Elektromanyetik Alan Teorisi - Fatih Üniversitesi Özet Ders Notları

8/10/2019 Elektromanyetik Alan Teorisi - Fatih Üniversitesi Özet Ders Notları

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CCE <43 ‟ Cfcatrme`kyctga @f `k Rcmrgsg J@RĸD SKGZC\_GRW

Zcatúrcf @k`fgz

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ZCARÚ\CF @K@Fĸ^

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Wcr bcĝgŝtgrclgfgr

Lgrfcŝtgrgfclgfgr


Zcatúrcf @k`fgz

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A`rtczyck Ammrbgk`t _gstceg


Zcatúrcf @k`fgz

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Zcatúr Lgfcŝckfcrg vc Lgrge Zcatúrfcrg

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_a`fcr lgfcŝckfcr , , x y z r r r

, , x y z ` ` ` Lgrge vcatúrfcr


Zcatúrcf @k`fgz

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A`rtczyck Ammrbgk`t _gstceg


Zcatúrcf @k`fgz

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Zcatúrök Ickfgĝg

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Zcatúrcf @k`fgz

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Zcatúrcf @k`fgz

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Kmat`s`f É`rpİe>

oms @L@ L @ L _mkué dcrzè`k sa`fcr

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Öé lmyutfu uz`yb`

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Zcatúrcf @k`fgz

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Lgr vcatúrök sa`fcr lgfcŝckgkg lufeà gégk>

y y L L `

ś`yct smkué pmsgtgj mfur.ś`yct smkué kci`tgj mfur.

8 78 L`

78 048 L`


Zcatúrcf @k`fgz

7 CCE <43 ‟ Cfcatrme`kyctga @f `k Rcmrgsg J@RĸD SKGZC\_GRW

Zcatúrcf @k`fgz

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Zcatúrcf É`rpİe>

_mkué dcrzè`k vcatúrcfbgr!

sgk K @L@ L ` @ L

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`K kmre`f vcatúr bör

Zcatúrcf é`rpİeb` ycr bcĝgŝtgrgfcecz


Zcatúrcf @k`fgz

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Zcatúrcf é`rpİe bctcregk`kt y`rbİeİyf` amf`yo` lufukur

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Zcatúrcf @k`fgz

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Zcatúrcf @k`fgz

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Lgr b`grcscf sgfgkbgr

Lgr y`r İe -bözfceg

Lgr -bözfceg z

_gfgkbgrga Ammrbgk`t _gstceg>


Zcatúrcf @k`fgz

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Lgr b`grcscf sgfgkbgr

Lgr y`r İe -bözfceg

Lgr -bözfceg z



Zcatúrcf @k`fgz

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Lgrge vcatúrfcr>

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Zcatúrcf @k`fgz

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_gfgkbgrga ammrbgk`tf`rb` bgjcr`ksgycf cfce`k

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Zcatúrcf @k`fgz

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A`rtczyck Ammrbgk`t sgstceg gfc gfgŝagsg>

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Aörcscf Ammrbgk`t _gstceg>

Ecraczg mrgngkbc mf`k lgr aörc

Ecraczg mrgngkbc mf`k lgr amkg

Lgr y`rİe -bözfceg


Zcatúrcf @k`fgz

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Lgrge vcatúrfcr>

Aörcscf Ammrbgk`t _gstceg>

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Aörcscf ammrbgk`tf`rb` bgjcr`ksgycf cfce`k


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Omufmel W`s`sİ vc Cfcatrga @f`k śgbbctg


Omufmel W`s`sİ vc Cfcatrga @f k śgbbctg

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Bckcyscf Omufmel W`s`sİ

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Lgrge tcst yöatcag auvvct cfcatrga f`k ŝgbbctg mf`rà t`kİef`keàt`bİr.



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P yöaökö aörcscf ammrbgk`t sgstcegk ecraczgkc ycrfcŝtgr, m zè`k

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@ykİ ŝcyg a`rtczyck ammrbgk t sgstcegkbc y`ze`yİ bckcscybga>



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Dcr gag yöaök cfcatrga `f`kİ bmĝrus`fbİr.

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Úrkca> _gfgkbgrga cfcatrmk aöecsg

@ŝ`ĝİb` iústcrgfck <-oe uzukfuĝukbàg cfcatrmk bcectgkgk dògescf yöa

ymĝukfuĝu gsc tmpfè yöaö lufuk.



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Égzigscf Wöa vc Cfcatrga @f`kİ

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Dògescf Wöa Wmĝukfuĝukuk Cfcatrga @f`kİ

sİjİr` yàİks`rack dògescf lgr yöa ymĝukfuĝukb`k a`ykàf`k`ktmpfè cfatrga `f`k `rtİes`f cfcatrga `f`kİk gktcir`fg gfc cfbc cbgfgr.

r Ꞇ kmat`sİkb` lufuk`k `rtİes`f lgr ∊P yöaökök r kmat`sİkb` örcttgĝg

`rtİes`f cfcatrga `f`kİ



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R`là` Wöaö vc Cfcatrga @f`k

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CCE <43 ‟ Cf catrme`kyctga @f`k Rcmrgsg J@RĸD SKGZC\_GRW

Cfcatrga @aİ Wmĝukfuĝu, Iùss W`s`sİ, vc Bgvcrn`ks

0

J`r`b`y‗İk Bckcyg

ĸag cŝecraczfg gfctack aörc auff`kİf`rà 0. +P yöaökö aöéöa aörcyc yöafcygk

<. Löyöa y`rİe aörc gfc a`p`tİk

?. Bİŝ`rbàg aörcyg aİs` sörcfgĝgkc tmpràf`yİk

2. ‟ P yöaö bİŝ aörcbc lgrgacocatgr



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J`r`b`y‗İk Bckcyg, Rmpràfè`b`k Úkoc

ĸé aörcbcag yöa , P, cŝgt vc zİt lgr yöaö, -P, bİŝ aörckgk gé yözcygkbc scrlcstcfcatrmkf`rİ pmzgtgj yöac bmĝru écacrca gkböafcr. Bmĝ`f mf`rà bİŝ aörckgk bİŝyözökbc tmpràf`ke`b`k úkoc +P yöaö mfuŝur.



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Bİŝ aörc tmpràf`kİko` bİŝ aörckgk bİŝİkbàg pmzgtgj yöa kútrfcŝgr. Bİŝ aörcbcagkct yöa gé yözcybcag ‟ P yöaöbör .

J`r`b`y‗İk Bckcyg, Rmpràfè`b`k _mkr`



22

J`r`b`y‗İk Bckcyg J`r`b`y, gé aörcbck bİŝ aörcyc bmĝru lgr yöa ‖ycrbcĝgŝgeg― mfbuĝusmkuouk

Wcrbcĝgŝgeg lgr àİe y`b` àİ, icrcatgrecatcbgr. Bgcfcatrga gécrgsgkbcaglu àİ ‖ycrbcĝgŝtgrck― yöa gfc cŝgt egat`rb`bİr.

Lur`b`k>



3

ĸag aörc r`sİkbàg ickcf lgr y`rİé`p r ecs`jcsgkbc

QO/e<U (` ≢ r ≢ l) `r`fİĝİkb` t`kİefİbİr.

Cfcatrga @aİ Wmĝukfuĝu



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Kmat`s`f Wöa ĸégk Cfcatrga @aİ Wmĝukfuĝu

ś`yct gé aörckgk y`rİé`pİkİ yöa egat`rİkİ s`lgt tut`rà aöéöftöp lgr kmat`d`fgkc ictgrgrsca vc bİŝ aörckgk y`rİé`pİkİ smksuz` yàf`ŝtİrİrsà kmat`s`flgr yöa cfbc cbcrgz. Cfcatrga àİ ymĝukfuĝu töe uz`yb` t`kİefİ mfur vcbcĝgŝecz.

O/e< (8 6 r 6 ∛ )

_crlcst uz`yb ag cfcatrga f`k ŝgbbctg gfc aİy`sf`rsà>

Z/e (8 6 r 6∛ )

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Wöa B`ĝİfİef`rİkb`k @f`kf`r

ĸagkog ökgtcbc>

Aİy`sf`y`rà>



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Iùss A`kuku

A`p`fİ lgr yözcyg tcra cbck cfcatrga aİ yözcygk gégkbc l`rİkbİrbİĝİtmpfè yöac cŝgttgr.

Bgjcr`ksgycf lgr vcatúrcf `f`kİk t`kİeİ

Lur`b` k yözcybck bİŝ` bmĝru

mf`k kmre`f vcatúrbör, vc b_ yözcybcag bgjcr`ksgycf p`r`kİk`f`kİbİr.



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Iùss A`kuku

W`b` sörcafg lgr yöa b`ĝİfİeİkb`k>

Égzigscf yöa>

Wözcyscf yöa>

Dògescf yöa>

Lur`bàg yöa kmat`s`f yöafcr ogksgkbck mf`lgfgr,

Dògescf lgr yöa gégk>



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Bgj`rcksgycf f`kf`r vc dòge



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Iùss A`kuku Auff`k`rà Lgr Wözcybc B Dcs`lİ Iùss a`kuku auff`k`rà lgfgkck P gfc B‗kgk éúzöeö>

_cégfck Iùss yözcygkgk ŝ`ĝİbàg gag ŝ`rtİ s`ĝfè`sİyf` éúzöe amf`yf`ŝİr

Lu burueb` gktcir`f l`sgtfcŝcrca>

_mkuét`>

lur`b`

0. _cégfck yözcybc B_ yözcygk dcrycrgkbc y` kmre`f y`b` tcĝctscfmfe`fİ ag, B_¹b _ smkuou B_ b_ y`b` sİjİr mfsuk.

<. _cégfck a`p`fİ yözcybc B_¹b _ smkuoukuk sİjİr mfe`bİĝİ ycrfcrbc,

B_ s`lgt mfe`fİ.



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Kmat`s`f lgr yöa gégk uyiuk mf`k Iùss yözcyg lgr aörcbgr

Iùss A`kukuk Kmat`s`f Lgr P Wöaökc Syiuf`kİŝİ

\`by`f àİ ymĝukfuĝu gfc l`ŝf`>

vc y`rİé`pİ ` mf`k vc yöaö s`re`f`y`k aörcscf lgr yözcy böŝökök, lur`b`>

Wözcybcag bgjcr`ksgycf `f`k>

bİŝ` bmĝru mf`k lgrge vcatúr gfc vcatúrcf `f`k>



02

ĸktcir`kb>

ĸktcir`fgkg `fİrsà>

5

5

02

Iùss A`kukuk Kmat`s`f Lgr P Wöaökc Syiuf`kİŝİ



0303 CCE <43 ‟ Cf catrme`kyctga @f`k Rcmrgsg J@RĸD SKGZC\_GRW


0:

Böziök égzigscf lgr yöa F z -casckg lmyuko` z ycrfcŝtgrgfegŝtgr.

Syiuk lgr Iùss yözcyg scéeca gégk úkocfgafc böŝökecegz icrcack >0. D`kig ammrbgk`t sgstcegkbc `f`k bcĝgŝecatcbgr =<. B‗kgk d`kig lgfcŝckfcrg ecvouttur =

Égzigscf lgr yöatck cfcatrga `f`kİk r`by`f yúkbc(z-casckgkc kmre`f ) mfbuĝuku lgfgymruz>

vc lu `f`k s`bcoc sgfgkbgrgk y`rİé`pİk` l`ĝfİ>

Úzctfc y`rİé`pİ vc uzukfuĝu F mf`k sgfgkbgrga lgr yözcy scéecfgygz.

Iùss W s`sİkİk Égzigscf Lgr Wöac Syiuf`kİŝİ



09

Iùss W s`sİkİk Égzigscf Lgr Wöac Syiuf`kİŝİ



04

Iùss W s`sİkİk Amàsgycf Lgr A`lfmy` Syiuf`kİŝİ z-casckg lmyuko` ycrfcŝtgrgfegŝ gag cŝ ecraczfg gfctacksgfgkbgr v`r. Wözcy yöa ymĝukfuĝu _ s`bcoc gé sgfgkbgrgkbİŝ yözcygkbc ecvouttur.

W`pİ gtgl`rİ gfc -yúkökbc lgr `f`k lcafckecatc vc luégzigscf yöatc mfbuĝu iglg s`bcoc gfc bcĝgŝackbgr. Luyözbck uzukfuĝu F vc y`rİé`pİ mf`k lgr sgfgkbgrg

Iùss yözcyg mf`r` scégymruz. Lur`b` ` 6 6 l.

