Sayısal Analiz (MATLAB) - Emre Özbay Ders Notları

8/10/2019 Saysal Analiz (MATLAB) - Emre zbay Ders Notlar

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_dauc kivdrsitdsi | Cimy` Mndkfisai!i | M`ta`j Khta`r :


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_dauc kivdrsitdsi | Cimy` Mndkfisai!i | M`ta`j Khta`r :,9,) 73))'+59)'/

i"`rdtikfdk shkr` chmut biriadjiair. Ndrn`kbi jir chmut y`psk chpy`a`ypy`p"tr`jiairsikiz. Ca`vydfd st hc vd `at hc chmut bdmi"i idrisikfd bdzikmdyi s`!a`r. oaochmutu dcr`kf` y`za ha`k chmuta`r tdmizadr. Fd!i"cdk tipi hthm`tic t`kma`kr. (Kumjdrs,On`r, _trikb, Jhhad`k)3 M`ta`jf` ie`fdadr bdkdaaicad fd!i"cdk = ie`fd vdy` s`fdod ie`fdehrmukf`fr.

rkdc7

;; `=6*sqrt(4)

` =

>.966?

ie`fdsikfd ` fd !i"cdk , 6 s`y , * i "ad , sqrt, ehkcsiyhkfur. Jir ie`fd = i "`rdti iad jirfd!i"cdkd `t`km`m" isd M`ta`j hthm`tic ha`r`c shkuou, `ks (`kswdr) `f vdriadk zda jirfd!i"cdkfd s`ca`r.

Chmuta`rf`k shkr` 3 i"`rdtikik cuaa`kam`sya` i"admadr y`par e`c`t dcr`k` y`zfram`z.Vdc s`trf` jirfdk e`za` chmut birmdc iik chmuta`r , vdy` 3 cuaa`kar.

;; oao, `=4, o=53

` =

4


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_dauc kivdrsitdsi | Cimy` Mndkfisai!i | M`ta`j Khta`r :#"!IOI&8>#"7 "FN=8G8# B, &N>#"L "$G8&G8#"

>/.D@+@9,(/.; "C'-,),/

;; `apn`=?


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_dauc kivdrsitdsi | Cimy` Mndkfisai!i | M`ta`j Khta`r :3@=0:

A.:,/*@).; F@+;4.0@+)'/


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_dauc kivdrsitdsi | Cimy` Mndkfisai!i | M`ta`j Khta`r :K#G8# B, ="H"&

! Bdkdaaicad tdc jhyutau m`trisadrd vdctr fdkir.! M`ta`jf` k fdrdodai jir vdctr iad 0xk vdy` kx0 aic jir m`trisik e`rc yhctur.! Udctr y`zfrm`f` cha`yac s`!a`m` `fk` 7 i"`rdti scaca` cuaa`kar.

;; U=?7:70:

U= ? 4 2 9 00

;; akk=aiksp`od(?,0


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_dauc kivdrsitdsi | Cimy` Mndkfisai!i | M`ta`j Khta`r : 9 0 9 0< 0:]3

M`x(J) , `ks=8

Ju ici i"admfdk fd `ka`"aò`! biji m`trisadrfdci ehkcsiyhka`r, vdriadr zdrikfd stuk t`j`ka ha`r`c

i"adtiair. Y`ki ju ehkcsiyhka`r ndr jir stuk` `yr `yr uybua`kr.

_hru @=!! ! !

! !! !

! !! !

J=! !! !

! !! !

! ! !

O=@*J F=S@3J]

! @ m`trisikik 0. _utuku x fizikd `t`yk

! J m`trisikik :. vd ?. sutkuku y m`tirisikd `t`yk

! F m`trisikik fdtdrmik`ktk nds`pa`ykz.

! J m`trisikfdci dk jyc s`yya` @ m`trisiki `rpk.

