl(r- ~=2l~+~ 1
A~e Ccn1NocS ~or p S~ F ts C 1 ~~~ p reg F( i z) I+ -2 2+ 2 - 61 = 0
(l) lE(i~)=2middotf~2+middot2Scf-l=o a ~ a J(rgt
t3~ bull~rr-c--t ~~-- nebull~ = c2) ~ete ts ~ C (4ec_ ttff ) f-1~ ~ Slick -tkt- Ft~) x6-tmiddotlbulll+ 1 -amp 1 == 0
c--) ~ = ~(~) ($tbullp ~) ~( ~ laquot f=(l 2) ~ amp4r~ ~~o~le
I s 2 2 j s ti~ I
middot 6-x + 2lCf + ~JC 11 ai +~ ~ =o bull -~ cl~-= _ 6c5+2~~~ At p = pound bull z gt x-=-bull ~-=-1 J 2~amp~+6~lmiddot DibullL_J_
fri- I+middot
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
t tCc 6cctt~ bull ~ Let f 1 f~middot lf2+~ ~ Lot tl~~+ ~
_ oJ f (w x 1 1 ~) = 0 ~ fl ( )C S I 2 ) 0
~ ~A ~olf~ (wo )(o ~o 2o)
(x1 (II be amptampjlftSStclll~ ll ~bullft ~~ (wz)
~e~ At (w0 to ~o 2o) SkOW -liAC
~ _ _ o(-ff) o(ff2-) ~- )(W1) ()()(J)
1 ~ _ oC1f~ a(ffJ ow ()(~ -~ ) a(Jtl~ )
f ~bull middot x~ w W)= o
for x I X W l- tetfWS of middotmiddot w ~ J ~et
oc _ aCf middot middot f ) jJ ( middot middot middot f) middot ~w j - ()(-~ x wj -~ middot middotv)j aamp _ A w middot~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
-x tfA rc 2 --t ( I )( bull j Z) -= (- bull 0 I I t ) ~
~ ~- ~~~~ ~~- ~=~xy -af z + ~ ~ ~f S r~ ~ ~= ~4)( ~=41 it -=1-z~
=-+ 0 -= 4
t)(f~-a) ( )~ -2 o_middot f _ _ 0 =- _as ~(~J) f 0 + - 4 ~t 2
~ ~Acca uefc middotse 2 2 At p ~
~ ~ - ~04 V(-S)= 0
~ ~ -l ~1 ~~ 1c-ampgt = l-1gtc-n-= i
~~-tk~ i~~~-~~~) 3 Jgt(tp~) S-4
~-t ~ leswf~f ( fo 6(f r) As A C f ft~k middot
bullr (l 1) ~e h amp Hmiddotr)() ( l(amp)_j )
-fW SoQ C 1 ~ctWw K tcf ecl ne
H l p) = ( 0) ) 0 I fM J J p ~ ) Fttgt-0 ~ - ~jtk
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
=o -
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~
-middot--middot middot-middot --middot---~ -----
reg let oltr lt ~2 1 t e 13o r) we wtf s~ow 6l V t E B(o1) Le~~c F -1(t) = S
-Me Jbullctcrw _F( S )= t hbulls 11 f~e S4l ~ C~eck F _ is C 1
inreg
S i~ 5fo1S)
l uj~fntss) J f F ( s) = t auf Ff lt J -= t fo~ ~ s ~fo1 ~ ) 1-t(e ( -t )
~
0 Ut- tn = flFtsl-Ffsgtll~ in~-su -~ (E~es+ec~) Note =i=gt Sc s
RsJ=t ~ 0 t- Ftsl ltraquo S=S+(t- RsJ) j
lX~ie pound(s) = S+(t- FCsJ) rt soffus + skow 3 7l ~
s E- uro~) s~k -tct tls) = s
s-rcct IIE~sl II-= h- nsl ~-i Vse 6on _ _ ~j meQ-vc-~ ~1
tiE(x)- E(j) t ~ f lhlt-~ 1-j EM~)
V ZE 6Co~) ~lo1 ~) 4~ rlt~2 ) i
IIE(z )tl ~ II EC)- Efol1 + UE(o)
~ 1nzu + llt ~ r-t- r-= 2r
- middot E 6 o zr) ~ alo 1 ~r) So ~ CotinufiVt i
~fmiddot~~ -amptOWCitJ ~ S ~ lgt(o1~r) C ~o1 ~) sck -M pound(s) = s ~
How to (etiULQ se~eA ClaquoSQ To srtcl Cas-t -middot
1gte~fe ltP1 y alt~~~~ b~
cgt(--)= x-t bull ftjl= 1gtFft)-i(~- Fr3l) --v--
_ ~s uses eet F ~~) =fO f e cf laquo(e C t -1 ~ ~ C t iftlltSe s
q -c) 1C-ta bull ~--r) -o Ft8 x 3 gt + H~) lhf 1- ll2-_ ~ b~ w~gt= fmiddot F bull Prxgt -rfe H(o)= f(F(fro)))= +(F(ampl)=O a~ H
(o)= 1f Ff3l) F ~1gt(ctt-)ro)
=(F~~gtt 1 Ff~) I = I
So we tftaj rr~ sfecclcse 3~ fo K -fb 3et ~ C f i ~erse H _ -de-
_ - bull H bull + = F - F = 4s -bull t-o
t AU c-f~-l~