Iùss a`kukukuk smf t`r`jİ>

…vc s`ĝ t`r`jİ>



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07

śgebg aİ ymuĝukfuĝuku luf`lgfgrgz>

vc cfcatrga f`k ŝgbbctg>

Iùss W s`sİkİk Amàsgycf Lgr A`lfmy` Syiuf`kİŝİ



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Iùss W s`sİkİk Amàsgycf Lgr A`lfmy` Syiuf`kİŝİ



<0 CCE <43 ‟ Cf catrme`kyctga @f`k Rcmrgsg J@RĸD SKGZC\_GRW


<<

Bgjcr`ksgycf Lgr Dòge Cfce`kİkb` Cfcatrga @aİ

Úk yözcygkg gkocfcrsca >

Cfcatrga àİ ymĝukfuĝu B dcrd`kig lgr X kmat`sİkb` a`rtczyck ammrbgk`tf`rb`,

. . A`p`fİ yözcygegzg ecraczg X kmat`sİkb` vc ack`rf`rİ∊ x, ∊ x, ∊ x mf`k aöéöa lgr autu scégp Iùss y`s`sİkİ uyiuf`rsà>

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Úk yözcy gégk>

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Rdcrcjmrc>

Lur`bàg casg gŝ`rctg `ra` yözcybck gécrg bmĝru B x8 àİb`kbİr.

, úk 8

8

'gk gfc bcĝgŝge mr`kİ<

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Röe smkuéf`r lgrfcŝtgrgfgkoc>

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5 P (Iùss W`s`sİ gfc)

Lur`b` P, v dòeg gécrgsgkbcag yöatör.




3



<3

Bgvcrn`ks vc E`xwcff‗gk ĸfa Bckafceg Lgr @ vcatúr `f`kİkİk lgr kmat`b` bgvcrn`ksİ (İràsè`sİ), kmat` ctr`jİkbàgdòge sİjİr` igbcrack lgrge dòge l`ŝİk` @‗kİk kct bİŝ`rİ àİsİ mf`rà t`kİef`kİrvc bgv @ mf`rà aİs`ftİfİr. E`tce`tgascf mf`rà,

B`d` úkoc cfbc cttgĝgegz smkuéf`r` uyiuf`rsà >

bgv @ 5

vc ŝ`yct vcatúrcf `f`k cfcatrga àİ ymĝukfuĝu gsc>

5 bgv B

E`xwcff‗gk gfa bckafceg



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Bgvcrn`ks



<9 CCE <43 ‟ Cf catrme`kyctga @f`k Rcmrgsg J@RĸD SKGZC\_GRW


<4

Bcf Mpcr`túrö

5 bgv B 5

bcf mpcr`túrö vcatúrcf bgjcr`ksgycf mpcr`túröbör>

@sfİkb >



<7

Bgvcrn`ks Rcmrceg

E`xwcff‗gk lgrgkog bckafceg (y`b` Iùss y`s`sİkİk kmat`s`f d`fg) lcfgrtgymrag>

Iùss W`s`sİkİk gktcir`f d`fg (löyöa-úfécafg uyiufè`f`rb`)>

Cŝgtfgĝg gfc Bgvcrn`ks Rcmrcegkg cfbc cbcrgz>



?8

Bgvcrn`ks Rcmrcegkgk @éİafè`sİ Lgr vcatúr `f`kİkİk bgvcrn`ksİkİk (İ ràsè`sİkİk) dògescf gktcir`fg m vcatúrök

lúficyg sİkİrf`y`k yözcybcag tmpfè bİŝ` bmĝru àİsİk` cŝgttgr.



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0


Ckcrng vc Xmt`ksgycf

0

D`rgog Lgr @f`kb` Kmat`s`f Wöa

Lgr cfcatrga `f`kİk àsg yúkökbc P yöaökö t`ŝİeà gégk m yöac cfcatrga`f`kb`k uyiuf`k`k iöoö ctagsgzfcŝtgrcoca àsg lgr iöé uyiufèà icrcagr.

+C

PJuyi

Juyi 5 - P C



Lgr Kmat`s`f Wöaö D`rgog Lgr Cfcatrga @f`kİk @asgWúkökbc R`ŝİrack D`ro`k`k ĸŝ

+

C

Juyi +

L (gfa) @ (smk)

bF

Kmat`s`f lgr P yöaökö l`ŝf`kiİé (gfa) kmat`sİ L‗bck v`rİŝ kmat`sİ (smk) @‗y` bgjcr`ksgycf lgr ecs`jc bF t`ŝİeà gégk d`ro`k`k gŝ>

Cfcatrga f`kİ böziök vc t`ŝİe`yİ cfcatrga `f`kİk asg yúkökbc v`rs`ybİa.Cfcatrga `f`k gfc ymf `r`sİkb` 048¸ j`z j`raİ v`rbİr.

bY 5 J uyi bF 5 PC bF 5 -PC b F QNU .

b F

Cfcatrga `f`kİk àsg yúkökbc t`ŝİe` mfurs` smkué pmzgtgj mfur.



Lgr Kmat`s`f Wöaö D`rgog Lgr Cfcatrga @f`kb`

Dcrd`kig Lgr Wúkbc R`ŝİeà

+

CJuyi 5 -P C

+

L

@

Syiuf`k`k auvvctgk d`rca`t yúkökbcag lgfcŝckg s`bcoc ctag cbcr.

Auvvctgk ickfgĝg J uyi oms(

b F

Lgr P yöaökö bF ecs`jcsg a`b`r t`ŝİrack d`ro`k`k bgjcr`ksgycf gŝ>

bY 5 J uyi oms( bF 5 PC b F.



Rmpfè D`ro`k`k ĸŝ

+C

Juyi 5 -P C

+

L (gfa)

@ (smk)

Wmf lmyuko` d`ro`k`k töe bgjcr`ksgycf gŝfcrg tmpf`rsà >

b F



Dcrd`kig Lgr Wmf Lmyuko` D`ro`k`k Rmpfè ĸŝ

L vc @ kmat`sİ `r`sİkbàg cfcatrga `f`kİk (C böziök gsc) égzigscfgktcir`fg gzfckck ymfb`k l`ĝİesİzbİr.

Böziök lgr C gégk>

L@Y P C F



Égzigscf ĸktcir`fgk Dcs`pf`ke`sİ

@eòİeİz égzigscf gktcir fg dcs`pfèà>

lur`b`

vc

auff`k`rà>



<



9

Úrkca > Égzigscf Wöa

<

F

C `

smk

0gfa

0<

8

FY P b

Y

` ` <

fk<

l F

`

F

Y P b

P lY

`

` ``) l)



Úrkca> Lgrgkog vgzc sİk`v smrusu <884



Úrkca Zcrgfck lgr cfcatrga `f`kİ>

@eòİeİz P 5 < O mf`k kmat`s`f lgr yöaö `ŝ`ĝİb` vcrgfck b`grckgk aİs` y`yİ lmyuko` t`ŝİrack d`ro`k`k gŝg lufeà.

L(0, 8, 0) l`ŝf`kiİé kmat`sİ vc @(8.4, 8.: ,0) v`rİŝ kmat`sİ gsc>

Rcecf auriuyu lu ŝcagfbc y`pe`fİyİz. Dcköz ymf` `gt lgfigfcrg auff`ke`bİa!



Úrkca (bcvèİ)

Y

vc lgrgkog gktcir`fbc y‗kgk x‗c l`ĝİefİfİĝİkİ vc gagkog gtcir`fbc x‗gk y‗ycl`ĝİefİfİĝİkİ cafceca zmrukb`yİz. Bgaa`t cbgk öéökoö gktcir`f z yúkökbclgr d`rca`t mfe`bİĝİ gégk sİjİrf`kİymr .

Zcrgfck b`grcscf ymf lgfigsgkg, auff`k`rà gktcir`fgyckgbck y`z`fİe>



Xmt`ksgycf J`ra

Lgr P yöaökö gfa kmat`b`k smk kmt`y` t`ŝİrackd`ro`k`k gŝg lgfgymruz. Lu `sfİkb` yöaökamkueuku bcĝgŝtgrgrack a`z`kbİĝİ pmt`ksgycfckcrngbgr.

Xmt`ksgycf j`ra (y`b` a`z`kİf`k pmt`ksgycf ckcrng) lgrge yöa l`ŝİk`d`ro`k`k gŝ mf`rà t`kİef`keİŝtİr. Lgrge mfrà Nmufcs/Omufmel, y`b` vmft >

Kgd`yctgkbc>



Kmat`s`f Lgr Wöa @f`kİkb` Xmt`ksgycf J`ra

@eòİeİz kmat`s`f lgr P yöaökök f`kİkb` pmzgtgj lgrlgrge yöaö L‗ bck @‗y` t`ŝİrack d`ro`k`k gŝg lufeà.

Lur`b`

@sfİkb` cfcatrga `f`kİk s`bcocr`by`f lgfcŝckg mfbuĝukb`k @‗b`k L kmat`sİk` tàgp cbgfck

ymf úkcesgzbgr.

+P

r L r @

.. L @



?



Kmat`s`f Lgr Wöa @f`kİkb` Xmt`ksgycf J`ra

+P

r L r

@

.. L @

Xrmlfceg tèèfèà gégk>

Kmat`s`f yöa gégk>

vc



Kmat`s`f Lgr Wöaök Xmt`ksgycf @f`kİ ĸag kmat` r`sİkbàg pmt`ksgycf j`ra>

Xmt`ksgycfg lgr kmat`b` lufeà gégk rcjcr`ks kmat`sİkb` pmt`ksgycfgk sİjİr mfbuĝul`ŝa` lgr kmat`yİ scéecfgygz. Lu rcjcr`ks kmat`sİ úrkcĝgk smksuzb` mf`lgfgr>

Lu smkué t`kİefİ lgr uz`yb` dcrd`kig lgr kmat`b` lgr pmt`ksgycf jmkasgymk y`b`

pmt`ksgycf f`kbİr.

ś`yct kmat`s`f yöa bİŝİkb` dcrd`kig lgr bo `f`k (O0) v`r gsc luku cafcecfgygz>



Mrgngk Bİŝİkbàg Kmat`s`f Wöaök Xmt`ksgycf @f`kİ

X

B`d` úkoc cfcatrga `f`k dcs`pfè`sİkb`W`ptİĝİeİz iglg yöa gfc amkue kmat`sİkİvcatúrfcr gfc gj`bc ctecfgygz.



Bmĝrus`ffİa úzcffgĝg auff`kİf`rà a`taİf`rİ tmpf`kİr >

Ickcffcrsca k yöaö gégk>

ĸag W b` B`d` J`zf` Kmat`s`f Wöaök Xmt`ksgycf @f`kİ



_örcafg Wöa B`ĝİfİef`rİkİk Xmt`ksgycffcrg

ś`yct aöéöa dògefcr sİjİr` igbcrack cfce`k s`yİsİ smksuz` igbcr vctmpfèf`r gktcir`fc búköŝör>

ś`yct dcr kmat`s`f yöa aöéöa lgr dògebcag aöéöa sörcafg yöab`ĝİfİeİ mf`rà tcesgf cbgfgrsc, bmĝrus`ffİa úzcffgĝg auff`k`rà>

v v



Wöa B`ĝİfİef`rİk` Iúrc Xmt`ksgycf Jmkasgymkf`r

Égzigscf Wöa>

R`là` Wöa>

Dògescf Wöa>

B`d` úkoc cfcatrga `f`k gégklufbuĝueuz jmreöf gfc aİy`sf`yİk



2



Úrkca > D`fa` ŝcagkbcag böziök lgr yöa ymĝukfuĝukuk

pmt`ksgycf `f`kİ

@e`é d`fa` ŝcagkbc x-y bözfcegkbc mrgngkbc

ycrfcŝga égzigscf lgr yöaök pmt`ksgycfgkg z -casckgkbc dcrd`kig lgr kmat`b` lufeà.

Jmreöföeöz>

lur`b`



Jmreöföeöz

Lgfgkecyckfcrg ycrgkc amy`rsà>

lur`b`

Úrkca > D`fa` ŝcagkbcag böziök lgr yöa ymĝukfuĝukuk

pmt`ksgycf `f`kİ



<0

Ckcrngkgk Amrukuk Úzcffgĝg

8b C F

Lgr yöaök dcrd`kig lgr a`p`fİ écvrge ymf özcrgkbc d`rcactg gfcy`pİf`k gŝ sİjİrbİr.

