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Page 1: Smakyli/3033/2016-2017... · ® let o

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~

Page 2: Smakyli/3033/2016-2017... · ® let o

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~

Page 3: Smakyli/3033/2016-2017... · ® let o

--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~

Page 4: Smakyli/3033/2016-2017... · ® let o

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

-----

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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~

Page 5: Smakyli/3033/2016-2017... · ® let o

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~

Page 6: Smakyli/3033/2016-2017... · ® let o

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~

Page 7: Smakyli/3033/2016-2017... · ® let o

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~

Page 8: Smakyli/3033/2016-2017... · ® let o

----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~

Page 9: Smakyli/3033/2016-2017... · ® let o

-----

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~

Page 10: Smakyli/3033/2016-2017... · ® let o

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~

Page 11: Smakyli/3033/2016-2017... · ® let o

_ 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~

Page 12: Smakyli/3033/2016-2017... · ® let o

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~

Page 13: Smakyli/3033/2016-2017... · ® let o

~ 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~

Page 14: Smakyli/3033/2016-2017... · ® let o

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~

Page 15: Smakyli/3033/2016-2017... · ® let o

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~

Page 16: Smakyli/3033/2016-2017... · ® let o

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~

Page 17: Smakyli/3033/2016-2017... · ® let o

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~

Page 18: Smakyli/3033/2016-2017... · ® let o

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~

Page 19: Smakyli/3033/2016-2017... · ® let o

-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~

Page 20: Smakyli/3033/2016-2017... · ® let o

=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~

Page 21: Smakyli/3033/2016-2017... · ® let 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~