8/13/2019 ca unit 2.2

1/22

:^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

^K^GEKMKML JMD QGHTI_ ^_IHGXXKML

^jrjeege ^rihgsskml

^kpgekmkml

Jrktb`gtkh kpgekmg

Kmstruhtkim ^kpgekmg

_KXH ^kpgekmg

Qghtir ^rihgsskml

Jrrjy ^rihgssirs

8/13/2019 ca unit 2.2

2/22

?^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

^J_JEEGE ^_IHGXXKML

Egvges ia ^jrjeege ^rihgsskml

- Fio ir ^rilrj` egvge

- Tjsc ir ^rihgdurg egvge

- Kmtgr-Kmstruhtkim egvge

- Kmtrj-Kmstruhtkim egvge

Gxghutkim ia Himhurrgmt Gvgmts km tbg hi`putkml

prihgss ti jhbkgvg ajstgr Hi`putjt kimje Xpggd

^jrje ege rihgsskml

8/13/2019 ca unit 2.2

3/22

8^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

^J_JEEGE HI@^WTG_X

Jrhbktghturje Hejsskakhjtkim

Mu`ogr ia Djtj Xtrgj`s

Mu`ogr ia

Kmst ruht kim

Xtrgj`s

Xkmleg

@uetkpeg

Xkmleg @uetkpeg

XKXD XK@D

@KXD @K@D

^jrje ege rihgsskml

Aeymm's hejsskakhjtkim

Ojsgd im tbg `uetkpekhkty ia Kmstru ht kim Xtrgj`sjmdDjtj Xtrgj`s

Kmstruhtkim Xtrgj`

Xgqugmhg ia Kmstruhtkims rgjd ari` `g`iry

Djtj Xtrgj`

Ipgrjtkims pgrair`gd im tbg djtj km tbg prihgssir

8/13/2019 ca unit 2.2

4/22

4^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

HI@^WTG_ J_HBKTGHTW_GX AI_ ^J_JEEGE^_IHGXXKML

Qim-Mgu`jmojsgd

Djtjaeiw

_gduhtkim

XKXD

@KXD

XK@D

@K@D

Xupgrshjejr prihgssirs

Xupgrpkpgekmgd prihgssirs

QEK\

Mimgxkstgmhg

Jrrjy prihgssirs

Xystiekh jrrjys

Jssihkjtkvg prihgssirs

Xbjrgd-`g`iry uetkprihgssirs

Ous ojsgdHrissojr swkthb ojsgd@uetkstjlg KM ojsgd

@gssjlg-pjsskml uetkhi`putgrs

Bypgrhuog@gsb_ghimaklurjoeg

^jrje eg e rihgsskm l

8/13/2019 ca unit 2.2

5/22

7^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

XKXD HI@^WTG_ X[XTG@X

HimtrieWmkt

^rihgssir

Wmkt

@g`iry

Kmstruhtkim strgj`

Djtj strgj`

Hbjrjhtgrkstkhs

- Xtjmdjrd vim Mgu`jmm `jhbkmg- Kmstruhtkims jmd djtj jrg stirgd km `g`iry- Img ipgrjtkim jt j tk`g

Ek`ktjtkims

Qim Mgu`jmm oittegmghc

@jxk`u` spggd ia tbg systg` ks ek`ktgd oy tbg@g`iry Ojmdwkd tb (okts/sgh ir oytgs/sgh)

- Ek`ktjtkim im @g`iry Ojmdwkd tb- @g`iry ks sbjrgd oy H^W jmd K/I

^jrje ege rihgsskml

8/13/2019 ca unit 2.2

6/22

1^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

XKXD ^G_AI_@JMHG K@^_IQG@GMTX

@uetkprilrj``kml

Xpiiekml

@uetkaumhtkim prihgssir

^kpgekmkml Gxpeiktkml kmstruhtkim-egvge pjrjeegeks`

- Xupgrshjejr- Xupgrpkpgekmkml- QEK\ (Qgry Eiml Kmstruhtkim \ird)

^jrje ege rihgsskml

8/13/2019 ca unit 2.2

7/22

8/13/2019 ca unit 2.2

8/22

2^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

XK@D HI@^WTG_ X[XTG@X

Himtrie Wmkt

@g`iry

Jeklm`gmt mgtwirc

^ ^ ^

@ @@

Djtj ous

Kmstruhtkim strgj`

Djtj strgj`

^rihgssir umkts

@g`iry `iduegs

Hbjrjhtgrkstkhs

- Imey img hipy ia tbg prilrj` gxksts- J skmleg himtrieegr gxghutgs img kmstruhtkim jt j tk`g

^jrje ege rihgsskml

8/13/2019 ca unit 2.2

9/22

;^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

T[^GX IA XK@D HI@^WTG_X

Jrrjy ^rihgssirs

- Tbg himtrie umkt orijdhjsts kmstruhtkims ti jee ^Gs,jmd jee jhtkvg ^Gs gxghutg tbg sj`g kmstruhtkims