Úrkca > Lgr BO-bcvrcsg

Lgr lgrge yöaök @ kmat`sİkb`k\<, \? vc \0 özcrgkbck tcar`r @kmat`sİk` d`rcactg sİr`sİkb`d`ro`k k tmpfè gŝ sİjİrbİr.(Agroddmjj )



<<

Cŝpmt`ksgycf Wözcyfcr

• Kmat`s`f lgr yöaök pmt`ksgycfgs`bcoc r ‗ yc l`ĝfİ lgr jmkasgymkbur.

• r‗ bcag aörcscf lgr yözcycŝpmt`ksgycf yözcyg tcesgf cbcr.

• Cŝpmt`ksgycf yözcy cfcatrga `f`k

égzigfcrgkc bgatgr.



Xmt`ksgycfbcag F ymfu lmyukoàg bcĝgŝgelu vcatúr vc cfcatrga f`k `r`sİkbàg éİy`l`ĝfİbİr 1 úrkcĝgk, `f`kİk ymf` gzböŝöeö>

y`b`

lur`b`k>

Eàsgeue bcĝcr >

ŝ`yct ymf vcatúrö cfcatrga `f`kİ gfc p`r`fcf gsc.

@rtİes`f Lgr Ecs`jc Lmyuko` Zmft`nb` Bcĝgŝge



Xmt`ksgycfbcag eàsgeue rtİŝ dİzİ cfcatrga f`kİk zİbbİ yúkbc mfur >

lgrge vcatúr cŝ pmt`ksgycf yözcyc bga vc rt`kpmt`ksgycf yúkökbcbgr.

C

C e`xgeue `z`fe` dİzİyúkökbcbgr, y`kg, Z ‗kgkkci`tgj bcĝgŝge (ir`by`kt) yúkökbcbgr.

Cŝ pmt`ksgycf yözcyfcrg

`K

Xmt`ksgycf @f`k vc Cfcatrga @f`k @r`sİkbàg ĸfgŝag



3



Bgjcr`ksgycf vmft`n bcĝgŝgeg Z ‗kgk öé yúkbcbc bcĝgŝgegk tmpfèİ ŝcafgkbc y`zİf`lgfgr >

ĸktcir`f d`fgkbck lgfgymruz ag>

Úzbcŝfcrsca>

Lúyfcoc>

A`rtczyck Amrbgk`tf`rb` Cfcatrga @f`kİk Z ĸfc ĸj`bcsg



C vc Z `r`sİkbàg gfgŝag>

Bcf mpcr`túrökö Z özcrgkbc auff`k`rà cfbc cbclgfgrgz.,

B`d` iúkcf vc aİs` gj`bcsgyfc>

Ir`by`ktİk yúk sa`fcr `f`kİk eàsgeue `rtİŝ dİzİ yúkökbcbgr vc cŝpmt`ksgycf yözcyfcrc bgatgr.

Cfcatrga @f`k vc Xmt`ksgycf Ir`bgyckt



<9

_a`fcr Lgr @f`kİk Ir`by`ktİ

Z C

Cfcatrga @f`k vc Xmt`ksgycf Ir`by`kt





@e`é dcr gag yöatcka`ykàf`k`k pmt`ksgycfg X

kmat`sİkb` lufup smkr`b`pmt`ksgycfbck cfcatrga f`kİklufuke`sİ.

Dcr yöac `gt mf`k pmt`ksgycfgk tmpfèİ>

Cfcatrgascf Bgpmfc



Szà-@f`k Wàf`ŝİeİ

ś`yct r ;;b gsc öé amkuevcatúrö lgrlgrgkc p`r`fcf a`lufcbgfclgfgr. Lu burueb` ŝuyàf`ŝİef`rİ auff`k`lgfgrgz>

vc

_mkuét`>



:



Bgpmfök Cfcatrga @f`kİ

Lufbuĝueuz pmt`ksgycf `f`k>

Cfcatrga f`kİ pmt`ksgycfgk kci`tgj ir`by`ktİkİ f`rà luf`lgfgrgz>

y`b`..

_mkuét`>



?<

Bgpmf ĸégk Cfcatrga @f`k vc Cŝ Xmt`ksgycf Égzigfcrg



Cfcatrga Bgpmf Emecktg

Bgpmf emeckt vcatúrö kci`tgj yöatck pmzgtgj yöa yúkökbcbgr >

X‗kgk yúkö `z yúkökbc mfbuĝukb`k>

M zè`k>

W`b` b`d` ickcf lgr gj`bc gfc, bgpmf mrgngk bİŝİkb` dcrd`kig lgr kmat`b` gsc>





ĸag Kmat`s`f Wöa _gstcegkbc Xmt`ksgycf Ckcrng

+ +\ <,0

P0 P<

P< yöaö smksuzfuab`klufukbuĝu kmat`y` ictgrgfbg.P0 ŝ`yct gzcfc gsc sİjİr ckcrngsg

v`rbİr.

P<‗yg lufukbuĝu amkue` ictgrgrack d`ro`k`k gŝ >

Lu sgstcebcag lgr `r`y` ictgrgfck gag yöaök bcpmf`k`k ckcrngsgbgr.



Öé Kmat`s`f Wöa _gstcegkbc Xmt`ksgycf Ckcrng

+ +\ <,0

P0 P<

P? yöaö smkuzfuab`k lufukbuĝuamkueuk` ictgrgfgymr, lur`b` P0

vc P< lufukbuaf`rİ amkueb`f`r .

Lur`bàg sgstce ckcrngsg b`d` úkocag <-yöa ckcrngsgkc gf`vctck P? yöaököAmkueuk` ictgrgrack d`ro`k`k gŝtgr.

+P?

\ ?,< \ ?,0

lur`b` vc



9



Búrt Kmat`s`f Wöa _gstcegkbc Xmt`ksgycf Ckcrng

+ +\ <,0

P0 P<

@ykİ ŝcagfbc P2 yöaö smksuzfuat`k lufukbuĝuamkue` ic tgrgfgr. P0, P<, vc P? lufukbuaf`rİycrbcbgrfcr.

_gstce ckcrngsg b`d` úkocag ?-yöaök ckcrngsgkc gf`vctck P2 yöaökö lufukbuĝuAmkue` ictgrgrack d`ro`k`k gŝtgr >

+P?

\ ?,< \ ?,0

Lur`b`> vc

+

P2 \ 2,0 \ 2,<

\ 2,?

Mf`y a`re`ŝİaf`ŝİymr !

Lur`b` bgaa`t cbgfcoca dusus lu yöafcr ykİ kb` lufukbuaf`rİ amkue` ictgrgfgymrf`r .



Ckcrng ĸégk Cŝbcĝcr ĸj`bc

Búrt yöa gégk bcpmf`k`k ckcrng>

Nmufc

ś`yct Z ke pmt`ksgycf t`kİef`rİk` là`rsà yua`rİbàgkc lckzcr lgr gj`bc lufuruz>

ĸag gj`bcyg tmpf`y`rà b`d` sgectrga gj`bc cfbc cbclgfgrgz>

Dcr lgr yöa bgĝcr yöafcrc `gt pmt`ksgycffcrfc é`rpİfeàt` vc vcrgfck yöaök amkueukb`dcs`pf`keàt`bİr.



Búrt @yrİa Kmat`s`f Wöa _gstcegkbc Bcpmf`k`kCkcrngkgk Ickcf ĸj`bcsg

B`d` úkoc>

Wcrcf pmt`ksgycffcrg t`kİef`>

..lur`b`k



k -Wöa Wöa Rmpfuĝu ĸégk Bcpmf`k`k Ckcrng

Lgr úkocag smkuou ickgŝfctcrc k yöac uyiuf bİĝİeİzb`>

Lur`b` e kmat`sİkbàg yöaök ycrcf ycrcf pmt`ksgycfg>

@sfİkb` lu e kmat`sİkb` ag yöa d`rgé bgĝcr töe yöafcrgk e kmat`sİkb`dcs`pf`k`k pmt`ksgycfgbgr.



_örcafg Wöa B`ĝİfİeİkb` Bcpmf`k`k Ckcrng

ś`yct sörcafg lgr yöa ymĝukfuĝu ogksgkbca yöa vcrgfegŝ gsc `ŝ`ĝİbàggj`bcyg bmf`yfİ mf`rà auff`ke`fİyİz.

@e` lur`b` P yöaökö bq 5 v bv gfc bcĝgŝtgrecfgygz vc tmpfè` yöaökdòeg özcrgkbck gktcir`fc búköŝör >

Lur`b` Z yöaök lmfukbuĝu dògebc amkue l`ĝİefİ pmt`ksgycfbgr..



Lgr Cfcatrga @f`kİkb` Bcpmf`k`k Ckcrng

E`xwcff bckafcegkg auff`k`rà dògescf yöa ymĝukfuĝuku B ogksgkbc y`ze`fİyİz>

Lur`b`, vcatúr úzbcŝfgĝgkg auff`kbİa.

_mkr`, lgrgkog tcrgebc ag dògescf gktcir`fg b gvcrn`ks tcmrceg auff`k`rà m

dòge özcrgkbcag yözcyscf gktcir`fc écvgrgrgz>



4



Lgr Cfcatrga @f`kİkb` Bcpmf`k`k Ckcrng (Bcvèİ)

Bckafcegegz>

Lur`b` gktcir`f lúficsg töe uz`yİ a`psèàt`, bgĝcr lgr t`lgrfc f`k vcpmt`ksgycfgk mfbuĝu dcr ycr. Lu yözbck yöac gt mf`k dògefc sİkİrfİ bcĝgf. Bgĝcrlgr t`lgrfc yözcy gktcir`fg smksuz lgr y`rİé`pt` fİke`fİbİr. _mksuz ecs`jcbcpmt`ksgycf vc B `f`kf`rİ kmat`s`f lgr yöaök f`kf`rİk` lckzcr >

Lur`b`k>

ĸktcir`kb y`rİé`pİk aöpö gfc bcĝgŝgrack gktcir`f yözcy özcrgkbck (y`rİé`pİka`rcsg) gfc bcĝgŝcocatgr. Lur`b`k gktcir`fgk smksuzb` sİjİr` igttgĝg ŝga`rbİr.



Cfcatrga @f`k Ckcrngsg vc Ckcrng Wmĝukfuĝu

@f`k ckcrng gj`bcsg>

è` lgfgymruz ag>

Lur`b`k kgd`g smkuo` v`rİrİz>

Lur`b` cfcatrga `f`kb` ckcrng ymĝukfuĝu `ŝ`ĝİbàg iglg t`kİef`kİr >





0


ĸfctackfcr vc Bgcfcatrgafcr

@aİe vc @aİe Wmĝukfuĝu

Xmzgtgj yöafcrgk d`rca`tİk` @aİe bgymruz. Q UbP

G @bt

@rtİes`f lgr aİe rtİes`f lgryözcybck icécrsc

G N _

Lur`b` N Q@/e<U àİe ymĝukfuĝubur. Rmpfè àİe gsc

_ G b N _

`K



v vP v _ F

vP _ x

v

v x

x v x

v

P x G _

t t

G _ v

N v

N v

Amkvcasgymk (R`ŝİkİe) @aİeİ Lgr v dòeg gécrgsgkbcag P yöaökö böŝökök, yöa pmzgtgj x yúkökbc v x

dİzİyf` d`rcact cbgymr >

ś`yct t zè`kİkb` yöa x 5 F 5 v x t ecs`jcsg d`rcact cbcrsc



Úrkca > ĸagkog vgzc sİk`v smrusu <884



@aİeİk _örcafgfgĝg

Pg(t )

Pg yöaö a`p`fİ lgr yözcy _ gfc t`kİefİ dògebck bİŝ`rİéİa`rà aİe ymĝukfuĝu N‗yg mfuŝturbuĝuku v`rs`y`fİe. Rmpfè yöa>

Lur`b` casg gŝ`rctg bİŝ`rİ bmĝru pmzgtgj àİ mfuŝe`sİ gégkgécrgbcag yöaök z`fbİĝİkİ sgeicfcr. śgebg bgvcrn`kstcmrcegkg uyiuf`rsà>

lur`b`k

y`b`

_mk gj`bcbcag gktcir`kbf`r cŝgtmfò`ĝİkb`k @aİeİk _örcafgfga

Bckafcegkg cfbc cbcrgz.



Ckcrng L`kt W`pİf`rİ

ĸfctackfcr > bİŝ yúrökicbcag cfcatrmkf`r écagrbcĝc icvŝca l`ĝfİbİrf`r vc gfctackl`kbİk` amf`yfİaf` icéclgfgrfcr. Éma s`yİb` scrlcst cfcatrmk v`rbİr vc ckcrngscvgycfcrg r`sİkb` lmŝfua ymatur. W`fİta`kf`r > bİŝ yúrökicbcag cfcatrmkf`r lgfc écagrbcĝc éma iöéfö l`ĝfİbİr. _crlcstcfcatrmkf`r ymatur vc ckcrng scvgycfcrg r`sİkb` löyöa lmŝfua v`rbİr. Bİŝ`rİb`kuyiuf`k`k lgr f`k b`dg cfcatrmkf`rİ d`rca`t cttgrcecz. W`rİgfctackfcr > Iúrcocfg mf`rà z s`yİb` scrlcst cfcatrmkf`r` s`dgptgr vc ckcrngscvgycfcrg r`sİkbàg lmŝfua zbİr. Bİŝ`rİb`k uyiuf`k`k cfcatrga f`kİ scrlcstcfcatrmkf`rİk d`rcactgkg s`ĝf`y`lgfgr.



Ect`fga ĸfctackfcr _crlcst cfcatrmkf`r cfcatrga f`kİk tcsgrgyfc d`rcact cbcrfcr. Lgr cfcatrmk yöaĝ

P 5 -c‗yc uyiuf`k`k auvvct

Cfcatrmk zmrukfu mf`rà gvecfckcrca bckicbcag söröafckge dİzİk` uf`ŝİr>

lur`b` c cfcatrmk bcvgkickfgĝgbgr (d`rcactfgfgĝg) vc lgrgeg e</Z-s. _öröafckge dİzİkİauff`k`rà aİe ymĝukfuĝuku lufuruz>

Lur`b` cfcatrmk aİŝİ gégk gfcatackfga > Mde W`s`sİkİk kmat`s`f d`fg

_/e

W`rİ gfctackfcrbc bcfga aİeİb` mfò`ĝİkb`k



<



ĸfctackfga Égzcficsg



Bgrcké Dcr gag uouk` lgr Z vmft`nİ uyiuf`k`k lgr sgfgkbgrga gfctack böŝökcfge. @aİe ŝcagfbcagyúkbc _ acsgt yözcygkbc böziök b`ĝİfeİŝ lgr ŝcagfbcbgr.Úkocfgafc, sgfgkbgrbcag f`k kgocfgĝg ogksgkbck aİe vc vmft`nİ y`z`lgfgrgz>

Mde W`s`sİkİ auff`k`rà>

_gfgkbgrbcag bgrckog lufuruz>

` l



Bgrcké ĸégk Ickcf ĸj`bc

` l



ĸfctackfcrgk Cfcatrmst`tga Úzcffgafcrg

0. Wöa s`bcoc yözcybc yözcyscf yöa ymĝukfuĝu s ŝcafgkbc v`r mf`lgfgr, gécrgbcyöa ymatur.

<. Cfcatrga f`k gécrgbc mfè`yò`ĝİ iglg yözcybc bc tcĝctscf lgfcŝckg ymatur (smkràg sf`ytf`rb` iústcrgfcoca).

?. ĸfctack lgr yözcygk fİkb` cŝpmt`ksgycf lgr yözcy mfbuĝuku <. amŝufb`k kfİymruz.

s

+

+

+++

+

+

++ +

+

+++

+

+

+ ++

+

+

C

ĸfctack

Wözcybcag cfcatrga f`kkmre`f yúkbcbgr .

ĸécrgbc C 5 8

Lgr gfctack özcrgkc j`zf`b`k lgr yöa amkufbuĝuku böŝökcfge



_İkİr Amŝuff`rİ

Lgrgkog sİkİr amŝufuku bckafcegkg

`↜l↜o↜b↜` ymfu gfc éúzcrca luf`lgfgrgz.

8b C F



_İkİr Amŝuff`rİ

ĸagkog sİkİr amŝufuku bckafcegkg sgfgkbgrga

Iùss yözcyg özcrgkbc éúzcrca luf`lgfgrgz.

_ b P B _



?



8t t

K K _

B C

B C

_İkİr Amŝuff`rİ



Úrkca >



Iúröktöfcec Ectmbu



Ect`f pfà`yİ a`fbİrİp ycrgkc ecvout yöafcrgk kci`tgjgkg sgectrgaecs`jcbc ycrfcŝtgrgk. Lu yöa mrngk`f yöaök iúröktösöbör .

Iúröktöfcec Ectmbu



Úrkca > ĸfctack lgr bözfcegk özcrgkbc égzigscf yöa

ĸag f`kİ tmpf`y`rà tmpfè f`kİ lufuruz>



X kmat`sİkbàg cfcatrga f`kİ lufbua>

vc

k

B

yöa ymĝukfuĝuku lufeà gégksİkİr amŝufuku auff`k`fİe >

k 5 `z

X kmat`sİkbàg yözcyscf yöa ymĝukfuĝu>

lur`b`

Úrkca > ĸfctack lgr bözfcegk özcrgkbc égzigscf yöa



2








Bgcfcatrga E`fzcecfcrgk Úzcffgĝg

Ickcffgafc (gstgsk`f`r v`r) bgcfcatrga e`fzcecfcr kútr yöaföbörfcr.Cfcatrmk lufutukuk ecraczg écagrbca gfc úrtöŝör. D`rgog lgr `f`kuyiuf`rsà yöafcrbc `tmega lmyutt` a`ye` mfuŝur vc cfcatrmkf`rİkecraczg écagrbcĝgkagsgkc iúrc a`y`r vc lgr bgpmf mfuŝturur. Lu yöafcrc lgz l`ĝİf yöafcr bgymruz.



Bgcfcatrgafcr

@tmef`r cfcatrga `f`kİkecvoubgyctgkbc cfcatrga bgpmffcr

mfuŝtururf`r. Röe bgpmffcrcfcatrga `f`kİ gfc dgz`f`kİrf`r.Dgz`f`k`k bgpmffcr kci`tgj lgr

cfcatrga `f`kİ mfuŝturur vc mrngk`f

`f`kİ `z`ftİr.



Cfcatrga Bgpmf vc Bgpmf Emecktg

Pb p 5 Pb z

Bgcfcatrgafcrbc yöafcr yúrökicfcrgkbc l`ĝfİ d`fbcbgrfcr vc scrlcst yöa iglgd`rcact cbcecbgafcrgkbck aİe mfuŝe`z. @tmef`r vc emfcaöffcr autups`fmf`lgfgr (pmzgtgj vc kci`tgj yöafcr `yrİŝeİŝ), y`b` cfcatrga `f`kİkecvoubgyctgkbc autupf`ŝeİŝ mf`lgfgr.

Lúyfc lgr `tme y`b` emfcaöfö böŝökök, lgr bgpmf emecktg p‗yc s`dgp,pmzgtgj vc kci`tgj yöa `yrİe ecs`jcsg b gfc yöa egat`rİ P‗kuk é`rpİeİmf`rà t`kİef`keİŝ. Bgpmf emecktg kci`tgj yöatck pmzgtgj yöac bmĝru mf`klgr vcatúrbör.



Xmf`rgz`symk @f`kİ

Qbgpmf emecktg/dògeU

y`b`

QO/e<U

v

Bgpmf s`yİsİ ymĝukfuamf`rà gj`bc cbgfgr,

lgrge dògebcag kbgpmfö.

Mrtèİk Xmf`rgz`symk @f`kİ `ŝ`ĝİbàg iglgt`kİefİbİr >



3



Xmf`rgz`symk @f`kİ (Syiuf`k`k Cfcatrga @f`kİyf`)

C

Lgr cfcatrga `f`kİk ecvoubgyctgkbc dcr lgr bgpmfbcag yöa `yrİeİ `rt`lgfgr, vctöe bgpmffcrg dgz`f`r. Ctag icrécatc aöéöatör vc lur`b` l`rtİf`rà égzgfegŝtgr!

Ctag X‗yg `rttİròàtİr .

5 kp

Lur`b` töe bgpmffcrg `ykİa`luf cttga.



L`ĝfİ Wöaök Iúé Ctecsg

C

ścagfbcag iglg yözcy kmre`fgkbck `éİsİyf` lgrcfcatrga f`k uyiuf`kbİĝİkİ böŝökcfge. L`ĝfİyöafcrbcag yrİŝe` (y`b` dgz`f`ke`) `rtİ lgrl`ĝfİ yöaök _ yözcygkbck yua`rİ bmĝru vckci`tgj l`ĝfİ yöaök gsc yözcybck ŝ`ĝİ bmĝruyúkcfecsgkc sclcp mfur.

Bgpmf ecraczfcrg (aİreİzİ kmat`f`r ) (0/<)b oms

yözcygk östö vc ftİ r`fİĝİkb` yöaö yözcylmyuko` tr`ksjcr cbcocatgr.



Xmf`rgz`symk @aİsİ Mf`rà L`ĝfİ Wöaök D`rcactg

C

Wözcyg icéck tmpfè l`ĝfİ yöa egat`rİ>

_

vmfuec

X



A`p`fİ Lgr Wözcy Lmyuko` Xmf`rgz`symk @aİsİ

Xmzgtgj l`ĝfİ yöafcrgk a`p`fİ lgr yözcy gécrgsgkbc tmpf`ke`sİpmf`rgz`symk vcatúrökök gécrg bmĝru mfbuĝu smkuoukubmĝurur. Lu kcbckfc>

_X

+

+

+ +

-

-

-

-

ql



_crlcst Zc L`ĝfİ Wöa

śgebg a`p`fİ lgr yözcy gécrgsgkbc l`ĝfİ yöafcr ql vc scrlcst yöafcr q mfbuĝukuböŝökcfge. Rmpfè yöa scrlcst vc l`ĝfİ yöafcrgk tmpfèİk` cŝgttgr . Iùss

W`s`sİkİ tmpfè yöa PR ogkogkbck y`z`rsà>

Lur`b`

PR 5 Pl + P

l`ĝfİ yöa

scrlcst yöa

_X

+

+

+ +

ql

+

++

+

C

q

PR



_crlcst Wöa ĸégk Iùss W`s`sİ

PR 5 Pl + P

Cfgegzbc mf`kf`r>

vc

lur`b`

Lgrfcŝtgrgp yckgbck y`z`rsà>

Úzbcŝfcŝtgrcrca>Iùss W`s`sİkbàg lgfgkckŝcafgyfc yckgbck y`z`lgfgrgz>



:



Wöa Wmĝukfuaf`rİ

Lgr úkocag smkuou `fİp Bgvcrn`ks Rcmrcegkg uyiuf`rsà yöa ymĝukfuaf`rİ

gégk kmat`s`f gj`bcfcrg cfbc cbcrgz>

L`ĝfİ Wöa>

Rmpfè Wöa>

_crlcst Wöa>



Cfcatrga D`ss`sgyct Zc Bgcfcatrga _`lgtg

B`d` auvvctfg lgr cfcatrga `f`k mrtèb` b`d` löyöa lgr pmf`rgz`symk`sclclgyct vcrgr. Bmĝrus`f lgr mrtèb`, X vc C `r`sİkbàg gfgŝagbcbmĝrus`fbİr vc ŝúyfc t`kİefİbİr >

lur`b` c mrtèİk cfcatrga d`ss`sgyctgbgr .

śgebg ŝúyfc y`z`lgfgrgz>

lur`b` bgcfcatrga s`lgtg, y`b` l`ĝİf icégrickfgĝg ŝúyfc t`kİef`keİŝtİr>

Mrtèİk tmpfè cfcatrga icégrickfgĝgkg mf`rà t`kİef`rsà

Ickcf gj`bcyfc>



_İkİr Amŝuff`rİ

Lgrgkog sİkİr amŝufuku bckafcegkg `↜l↜o↜b↜`

ymfu gfc éúzcrca luf`lgfgrgz.

8b C F



_İkİr Amŝuff`rİ



ĸagkog sİkİr amŝufuku bckafcegkg sgfgkbgrga

Iùss yözcyg özcrgkbc éúzcrca luf`lgfgrgz. _

b P B _

_İkİr Amŝuff`rİ



_İkİr Amŝuff`rİ



9



_İkİr Amŝuff`rİ

Bgcfcatrga e`fzcecfcrbc yözcy yöa ymĝukfuĝu ymatur, 8 s

0 <

0 <

R R

K K

C C

B B



0 0 0

< < <

oms

oms

K

K

B B

B B

0 < K K B B sİkİr amŝufuku auff`kİrsà

0 <

< 0

oms

oms

B

B

0 0 0

< < <

sgk

sgk

R

R

B B

B B

< 0 0 <R R B B sİkİr amŝufuku auff`kİrsà

0 0

< <

t`k

t`k

_İkİr Amŝuff`rİ





0


A`p`sgt`ks

A`p`sgt`ksİk R`kİeİ

ĸag zİt yöafö gfctack böziök lgr bgcfcatrga gfc écvrgfg gsc l`sgt lgr a`p`sgtúr mfuŝturur.