- KEEKJH KQ, LA-::, Himmghtkim @jhbkmg, DJ^, @^^

Xystiekh Jrrjys- _gluejr jrrjmlg`gmt ia j ejrlg mu`ogr ia

vgry sk`peg prihgssirs himstruhtgd imQEXK hkrhukts

- H@W \jrp, ^urdug HBk^

Jssihkjtkvg rihgssirs

- Himtgmt jddrgsskml- Djtj trjmsair`jtkim ipgrjtkims ivgr `jmy sgts

ia jrlu`gmts wktb j skmleg kmstruhtkim

- XTJ_JM, ^G^G

^jrje ege rihgsskml

:>^k e k k d Q ^ k

8/13/2019 ca unit 2.2

10/22

:>^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

@K@D HI@^WTG_ X[XTG@X

Kmtgrhimmghtkim Mgtwirc

^ @ ^ @^ @

Xbjrgd @g`iry

Hbjrjhtgrkstkhs

- @uetkpeg prihgsskml umkts

- Gxghutkim ia `uetkpeg kmstruhtkims im `uetkpeg djtj

Typgs ia @K@D hi`putgr systg`s

- Xbjrgd `g`iry `uetkprihgssirs

- @gssjlg-pjsskml `uetkhi`putgrs

^jrje ege rihgsskml

::^k e k k d Q t ^ k

8/13/2019 ca unit 2.2

11/22

::^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

XBJ_GD @G@I_[ @WETK^_IHGXXI_X

HbjrjhtgrkstkhsJee prihgssirs bjvg gqujeey dkrght jhhgss ti

img ejrlg `g`iry jddrgss spjhg

Gxj`peg systg`sOus jmd hjhbg-ojsgd systg`s

- Xgqugmt Ojejmhg, Gmhirg @uetk`jx

@uetkstjlg KM-ojsgd systg`s- Wetrjhi`putgr, Outtgraey, _^8, BG^Hrissojr swkthb-ojsgd systg`s

- H.``p, Jeekjmt AR/2

Ek`ktjtkims@g`iry jhhgss ejtgmhy

Bit spit prioeg`

Kmtgrhimmghtkim Mgtwirc(KM)

^ ^^

@ @@

Ousgs,@uetkstjlg KM,Hrissojr Xwkthb

^jrje ege rihgsskml

:?^k e k k d Q t ^ k

8/13/2019 ca unit 2.2

12/22

:?^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

@GXXJLG-^JXXKML @WETKHI@^WTG_

Hbjrjhtgrkstkhs

- Kmtgrhimmghtgd hi`putgrs- Gjhb prihgssir bjs kts iwm `g`iry, jmd

hi``umkhjtg vkj `gssjlg-pjsskml

Gxj`peg systg`s

- Trgg struhturg6 Tgrjdjtj, DJDI- @gsb-himmghtgd6 _gdkaeiw, Xgrkgs ?>:>, F-@jhbkmg- Bypgrhuog6 His`kh Huog, k^XH, MHWOG, A^X T Xgrkgs, @jrc KKK

Ek`ktjtkims

- Hi``umkhjtkim ivgrbgjd

- Bjrd ti prilrj``kml

@gssjlg-^jsskml Mgtwirc

^ ^^

@ @ @

^ikmt-ti-pikmt himmghtkims

^jrje ege rihgsskml

:8^k e k k d Q t ^ k ^k e k k

8/13/2019 ca unit 2.2

13/22

:8^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

^K^GEKMKML

_: Jk, _? Ok Eijd Jkjmd Ok_8 _: * _?, _4 Hk @uetkpey jmd eijd Hk_7 _8 + _4 Jdd

J tghbmkqug ia dghi`piskml j sgqugmtkje prihgsskmti suoipgrjtkims, wktb gjhb suoprihgss ogkml

gxghutgd km j pjrtkje dgdkhjtgd sgl`gmt tbjtipgrjtgs himhurrgmtey wktb jee itbgr sgl`gmts.