P‗bc dcrd`kig lgr a`ts`yİyf` rtİŝ C vc B‗bc rtİŝ` sclcp m fur.

d`tİrf`y`fİe>

`ykİ a`ts`yİyf` `rtİŝ` sclcp mfur. Bgĝcr lgr gj`bc gfc P

vc Z 8 `r`sİkbàg a`ts`yİ s`lgttgr . Lur`b`k y`pİkİka`p`sgt`ksİkİ bcpmf`k`k yöaök uyiuf`k`kpmt`ksgycfc mr`kİ mf`rà t`kİefİymruz, y`b`

lgrgeg O/Z y`b` J`r`b ‗bİr.

_mkuét`, gfctackfcr r`sİkbàg pmt`ksgycf j`ra>

P

-P C, B

_

L

@.

.


A`p`sgt`ks

X`r`fcf Xfà` A`p`sgtúrö

Xfà` yözcyg 5 _

Eöaceecf gfctack yözcy özcrgkbc B gégk sİkİr amŝuff`rİkİ uyiuf`rsà>

@ft Xfà`>

Öst Xfà`>Dcr burueb` ykİ smkué!

Xfà`f`r r`sİkbàg cfcatrga f`k>

W t`y buruebàg pfà` lmyutf`rİkİ pfà`f`r r`sİkbàg ecs`j` b ‗ bck éma löyöa a`lufcbcfge. Lu burueb` cfcatrga f`k s`bcoc z yúkökbcbgr, vc pmt`ksgycf s`bcoc z gfc

bcĝgŝgr .

Xfà`f`r r`sİkbàg tmpf`k f`kİlufeà gégk sİkİr amŝufuku s`bcoc lgrpfà` yözcygkbc uyiufèà yctcrfg.


A`p`sgt`ks

X`r`fcf Xfà` A`p`sgtúrökök A`p`sgt`ksİ

Xfà` yözcyg 5 _

auff`k`rà pfà`f`r r`sİ vmft`n lufuk`lgfgr >

smkr` auff`k`rà>


A`p`sgt`ks

A`p`sgtúrbc Bcpmf`k`k Ckcrng

A`p`sgtúr gécrgsgkbcag cfcatrga f`kİk ckcrng ymĝukfuĝukuk dògescf gktcir`fgkg`f`rà a`p`sgtúrbc bcpmf`k`k ckcrngyg luf`lgfgrgz >

O Z 8<

_

Ckcrngyg öé j`rafİ ŝcagfbc y`z`lgfgrgz>

y`b`


A`p`sgt`ks

Úrkca > Amàsgycf ĸfctge D`ttİ

bgĝcr ycrfcrbc gsc C 5 8, gé vc bİŝ gfctackfcrbccŝgt egat`rb` zİt yöafcr v`r .

B`d` úkoc Iùss W`s sİkİ auff`k`rà lufbuĝueuz>

_

C

0

ĸfctackfcr r`sİkbàg pmt`ksgycf j`ra>

…vc gé gfctackbcag lgrge uzukfua gégk yöa egat`rİ>

_mkuét`>

z —bc lgrge uzukfua `f


A`p`sgt`ks

Úrkca > Aörcscf A`p`sgtúr W`rİé`pf`rİ ` vc l mf`k gag cŝecraczfg aörc böŝökök. Cŝgtegat`rb` jà`t zİt P yöafcrg gé vc bİŝ aörc yözcygkbc v`r .

`

l

PC

-P Iùss W s`sİ lgzc cfcatrga f`kİk s`bcoc aörcfcr r`sİlúficbc mfò`ĝİkİ kf`tİymr>

ĸé vc bİŝ aörc r`sİkbàg pmt`ksgycf j`ra>

Zc a`p`sgtc>ś`yct (y`fİtİfeİŝ aörc)



<


A`p`sgt`ks

Bgcfcatrga ĸfc A`pf`keİŝ W`fİtİfeİŝ Aörc

`

r 0

C0 C<

P

W`rİé`pİ ` mf`k lgr gfctack aörcbc P yöaö v`r . ĸfctackaörcyg y`rİé`pİ r 0 - ` mf`k vc cfcatrgascf icégrickfgĝg 0 mf`k lgr bgcfcatrga écvrcfcegŝtgr. Dcr gag lúficbc

cfcatrga `f`k Iùss W`s`sİ gfc>

_mksuzb` sİjİr rcj`rksİ auff`k`rà gfctack aörcbcag pmt`ksgycf>

5 Z 8

vc a`p`sgt`ksİ>


A`p`sgt`ks

ĸag A`te`kfİ Bgcfcatrga A`p`sgtúr

C <

C 0 BK 0

BK <

Lu burueb`, sİkİr amŝufuku auff`kİrsà gag bgcfcatrga r`sİkb` B‗kgk kmre`f lgfcŝckgsörcafg mfò`ĝİkb`k (bgcfcatrga r`yözcybc yözcyscf yöa mfe`bİĝİkİ v`rs`y`rà)>

vc

ĸag gfctack pfà` r`sİkbàg pmt`ksgycf j`ra>

sİkİr amŝufu auff`k`rà>

@ft gfctack pfà`b` yözcyscf yöaymĝukfuĝu>

_mkuét` a`p`sgt`ks>


A`p`sgt`ks

Xmgssmk‗s vc F`pfòc Bckafcefcrgkgk Rörctgfecsg ś`yct sİkİrf`rb` pmt`ksgycf bcĝcrfcrg lgfgkgymrs` lu bckafcefcr auff`k`ràdcrd`kig lgr lúficbc pmt`ksgycf dcs`pf`k`lgfgr .

E`xwcff‗gk lgrgkog bckafceg gfc l`ŝf`rsà>

lur`b`

vc

Auff`k`rà

_mkuét`>


A`p`sgt`ks

B`d` úkoc bgvcrn`ksİ t`kİefèİŝtİa>

…vc ir`by`ktİ>

Lcr`lcr uyiuf`rsà>

aİs`ftİf`rà mf`rà y`zİfİr vc F`pf`sy`k mpcr`tmr ö mf`rà `bf`kbİrİfİr.

Xmgssmk‗s vc F`pfòc Bckafcefcrgkgk Rörctgfecsg

<


A`p`sgt`ks

Xmgssmk Zc F`pfòc Bckafcefcrg

Lgfbgĝgegz>

Bgĝcr lgr gj`bcyfc>

Xmgssmk bckafceg mf`rà a`rtczyck amrbgk`tf`rb` bf`kbİrİfİr.

ś`yct dògecf yöa ymĝukfuĝu sİjİr gsc , bckafcegk s`ĝ t`r`jİ sİjİr mfur, vc>

F`pfòc bckafceg


A`p`sgt`ks

F`pf`sy`k Mpcr`túrö



?


A`p`sgt`ks

_mkr` ŝ`ĝİbàg ŝè`f`rİ tàgp cbcrca a`p`sgtcyg lufuruz

0. Z lgfgkgymr gsc , ‗yg auff`k`rà C‗yg luf.

<. ‗yg auff`k`rà B‗yg luf.

?. B‗yg a`p`sgtúrök dcr gag pfà`sİkb` gkocfc, .

2. D`tİrf`,

3. P ‗yö yözcy gktcir`fg gfc a`p`sgtúr özcrgkbc luf ,

:. A`p sgtcyg gfc luf

B C

Z C

_ s

P b_ P

O Z

_ K B

_ K K B B B `

A`p`sgtc Xrmlfcefcrg

ś`yct sİkİr amŝuff`rİ lgfgkgymrs` Xmgssmk ( ) y`b` F`pfòc

( ) bckafcegkg auff`k`rà pmt`ksgycfg luf`lgfgrgz.

8v

8v


A`p`sgt`ks

X`r`fcf Xfà` ‟ ĸécrbcag Xmksgycf @f`k

F`pfòc bckafcegkbck>

_İkİr amŝufu 0 uyiuf`>

8 5 @(8) + L

_İkİr amŝufu < uyiuf`>

Z 8 5 @b

_mkuét`>

b

8

x

Z 5 Z 8

Z 5 8

_İkİr amŝuff`rİ>

0. x 5 8‗b` Z 5 8

<. x 5 b ‗bc Z 5 Z 8

Cŝ pmt`ksgycf yözcyfcr

Lu jmkasgymk a`p`sgtúrbcag cŝ pmt`ksgycf yözcyfcr mf`ràégzgfegŝtgr. Lgrlgrgkc ameŝu cŝ pmt`ksgycf yözcyfcrbc s`lgtpmt`ksgycf j`raİ v`rbİr.


A`p`sgt`ks

Cfcatrga @f`k, Wöa Zc A`p`sgt`ks Dcs`pfè`sİ

L`ŝf`rack>

_mkr`>

auff`k`rà>

b

8

x

Z 5 Z 8

Z 5 8

Cŝ pmt`ksgycf yözcyfcr

C

+ + + + + + + + + + + + + +

- - - - -- - - - - - - - -

Wözcy @f`kİ 5 _

k

@ft pfà` yözcygkbc ( x 5 8)> vc k 5 x

_mkr`> auff`k`rà

@ft t`là`bàg yöa>

vc a`p`sgt`ks


A`p`sgt`ks

Z 8

C

F

Z 5 8

Amàsgycf ĸfctge D`ttİ

_İkİr amŝuff`rİ>. l‗bc Z 5 8

<. `‗b` Z 5 Z 8

Amàs gécrgsgkbc Z s`bcoc y`rİé`p gfc bcĝgŝgr , lu

burueb` F`pfòc bckafceg>

( 8‗b` icécrfg bcĝgf)

@eòİeİz pmt`ksgycf jmkasgymku (` 6 l) lúficsgkbc lufeà>

Lgr acrc gktcir`f fİrsà>

.. gagkogsgkbc>


A`p`sgt`ks

Amàsgycf ĸfctge D`ttİ

Lgfbgĝgegz>

_İkİr amŝufu 0 uyiuf`rsà>

_İkİr amŝufu < uyiuf`rsà>

_mkuéf`rİ lgrfcŝtgrgrsca>

Z 8

C

F

Z 5 8

_İkİr amŝuff`rİ>. l‗bc Z 5 8

<. `‗b` Z 5 Z 8


A`p`sgt`ks

Amàsgycf ĸfctge D`ttİ A`p`sgt`ksİ

Z 8

C

F

Z 5 8

ĸfctackfcr r`sİkbàg pmt`ksgycf `f`kİ lufeuŝtua>

_mkr`>

ĸé gfctackbcag yözcyscf yöa ymĝukfuĝu>

ĸé gfctackbcag tmpfè yöa>…vc smkuét` a`p`sgt`ks>



2


A`p`sgt`ks

Cŝecraczfg Aörcscf Icmectrg

`

l

Z 8 C

Z 5 8

_İkİr amŝuff`rİ>0. r 5 l‗bc Z 5 8

<. r 5 `‗b` Z 5 Z 8

Z s`bcoc y`rİé`p gfc bcĝgŝcocĝgkbck F`pfòc bckafceg>

y`b`>

gktcir`fgkg fİrsà> ..vc lgr b`d`>

_İkİr amŝufu 0>

_İkİr amŝufu <>

_mkuét`>


A`p`sgt`ks

Cŝecraczfg Aörcscf A`p`sgtúr

`

l

Z 8 C

Z 5 8

Lgfbgĝgegz> (` 6 r 6 l)

ĸfctackfcr r`sİkbàg cfcatrga f`k>

ĸé gfctackbcag yöa ymĝukfuĝu>

ĸé gfctackbcag tmpfè yöa>

A`p`sgt`ks>


A`p`sgt`ks

@éİfİ Xfà` Icmectrgsg _gfgkbgrga ammrbgk`tf`r auff`k`rà pmt`ksgycfgk s`bcoc gfc

bcĝgŝtgĝgkg v`rs`y`fİe.

x

_İkİr amŝuff`rİ>. 8‗b` Z 5 8

<. ‗ b` Z 5Z 8

Lu burueb` F`pfòc bckafceg>

ĸktcir`f fİrsà>

…vc lgr b`d`>

Lgrgkog sİkİr amŝufu>

ĸagkog sİkİr amŝufu>

_mkuét`> _mkr`>


A`p`sgt`ks



A`p`sgt`ks

Úrkca > Jgk`f sİk`v smrusu <884


A`p`sgt`ks



3


A`p`sgt`ks



0


A`fİoİ E`kyctga @f`k

E`kyctga @f`kf`r

• E`kyctga @f`k śgbbctg D (@/e)

(Cfcatrga f`k ŝgbbctg gfc lckzcr, C (Z/e)

• 04<8 ‟ Mcrstcb ‟ Rcf bcag àİe e`kyctga `f`k örctgymr



Mcrstcb‗İk Bckcyg

ĸfctack tcfbck icéck aİe e`kyctga

`f`kf`r örctgymr vc lu `f`kf`r

gfctackgk ctr`jİkb` búkiö mfuŝturuymr.



Lgmt-_`v`rt W`s`sİ

Lgmt-_`v`rt W`s`sİ bgjcr`ksgycf uzukfuatàgkmat`s`f lgr aİe cfce`kİkb`k a`ykàf`k`ke`kyctga `f`k D‗yİ lcfgrfcr.

Bgaa`t cbgfgrsc ecs`jc gfc tcrs gfgŝagv`r vc vcatúrcf é`rpİeb`k bmf`yİe`kyctga f`kİk yúkö s`ĝ cf aur`fİgfc s`yj`y` bmĝrubur.

Omufmel‗s W`s`sİ gfc lczcrfgafcr v`r.Kmat`s`f lgr bP0 yöaö amkue 0‗bck amkue<‗yc bmĝru mfuŝturbuĝu cfcatrga f`k>

D‗kİk lgrgeg Q@/eU



Búkiöscf Lgr @aİeb`k A`ykàf`k`k E`kyctga @f`k

Bgjcr`ksgycf GbF àİe cfce`kİkb`ka`ykàf`k`k X kmat`sİkbàge`kyctga `f`k>

Rmpfè f`kİ lufeà gégk töe bgjcr`ksgycf cfce`kf`rİk a`taİsİkİtmpfè`fİyİz. Bgĝcr lgr gj`bc gfc gktcir`fgkg fe`fİyİz.



ĸag vc Öé Lmyutfu @aİef`r

Wözcybc böziök lgr A Q@/eU yözcy àİeymĝukfuĝu v`r gsc, l ickgŝfgĝgkbcag aİe>

Lgmt-_`v`rt W`s`sİkbàg bgjcr`ksgycf aİecfce`kf`rİ ycrgkc ŝ`ĝİbàg gfgŝagyg y`z`rsà>

Lgr t`là` aİeİkb`k a`ykàf`k`k e`kyctga`f`k gag lmyutfu Lgmt-_`v`rt W`s sİ gfc lufuk`lgfgr >

@ykİ ŝcagfbc dògescf lgr àİeb`k a`ykàf`k`ke`kyctga `f`k öé lmyutfu Lgmt-_`v`rt W`s`sİ gfc

lufuk`lgfgr>



_mksuz Szukfuatàg Böz Lgr Jgfè`k ĸégk E`kyctga @f`k

Lu úrkcatc, z-casckgkbc ycrfcŝtgrgfegŝ smksuz lgr aİe jgfè`kİkb`k a`ykàf`ke`kyctfga `f`k ŝgbbctgkg y -casckgkbc (y`b` xy-bözfcegkbc) gkocfcycocĝgz

ścagfbck>

vc

_mkuét`>



<



Cfgegzbc mf`k>

Zcatúrcf é`rpİeİ y`pİp jgfè`k lmyuko`gktcir`fgkg fİrsà>

_mksuz Szukfuatàg Böz Lgr Jgfè`k ĸégk E`kyctga @f`k



Eìkctgo Jgcfb Gktcksgty jmr gkjgkgtcfy fmki str`gt jgfèckt

Cfgegzbc>

_mkuétt`>

@aİe s`yj`y bmĝrubur . E`kyctga `f`kégzigfcrg cŝecraczfg mfup casckbckuzàf`ŝtİaé` `z`fİr.



_mkfu Lgr @aİe Cfce`kİkb`k A`ykàf`k`k @f`k

Lu burueb` `f`k xy-bözfcegkbc amkue <‗bc lufuk`lgfgr . Lgmt-_`v`rt gktcir`fgtcf lmyuko` fİkİr >

Lgr a`é gŝfce y`ptİat`k smkr` (Xrmlfce 9.4‗clàİkİz) e`kyctga f`kİ lufuruz>



Úrkca> Écelcr jgfè`kbàg aİe

<2

\ Gb

\

F `D

Gb G`b F `

< <

,

z

\ z

` d

` d \ ` d

\ \

\ ` `

` ` `

<z

?< < <

8 2

G`b d `

d `

` ` `D



<< <

zz? ?

< < < << <8

.

2 <

G` G`b

d d

`

D `

@t d 5 8,z<

G

`

D `

Úrkca> Écelcr jgfè`kbàg àİe (bcvèİ)





?



Búkiöscf @epcrc W`s`sİ

_gectrg úzcffgĝgkgk auff`kİf`lgfecsg gégk scégfck ymf úyfc scégfecfgag D y` ymf

lmyuko` s`lgt mfe`fİ (tcĝctscf) y`b` sİjİr mfe`fİ (ymf` bga).

Búkiöscf @epcrc W s`sİ D‗kİk dcrd`kig lgr a`p`fİ ymf özcrgkbck égzigscfgktcir`fgkgk gégkbc l`rİkbİrbİĝİ aİe` cŝgt mfbuĝuku gj`bc cbcr.

D‗kİk a`p`fİ ` vc l ymff`rİ özcrgkbck gtcir`fg tmpfè aİe G‗yİ vcrgrack, o ymfuözcrgkbck fİk`k gktcir`f gsc ymfuk a`ps`bİĝİ a`b`r aİe mr`kİkİ vcrgr.



@epcrc W s`sİkİk _mksuz Lgr Jgfè`k` Syiuf`kİŝİ

D‗kİk gktcir`fgkg y`rİé`pİk` s`dgp vc aİeİgégkbc l`rİkbİr`k lgr ymf özcrgkbck fİrsà>

B`d` úkocbc lufubuĝueuz iglg>

D‗kİk b`grcscf mfbuĝuku vc jgfè`kb`kdcrd`kig lgr y`rİé`p uzàfİĝİkb` s`lgt

mfbuĝuku lgfgymruz.



Úrkca> _gfgkbgr‗bcag àİe

a`ps G b D F

_gfgkbgrgk gécrgsgkbc vc

bİŝ`rİsİkb` D‗yİ lufeàgégk gag ymf auff`ke`fİyİz.



Úrkca> _gfgkbgr‗bcag aİe (bcvèİ)

_gfgkbgrg lgréma jgfè`kb`k mfuŝeuŝ v`rs`y`fİe. π

lgfcŝckfcrg sgectrgbck bmf`yİ lgrlgrgkg iútörör.



Úrkca> _gfgkbgr‗bcag aİe (bcvèİ)



Úrkca> Amàsgycf a`lfm

<

< <

< <

( )<

( )<

( )<

8 ( )

G D `

`

G D ` l

G o D l o

o l

D o



2



Lgr Wözcyscf @aİeb`k A`ykàf`k`k E`kyctga @f`k

_gectrgbck bmf`yİ y-yúkökbcag böziök lgr bözfcescf aİeb`k x -yúkökbc lgr D

`f`kİ lcafcecatcygz. B`grcscf @epcrc y`s`sİkİ 0-0‗-<‗-<-< ymfuk` uyiuf`rsà>

y`b`

Bgĝcr lgr gj`bc gfc yözcy aİe ymĝukfuĝukb`k mfuŝ`k e`kyctga f`k aİe yözcyglmyuko` sörcafg bcĝgfbgr.



ś`yct yua`rİbàg 0-0‗ ymfu ?-?‗ amkueuk` a`ybİrİfİrs` búkiökök gécrgsgkbcagàİe bcĝgŝecycocatgr.

Lur`b`k ŝu smkuo` v`r`lgfgrgz.

_gectrga úzcffga lgzc e`kyctga f`kİkyözcy özcrgkbc vc ftİkb` ickfga mf`rà`ykİ mfbuĝu smkuouku vcrgr. Wúkfcrbúkiöbck bmf`yİ zİtbİr.

Lu éİa`rİef` `f`kİk yözcy özcrgkbc vc ftİkb` s`lgt mfbuĝu smkuou éİa`r.




ścagfbc bc iústcrgfbgĝg iglg e`kyctga f`kf`r ickfga mf`rà cŝgt jà`t zİtyúkbcbgrfcr.

Ickcf lgr gj`bc gfc f`kİ dcrd`kig lgrlúficbc (yua`rİ y`b` ŝ`ĝİ) jmreöfgzccbcrsca>

lur`b` `K yözcy aİeİk` kmre`f mf`klgrge vcatúrbör vc f`kİ dcs`pf`yò`ĝİeİzamkue` yúkcfgatgr.




ĸag Wözcyscf @aİeb`k A`ykàf`k`k E`kyctga @f`k

@ŝ`ĝİb` p`r`fcf pfà` gfctge d`ttİkbàg iglg gag cŝgt egat`rb` jà`t zİt yúkbc pfà`àİef`rİ v`r . ś`yct pfà`f`r r`sİ ecs`jc pfà` yözcygkbck éma aöéöa gsc e`kyctga`f`k pfà`f`r r`sİkb` ecvout mfup bİŝ`rİb` gsc kcrcbcysc sİjİrbİr (pfà`f`r smksuzmfurs` acsgk sİjİrbİr).

A 0 5 -A y y

A < 5 A y y

D x0 (z 6 -b/< )

D x0

(-b /< 6 z 6 b/< )

D x< (-b /< 6 z 6 b/< )

D x< (z 6 -b/< )

D x0 (z ; b/< )

D x< (z ; b/< ) Lu `f`kf`r pfà`f`r smksuzlöyöaföatc mfurs` lgrlgrgkg iútörör.

Lu `f`kf`r pfà`f`r smksuzlöyöaföatc mfurs` lgrlgrgkg iútörör.

Lu f`kf`r ykİ yúkbc tmpf`kİr>

D 5 A x K (-b/< 6 z 6 b/< )

lur`b` A y` A0 y`b` A< mf`lgfgr.



Búkiöscf @aİeİk @f`kİ

B`d` úkoc Lgmt-_`v`rt W`s sİkİ auff`k`rà b`grcscf lgr àİe cfce`kİkb`kmfuŝ`k e`kyctga f`kİ z -casckgkbc lgr kmat`b` dcs`pfèİŝtİa>

Lu smkuou auff`k`rà z-casckg lmyuko``ykİ lmyuttàg aİe búkiöfcrgkgk öst östcbgzgfecsg gfc mfuŝ`k s`re`f lmlgkbcag`f`kİ dcs`pf`y`fİe.



_`re`f Lmlgk ĸécrgsgkbcag Casckcf @f`k Rca s`rİefİa f`kİk a`taİsİkİ bgjcr`ksgycf a`taİ mf`rà bcĝcrfckbgrgp K a`b`r émasİaİ s`re`fİk mfuŝturbuĝu f`k gégk auff`k`fİe. _`re`fb` G àİeİ v`rbİr . _`re`fİkickgŝfgĝg b gsc s`re`f ymĝukfuĝu K/b mfur.

śgebg búkiöbcag bgjcr`ksgycf lgr uzukfua bz ‗bcagàİe>

Úyfcag D gégk lgr úkocag tca s`rİeb`k mfuŝ`ksmkué>

śuk` búköŝör >

lur`b` z tcfgk ecraczgkbck dcs`pf`kİr .

Luku bgjcr`ksgycf ‖búkiöscf aİe― a`luf cbcfge.



3



z-casckgkbcag tmpfè `f`k z 5 8‗b` töe s`rİef`rİk f`k a`taİf`rİ tmpf`k`rà,bgĝcr lgr gj`bc gfc gktcir`fg fİk`rà lufuk`lgfgr.

_`re`f Lmlgk ĸécrgsgkbcag Casckcf @f`k



Szuk Lgr Lmlgk _`re`fİ gégk Wàf`ŝİe

_`re`f lmlgk gécrgsgkbcag casck lmyuko` (z 5 8)‗bàg e`kyctga f`k>

ś`yct lmlgk s`re`fİ éma uzuk mfurs` ,smkué l`sgtfcŝcrca>

( )



Lgr L`ŝa` Wmrue> _örcafg Wözcy @aİeİ Lgr úkocag úrkcatc s`re`f lmlgk lgr bgjcr`ksgycf uzukfuat`, bz , lgrlgrgkc éma sİaİ s`rİfİbúkiöfcrbck mfuŝtuĝuku v`rs`yeİŝtİa. Lúyfc lgr embcfg `sfİkb` sörcafg lgr yözcyàİe ymĝukfuĝuyf` A 5 A` ` @/e embcffcyclgfgrgz.