Jk* Ok+ Hk air k 0 :, ?, 8, ... , tjscs ti og gxghutgd- : tjsc km mim-pkpgekmgd systg`3 ?>*4 0 2>mX

^kpgekmgd Xystg`(c + m - :)*tp0 (4 + ;;) * ?> 0 ?>1>mX

Mim-^kpgekmgd Xystg`m*c*tp0 :>> * 2> 0 2>>>mX

XpggdupXc0 2>>> / ?>1> 0 8.22

4-Xtjlg ^kpgekmg ks ojskhjeey kdgmtkhje ti tbg systg`wktb 4 kdgmtkhje aumhtkim umkts

^kpge km kml

:2^kpge km kml jmd Qghtir ^rihgsskml Jrk tb` gt kh ^kpge kmg

8/13/2019 ca unit 2.2

18/22

:2^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

J_KTB@GTKH ^K^GEKMG

Aeijtkml-pikmt jddgr

S:P Hi`pjrg tbg gxpimgmtsS?P Jeklm tbg `jmtkssjS8P Jdd/suo tbg `jmtkssjS4P Mir`jekzg tbg rgsuet

R 0 J x ?j

[ 0 O x ?o

_

Hi`pjrggxpimgmts

oy suotrjhtkim

j o

_

Hbiisg gxpimgmt

Gxpimgmts

_

J O

Jeklm `jmtkssj

@jmtkssjs

Dkaagrgmhg

_

Jdd ir suotrjht`jmtkssjs

_

Mir`jekzgrgsuet

_

_

Jdfustgxpimgmt

_

Xgl`gmt :6

Xgl`gmt ?6

Xgl`gmt 86

Xgl`gmt 46

Jrktb` gt kh kpge kmg

:;^kpge km kml jmd Qghtir ^rihgsskml Jrk tb` gt kh ^kpge kmg

8/13/2019 ca unit 2.2

19/22

:;^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

4-XTJLG AEIJTKML ^IKMT JDDG_

J 0 j x ?p O 0 o x ?q

p j q o

Gxpimgmtsuotrjhtir

Arjhtkimsgeghtir

Arjhtkim wktb `km(p,q)

_klbt sbkatgr

Itbgrarjhtkim

t 0 |p - q|

r 0 `jx(p,q)

Arjhtkimjddgr

Egjdkml zgrihiumtgr

r h

Egat sbkatgr

h

Gxpimgmtjddgr

r

s d

d

Xtjlgs6

X:

X?

X8

X4

H 0 J + O 0 h x ? 0 d x ?r s

(r 0 jx (p,q), >.7 d 5 :)

Jrktb` gt kh kpge kmg

?>^kpge km kml jmd Qghtir ^rihgsskml Kmstruht kim ^kpge kmg

8/13/2019 ca unit 2.2

20/22

?>^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

KMXT_WHTKIM H[HEG

Xkx ^bjsgs* km jm Kmstruhtkim Hyheg

S:P Agthb jm kmstruhtkim ari` g`iry

S?P Dghidg tbg kmstruhtkimS8P Hjehuejtg tbg gaaghtkvg jddrgss ia tbg ipgrjmdS4P Agthb tbg ipgrjmds ari` `g`iryS7P Gxghutg tbg ipgrjtkimS1P Xtirg tbg rgsuet km tbg pripgr pejhg

* Xi`g kmstruhtkims sckp si`g pbjsgs* Gaaghtkvg jddrgss hjehuejtkim hjm og dimg kmtbg pjrt ia tbg dghidkml pbjsg

* Xtirjlg ia tbg ipgrjtkim rgsuet kmti j rglkstgrks dimg juti`jtkhjeey km tbg gxghutkim pbjsg

00= 4-Xtjlg ^kpgekmg

S:P AK6 Agthb jm kmstruhtkim ari` `g`iryS?P DJ6 Dghidg tbg kmstruhtkim jmd hjehuejtg

tbg gaaghtkvg jddrgss ia tbg ipgrjmdS8P AI6 Agthb tbg ipgrjmdS4P GR6 Gxghutg tbg ipgrjtkim

Kmstruht kim kpge kmg

?:^kpge km kml jmd Qghtir ^rihgsskml Kmstruht kim ^kpge kmg

8/13/2019 ca unit 2.2

21/22

?:^kpge km kml jmd Qghtir rihgsskml

Hi`pu tgr Irljmkzjt kim Hi`pu tgr Jrhb ktghturgs Ejo

KMXT_WHTKIM ^K^GEKMG

Gxghutkim ia Tbrgg Kmstruhtkims km j 4-Xtjlg ^kpgekmg

Kmstruht kim kpge kmg

AK DJ AI GR

AK DJ AI GR

AK DJ AI GR

k

k+:

k+?

Himvgmtkimje

^kpgekmgd

AK DJ AI GR

AK DJ AI GR

AK DJ AI GR

k

k+:

k+?

??^kpge km kml jmd Qghtir ^rihgsskml Kmstruht kim ^kpge kmg

8/13/2019 ca unit 2.2

22/22

??^kpge km kml jmd Qghtir rihgsskml

KMXT_WHTKIM GRGHWTKIM KM J 4-XTJLG ^K^GEKMG

: ? 8 4 7 1 < 2 ; :> :? :8::

AK DJ AI GR:

AK DJ AI GR

AK DJ AI GR

AK DJ AI GR

AK DJ AI GR

AK DJ AI GR

AK DJ AI GR

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8

4

7

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