Lukb`k bmf`yİ>

Bgĝcr lgr gj`bc gfc, aİe z -casckgkbc búköymr vcsgfgkbgrgk uzukfuĝu y`rİé`pİkb`k éma b`d` löyöagsc casckcf e`kyctga f`k yözcy aİeymĝukfuĝuk` cŝgttgr.



@epcrc W s`sİkİk Aöéöa A`p`fİ Lgr Búkiöyc Syiuf`kİŝİ

ścagfbcag iglg e`kyctga f`k, D, vcrgfck kmat`b` lgfgkgymr mfsuk. E`kyctga f`kİ0-<-?-2 ymfu özcrgkbc yàf`ŝİef` luf`lgfgrgz.

Lu úrkcatcag eòİeİz @epcr W`s`sİkİ vcrgfck ymf özcrgkbc uyiuf`y`rà kmat`s`fd`fgkg lufeàtİr .



D‗kİk 0-< Wmfu Özcrgkbcag Wàf`ŝİeİ

0-< ymfu özcrgkbc ŝúyfc y`z`lgfgrgz>

lur`b`

Lu kcbckfc>



y -Wúkökbcag Wmf X`ré`f`rİkİk A`taİf`rİ

Úk ymfuk a`taİsİ>

@ra` ymfuk a`taİsİ>

Jmreöffcrbcag gŝ`rctfcr ŝcagfbcag yúkfcrc iúrc fİkeİŝtİr .



:



_`ĝ ymfuk a`taİsİ>

_mf ymfuk a`taİsİ>

Lgr smkràg ŝè`b` töe ymff`rİk a`taİf`rİkİ tmpfè`fİyİz.

x -Wúkökbcag Wmf X`ré`f`rİkİk A`taİf`rİ



Kct A`p`fİ Wmf ĸktcir`fg ĸktcir`fgk tèèİ töe ymf a`taİf`rİkİk tmpfèİbİr >

Lgr úkocag cfbc cttgĝgegz smkuéf`rİ auff`k`rà>



@aİe Wmĝukfuĝu ĸfc ĸfgŝagsg

@epcr W s`sİ D‗kİk a`p`fİ ymf gktcir`fg gégkbc l`rİkbİrbİĝİ aİe` cŝgttgr bgymr. Lgzyàf`ŝİef` aİe ymĝukfuĝuku ecraczbc lufup yözcy f`kİ gfc é`rptİa.

Búkiökök f`kİk` lúfcrsca>

Lu yàf`ŝİe yözcy f`kİk fgegtgburueukb` acsgk smkuo` igbcr>



Bgĝcr Búkiö Wúkfcrg

Lgr úkocag yàf`ŝİeİeİzİ bgĝcr mrtmimk`f búkiö yúkfcrgkcbc uyiuf`y`lgfgrgz,smkuét`>

yz-bözfcegkbcag búkiö>

Lu aİe ymĝukfuĝukuk öé lgfcŝckgkgbc vcrgr .

xz-bözfcegkbcag búkiö>

xy-bözfcegkbcag búkiö>



Lgr Zcatúr @f`kİkİk Búkcfg-\mt`symkcfg (Ourf)

A`rtczyck ammrbgk`tf`rb` y`pİf`k lgr úkocag fİŝtİre` gfc D‗kİk rmt`symkuku (ourf)lufeuŝtua. Ickcffcŝtgrgrsca, lgr vcatúr f`kİkİk rmt`symku mrngk`f `f`k` kmre`fyúkbc l`ŝa` lgr vcatúr f`kİbİr.

ĸktcir`f búkiö bözfcegkc kmre`f K yúkökbcag rmt`symk lgfcŝckg >

K‗kgk yúkö s`ĝ cf aur`fİ gfc lufukur > _`ĝ cfgegzgk p`reàf`rİ gktcir`fyúkökbcyack l`ŝ p`re`ĝİeİz kmre`f yúkbcag rmt`symk yúkökö iústcrgr.

Lur`b` ∊_K gktcir`f bözfcegkbcag búkiökök f`kİbİr.



A`rtczyck Ammrbgk`tf`rb` \mt`symkcf

B`d` úkocag `fİŝtİreèİzbàg D‗kİk rmt`symkcf smkuéf`rİkİ lgrfcŝtgrgrsca>

Luku czlcrfcecatcksc bctcregk`k ŝcafgkbc b`d` amf`y lufuruz>

@sfİkb` lu gfc D vcatúrökök vcatúrcf é`rpİeİbİr >



9



Bgĝcr Ammrbgk`t _gstcefcrgkbc \mt`symkcf (Búkcf)



\mt`symkcfgk O`kf`kbİrİfe`sİ

ścagfbcag iglg su aİktİsİ gécrgsgkc lgr a`k`tfİ é`ra ycrfcŝtgrcfge. É`ra casckgcar`k` bmĝru mfsuk vc su dİzİ bcrgkfcŝtgaéc z`fİymr mfsuk.

É`ra s``t yúkökbc búkcocatgr vc s`ĝ cf aur`fİk` iúrc car`k` bmĝru yúkömfòàtİr.

É`raİ bgĝcr mrtmimk`f yúkfcrbc bc ycrfcŝtgrcrca rmt`symkuk töe lgfcŝckfcrgkgúféclgfgrgz. Bgaa`t cbcrsckgz rmt`symk dce f`k (dİz) dcebc bcĝgŝge yúkökc(bcrgkfga) bga yúkbcbgr.



Lgr L`ŝa` E`xwcff Bckafceg

B`d` úkoc lufbuĝueuz>

Lu sfİkb` st`tga f`kf`r gégk E`xwcff bckafcefcrgkbck lgrgsgbgr>

Bgĝcr lgr gj`bc gfc @epcr y`s`sİkİk kmat`s`f d`fgbgr .



Lgr L`ŝa` E`xwcff Bckafceg B`d`

B`d` úkoc st`tga cfcatrga `f`kf`r gégk lgfgymruz ag>

Bgĝcr d`fg gfc>

@f`kİk amrukue ŝ`rtİkİ d`tİrf`y fİe, búkiöscf gktcir`fg dcr z e`k sİjİrbİr .

Lu kcbckfc lgr f`k gégk amrukue a`kuku v`r gsc m f`kİk t`kİefİ mfbuĝu töekmat`f`rb` búkcfg (rmt`symkcfg) sİjİrbİr.

(st`tga cfcatrga `f`kf`r gégk icécrfg)



Löyöa Wözcy X`ré`f`rİk` Búkcf Syiuf`ke`sİ

_ yözcyg aöéöa ∊_ yözcyfcrc p`ré`f`keİŝtİr. Wözcy cfce`kİk` kmre`f mf`kbúkcf lgfcŝckgkg búkcfgk t`kİeİkb`k ŝúyfc y`z`lgfgrgz>

y`b`>

@ykİ e`ktİĝİ yözcygk töe cfce`kf`rİk` uyiuf`yİp tmpf`y`fİe.



Röe Wözcyfcrgk A`taİf`rİkİ Rmpf`y`fİe

Röe yözcy cfce`kf`rİkİk búkcf a`taİf`rİkİ tmpf`y`fİe. @r`bàg mrtà égzigfcrgka`taİf`rİ lgrlgrgkg iútörcocĝgkbck s`bcoc löyöa yözcygk écvrcscf a`taİf`rİ a`fİr.

B`d` úkocag smkuéf`rİauff`k`rà ŝúyfc y`z`lgfgrgz>



4



_tmacs Rcmrceg

B`d` úkc cftc cttgĝgegz smkuéf`r` fgegt ∊_↜8 uyiuf`rsà>

Fgegt fİkbİĝİkb` lu t`r`jD‗kİk _ yözcygkgk bİŝ écvrc ĸktcir`fgkc búköŝör.

Fgegt fİkbİĝİkb` lu t`r`j _ yözcyg özcrgkbc D‗kİk búkcfgkgk gktcir`fgkcbúköŝör .

Lúyfcoc _tmacs Rcmrcegkg cfbc cbcrgz>

Lu sfİkb` bgvcrn`ks tcmrcegkbcagkc lckzcr, jà`t ŝgebg égzigscf gktcir`fgyözcy gktcir`fgkc écvgrck úkcefg lgr cŝgtfgatgr.



Búkiöscf @epcr W`s`sİkİk ĸktcir`f D`fgkgk_tmacs Rcmrceg Auff`k`rà Lufuke`sİ

_t`tga f`kf`r gégk @epcrc y`s`sİkİk kmat`s`f d`fgyfc l`ŝf`y`fİe>

Dcr gag t`r`jİk _ yözcyg özcrgkbck gktcir`fgkg f`fİe>

Lur`b` gktcir`f ymfuku s`ĝ-cf aur`fİk` iúrcuyiufuymruz.

Mrt`bàg gj`bc _ yözcygkgk a`ps`bİĝİ kct aİeİ gj`bccbcr. Bgĝcr lgr gj`bc gfc @epcrc W`s`sİkİk gktcir`f d`fg>



Úrkca 9.?> _tmacs tcmrcegkgk dcr gag t`r`jİkİ dcs`pf`yİk

: sgk 04 sgk omsr

r r

D ` `



Úrkca> Jgk`f smrusu <889-<884Iöz



E`kyctga @aİ vc @aİ Wmĝukfuĝu

Lur`b` cfcatrga aİ ymĝukfuĝu scrlcst uz`yb`>

Cfcatrga aİsİkİk kc mfbuĝuku lgfgymruz>

O

@ykİ ŝcagfbc e`kyctga àİyİ ŝúyfc t`kİef`rİz>

Yl (Yclcr)

lur`b` e`kyctga aİ ymĝukfuĝu (y`b` e`kyctga ckböasgymk) scrlcst uz`yb`>

vc lur`b` scrlcst uz`yİk e`kyctga icégrickfgĝg>

vc scrlcst uz`yİk cfcatrgascf icégrickfgĝg>

Lu @epcr W`s`sİ gfc gfgŝagfg t`kİefİ lgr kgocfgatgr.



L‗kgk Úkcefg Lgr Úzcffgĝg

ś`yct cfcatrgascf aİ a`p`fİ lgr yözcyc uyiuf`kİrs` Iùss W`s`sİkİ cfbc cbcrgz >

@ykİ jmreöf`symku e`kyctga àİ ymĝukfuĝuk` uyiuf`rsà>

Lu sfİkb` e`kyctga lgr yöa a`yk`ĝİkİk mfe`bİĝİkİk iústcricsgbgr. E`kyctga`f`kf`r búkiöscf úzcffgĝg sclcp mfeàt`bİr.



7



E`kyctga @f`k Égzigfcrg

E`kyctga autupf`rgzmfc cbgfcegymr



Lgr L`ŝa` E`xwcff Bckafceg

Bgvcrn`ks Rcmrcegkg L‗kgk a`p`fİ yözcy gktcir`fgkc uyiuf`rsà>

_mkuouk sİjİr mfe`sİ koà gktcir`ktİk sİjİr mfe`sİyf` eöeaökbör>

Lu sfİkb` Iùss W`s`sİkİk e`kyctga f`k gégk kmat`s`f uyiufè`sİbİr .



_t`tga @f`kf`r ĸégk E`xwcff Bckafcefcrg śgebg st`tga f`kf`r gégk töe E`xwcff Bckafcefcrgkg törcttga. Kmat`s`f d`fbc>

Cfcatrga f`kf`r gégk Iùss W s`sİ

_t`tga cfcatrga f`kİk amrukue úzcffgĝg

Búkiöscf @epcrc W s`sİ

E`kyctga `f`kf`r gégk Iùss W`s`sİ

Lur`b` lökyc bckafcefcrg(scrlcst uz`yb`)>

Wua rİbàg bckafcefcr zè`k` iúrcbcĝgŝck f`kf`r gégk bcĝgŝcocatgr. Lukf`rcfcatrmst`tgatc icécrfgbgr.



E`xwcff Bckafcefcrgkgk ĸktcir`f D`fg Lgr úkocag bckafcefcrc @epcrc vc Bgvcrn`ks Rcmrcefcrg uyiuf`k`rà st`tga`f`kf`rb` E`xwcff bckafcefcrgkgk gktcir`f d`fg lufukur>

Cfcatrga f`kf`r gégk Iùss W`s`sİ

_t`tga cfcatrga f`kİk amrukue úzcffgĝg

Búkiöscf @epcrc W s`sİ

E`kyctga `f`kf`r gégk Iùss W`s`sİ



Úrkca> Amàsgycf Lgr D`t ĸécrgsgkbcag E`kyctga @f`k

ścagfbcag iglg b uzukfuĝukbàg amàsgycf gécrgsgkbcag e`kyctga f`k>

vc>

E`kyctga àİ L‗kgk ŝcagfbcag iglg bözfceözcrgkbc ` vc l y`rİé`pf`rİ r`sİkb` vc buzukfuĝukb` gktcir`fg fİk`rà lufukur >

_mkué>

@sfİkb` amàsgycf d`t e`kyctga àİyİ gfctackfcr `r`sİkb` bcpmf`r. Lu ckböat`ksgégk úkcefg lgr úzcffgatgr.



_a`fcr E`kyctga Xmt`ksgycf_a`fcr pmt`ksgycf gfc cfcatrga f`k `r`sİkbàg l`ĝİ lgfgymruz>

Lur`b` eòİeİz sa`fcr e`kyctga pmt`ksgycf gégk lckzcr lgr gfgŝagkgksmriuf`ke`sİbİr >

Lúyfc lgr gfgŝagyg a`luf cbcrsca lu E`xwcff bckafcefcrg gégkbc icécrfg mfe`fİ>

Jà`t vcatúr úzcffgafcrgkbck lgfgymruz ag dcrd`kig lgr jmkasgymkuk ir`bycktgkgkbúkcfg sİjİrbİr. Lu kcbckfc sa`fcr e`kyctga pmt`ksgycf aİe ymĝukfuĝukuk sİjİrmfbuĝu ycrfcr gégk icécrfgbgr (scrlcst uz`y).

Lu kcbckfc sa`fcr e`kyctga pmt`ksgycfg lgr ŝ`rtf` t`kİef`rİz>



08



_a`fcr E`kyctga Xmt`ksgycf ĸégk Bgĝcr Amŝuff`r

E`kyctga f`k gfc gfigfg bgĝcr E`xwcff bckafcefcrg gégkbc icécrfg mfe`sİ f`zİe>

_crlcst uz`yb`

Lu kcbckfc>

vc lúyfcoc aİe ymĝukfuĝukuk sİjİr mfbuĝu ycrfcrbc F`pfòc bckafcefcrgkgbc s`ĝfèİŝ mfuymr >



Úrkca> Amàsgycf ĸfctge D`ttİ

ĸé gfctackbck car`k bİŝİk` bmĝru lgr àİe v`r gsc, gfctackfcr r`sİ e`kyctga f`k>

Jmreöfc uyiuf`rsà>

Éúzecegz icrcack>

smkuét`>

Lur`b` gktcir`f s`lgtgkg sİjİr a`luf c ttga



_a`fcr Xmt`ksgycfbcag Lcfgrsgzfgafcr

Lufbuĝueuz sa`fcr pmt`ksgycf>

lur`b` pmt`ksgycf ‗b` sİjİrbİr.

X kmat`sİkb` ( ) pmt`ksgycf

Jà`t ŝ`yct `rt`rà mfurs` ykİ amkue` icfecegzc r`ĝeck bcĝcrg ‟ G mfur. Lu burueb` lgrgagfga mfur.

Ickcfbc X kmta`sİkbàg pmt`ksgycf éma bcĝcrfg mfup xy-bözfcegkbc dcr lgr turb`yckg lgr bcĝcr mfuŝur >



Lcfgrsgzfgĝgk Igbcrgfecsg

L`rgycr>

Lcfgrsgzfgĝg igbcreca gégk ‗kgk dcrd`kig lgr bcĝcrgkbc e`tce`tgascf lgr l`rgycrycrfcŝtgrcfge. @éİs`f lúfic dgélgrz e`k lu l`rgycrg icécecsgk. Lu burueb` lgzl`rgycrg ‗bc ycrfcŝtgrcfge.

Lu burueb` X kmat`sİkbàg pmt`ksgycftca bcĝcrfg mfur >

_a`fcr pmt`ksgycf gagfgĝc sclcp mfbuĝugégk tcrogd ctegymruz. Lu kcbckfcvcatúrcf lgr e`kyctga pmt`ksgycfgkecvoubgyctgkg r`ŝtİr`fİe.



Zcatúrcf E`kyctga Xmt`ksgycf

Lu E`xwcff bckafcegkg auff`k`fİe>

Zcatúr úzcffgafcrgkbck lgfgymruzag dcrd`kig lgr vcatúrök búkcfgkgk bgvcrn`ksİdcrzè`k sİjİrbİr>

Lgr úkocag bckafcefc úzbcŝfcŝtgrgrsca e`kyctga vcaúrcf f`kİ, @, t`kİef`rİz>

Lur`b`k>

Kmat`s`f @epcrc y`s`sİ>



Zcatúr Xmt`ksgycf ĸégk Bckafce

Lúföe 9.9‗bc kf`tİf`k prmscbörö uyiuf`rsà iústcrclgfgrgzag>

Lukukf` l`ŝf`y`fİe>

Zcatúr F`pf`sy`kİ t`kİef`y`k vcaúr úzbcŝfgĝgkg suk`fİe>

Jmreöfbc ycrgkc amyuko`>



00



@‗kİk Wúkö

śgebg cfgegzbc>

A`rtczyck ammrbgk`tf`rb`>

Bckafceg yrİŝtİrİrsà>

Lur`b`k @‗kİk yúkö N‗kgk yúkö gfc `ykİ mfbuĝu smkuouk` v`rİrİz.

(bgĝcr ammrbgk`t sgstcefcrgkbclu a`b`r amf`y bcĝgf!)

Zcatúrcf f`k, @, töe uz`yb` ecvout, l`zck ackbgsgkg mfuŝtur`k aİeymĝukfuĝukuk ‖luf`kİa iúröktösö― mf`ràt` bf`kbİrİfİr .



Xmt`ksgycf ĸégk ĸj`bcfcr

ścagfbcag bgjcr`ksgycf cfè`kf`rİ böŝökcfge. _mfb` kmat`s`f lgr yöa bgjcr`ksgycfuzukfuatàg égzigscf lgr yöa gfc tcesgf cbgfecatcbgr. _`ĝb` gsc bgjcr`ksgycf lgr aİecfce`kİ v`rbİr. Dcr gag burueb` b` pmt`ksgycfg c fbc cteca gégk ykİ auriu v`rbİr.

Égzigscf Wöa Égzigscf @aİe

_a`fcr Cfcatrmst`tga Xmt`ksgycf Zcatúr E`kyctga Xmt`ksgycf



Zcatúr Xmt`ksgycffcr ĸégk Ickcf ĸj`bcfcr

Löyöa úfécafg yöa y`b` aİe b`ĝİfİef`rİ gégk töe bgjcr`ksgycf a`taİf`rİk gktcir`fg`fİk`rà tmpfè pmt`ksgycf lfukur, smkuét`>

vc

A`p`fİ ymf gktcir`fg aİeİk ackbgkg a`p`t`rà (búkiö) tèlgr bcvrc mfuŝture`sİ gégkbgr.

Wözcy vc dòge àİe ymĝukfuaf`rİ gégk sİr`sİyf` >

mr



Úrkca

ścagfbcag iglg bgjcr`ksgycf lgr aİe cfè`kİ gégk bcvè cbcfge>

Lu burueb`

X kmat`sİkb`>

śgebg búkcfg sgfgkbgrga ammrbgk`tf`rb` fİrsà>

Lu lcafcbgĝgegz iglg b`d` úkoc Lgmt-_`v`rt W s`sİ gfc lufbuĝueuz smkué gfc `ykİ!



0

CCE <43 ‟ Cfcatrme`kyctga @f`k Rcmrgsg J@RĸD SKGZC\_GRW

E`kyctga Auvvctfcr, E`fzcecfcr,vc Ckböat`ks

Cfcatrga `f`k'b`

E`kyctga `f`k'b`

( ) Cfcatrme`kyct

Fmrcktz Auvvct Bck

ga `f`k'b`

afceg

P

P

P

J C

J v L

J C v L

E`kyctga Auvvctfcr


E`kyctga Auvvctfcr, E`fzcecfcr, vc Ckböat`ks

b bP J v L

D`ff ctagsg

Bgjcr`ksgycf àİe cfce`kb` auvvct



b bP J v L v

v

bP bv

N v

b bv

b b_

b Gb

J N L

J A L

J F L

Bgjcr`ksgycf aİe cfce`kİ

bv b_ Gb N A F

Gb G b J F L L F



Úrkca > Rcf búkiöbcag tmpfè auvvctg lufukuz



Úrkca> ĸag jgfè`k gfctack r`sİkbàg auvvctg lufukuz



Rmra

G b J L F

R \ J



<



Úrkca > E`kyctga lgr L `f`kİkb` bgjcr`ksgycf écvrg

b Gb

b Gb

b Gb

b b

J F L

R _ L

e _

R e L

G R _ L e L

Böziök lgr L `f`kİkb`

E`kyctga bgpmf emecktg



E`kyctga bgpmf emecktg

0

l

k v

tmt`f g

g

G b

e _

e e

Eİak`tİsfè` Zcatúrö

80

0fge

k v

gv

gv

E e





Écagrbca yúrökicsgkbc búkck cfcatrmk

Cfcatrmkuk écagrbca yúrökicsgkbcag b`vr`kİŝİ • Wúrökicscf e`kyctga bgpmf emecktg • _pgk e`kyctga bgpmf emecktg

• Köafccr e`kyctga bgpmf emecktg (gde`f cbgfclgfgr)

Lu emecktfcrgk a`taİ bcrcocfcrg e`fzceckgk ogksgkg lcfgrfcr



Lgréma e`fzcecbc> Wúrökicscf e`kyctga bgpmf emecktg spgk e`kyctgabgpmf emecktgkg iútöröymr , vc ζ

r ≄0

• Bgè`kyctga e`fzcecfcr > Wúrökicscf e`kyctga bgpmf emecktg spgke`kyctga bgpmf emecktgkbck lgr`z `z1 (úrkca > Lgseut ζ

r 5 8.7774?)

• X`rè`kyctga E`fzcecfcr> Emecktfcr cŝgt bcĝgf, emecktfcrgk bgzgfgŝfcrgicfgŝg iözcf è` e`kyctga `f`k mfurs` dgz`f`k`lgfgrfcr

• Jcrrme`kyctga E`fzcecfcr> Bcĝgŝtgrec aupf`nf`rİ vc `f`k mfuŝuef`rİkb`kbmf`yİ a uvvctfg mf`rà e`kyctgafcrbgr

E`kyctga E`fzcecfcr



8 ( )

l

e

G b

G b

E F

L D E

D F

E D

L D



?



E`tcrg`f r

Bgèìkctgo lgseutd

imfb

sgfvcr

omppcr

w`tcr

8.7774?

8.7774:

8.77774

8.777770

8.777770

X`rèìkctgo `gr

`fuegkue pf`tgkue

0.8888882

0.8888<0.888?

Jcrrmeìkctgo

(kmkfgkc`r)

oml`ft

kgoacf

grmk (77.4% purc)

grmk (77.7:% purc)

Em/Kg supcre`ffmy

<38

:88

3888

<48,888

0,888,888

E`kyctga E`fzcecfcr

8( ) L D E e E D

0r e

8 8(0 )e r L D D D

lur`b` Eİak`tİsfİa vcatúröbör Lúyfcoc

lur`b` E`kyctga icégrickfgĝgbgr



Bcĝgŝge aupf`nİ vc `f`kf`rİ • bcĝgŝge aupf`nİ ‟ lgtgŝga `tmef`rb ag cfcatrmk búköŝfcrgdgz`f`ke` cĝgfgegkbcbgrfcr • `f`kf`r ‟ bgpmffcrgk dgz`f`kbİĝİ lúficfcr ‟ icfgŝg iözcfdgz`f`ke` sgstce ckcrngsgkg egkgec cbcr

Icfgŝg iözcf dgz`f`ke` R e dgz`f`ke` Lcfgrfg `f`kf`rb` dgz`f`ke`



0 <

0 <

K K

t t

L L

D D A

_İkİr Amŝuff`rİ



a`ps G b D F bckafcegkg `↜l↜o↜b↜` búkiösökc uyiuf`

_İkİr Amŝuff`rİ



_İkİr Amŝuff`rİ



_İkİr Amŝuff`rİ







<0 0< <

D vmf vmf

Y bv D bv L D

E`kyctga `f`kb` tmpfè bcpmf`k`k ckcrng



E`kyctga Bcvrc



E`kyctga Bcvrc

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