! @ iad J m`trisiki dadm`k da`m`k` `rpk

_hru Cuaa`kof`k jiabi àp e`ctryda nds`j y`pp cuaa`koy` `ca`yo jiabi vdrdk jir prhbr`my`zkz.

K=ikput('E`ctriydai àkò`c s`yy birik=')3

\=S0707K]3

_hkuo=prhf(\)3

eprikte('Birmi! hafu"ukuz s`ykk e`triydai %.


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_dauc kivdrsitdsi | Cimy` Mndkfisai!i | M`ta`j Khta`r :N7Z&GN#Z "$G8&G8#"

=,+;),9 >'+59)'9'

M`ta`jf` t`kma`m`c istdfi!imiz fdkcadmi kd iik cuaa`k`o`!mz` j`!a ha`r`c t`kma`m` "dciaadrifd!i"djiair.

Fdkcadm ie` dtti!i ehkcsiyhk` brd "u "dciafd t`kma`k`jiair7 y=!!

!!!"# ! !!

!"#$!

fdkcadmim.m fa fhsy`7

eukotihky=fdkcadmim(x)

y=(?*x[:+sik(x)--!4)/(ohs(x)[:)3

dkf

Fdkcadmik x=? icdk M@VA@J `k` prhbr`mf` cuaa`km7

;; ey=fdkcadmim(?)

ey=

::.490RONI

;$76&$JO?ON.=$76&$JO=J?NONIZ14! #9I

Kis`k 0? `r!`mj`
mailto:[email protected]:[email protected]:[email protected]


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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt

hfd64 iad Fiedr`ksiyda Fdkcadm zm - _hru

Yuc`rf` vdriadk s`jit c`ts`ya aikddr fiedr`ksiyda fdkcadmik zm, t=S


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fshavd iad Fiedr`ksiyda Fdkcadmadrik zm

! !"#$%&chmutu `fi fiedr`ksiyda fdkcadmadrik zm bdrdcad"tiriair.

! Ju chmut "=>6#$42 ?##$6#;idrisikfd juaukur.

! f/ft "dcaikfdci fiedr`ksiyda ie`fdyi F n`rff tdmsia dfdr.

! D!dr skr "`rta`r jdairtiamdmi"isd rdtiadodc ha`k sdmjhaic fdkcadmfd obiji s`jitadr ha`o`ctr.

!!!!

!!!

!

!! ! !

!!!

!!!! !

!!!

!!! ! !! !

Kis`k 0? `r!`mj`


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fshavd iad Fiedr`ksiyda Fdkcadmadrik zm

!!!!! !!

!! ! ! !

!!!

!!!! !

!!!

!!!! ! ! !

WW ;E?@!"#$%&JO_-;\


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fshavd iad Fiedr`ksiyda Fdkcadmadrik zm - _hru

!!!! !

!! !!

$dcaikfdci fiedr`ksiyda fdkcadmi `"`!f`ci skr "`rta`r iad fshavd chmutuiad zfrp br`ff!iki izik.

! ! ! !

!! ! ! !

!!! ! ! !

WW X@!"#$%&JO_-;Y;@,^?O.O;[email protected]_;JBN@:O.O_,;JBN@-ON

X @

,^? Y


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fshavd iad Fiedr`ksiyda Fdkcadmadrik zm - _hru

!!!! !

!! !!

Kis`k 0? `r!`mj`


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_DATC_DM :


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_dmjhaic V kma`m`! _dmjhaic i!admadrfd c`r`ctdradr m`ta`j hrt`mk` s`ysà fd"drmi!biji

t`kma`kr.

! _trikb jir fd"i!cdk fd"ia s`ysà jir fd"i!cdkmi!biji àba`kr.

! #u !dciafd t`kma`mà`r mmckfr7

!! #$%&'()*)+# $*

%&'% *,-.

!! #$%&'()*)/)


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_dmjhaic Jiimd Fk!trmd!! 5 10=0


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_dmjhaic Jiimfdk _`ysà Jiimd Fk!trmd

! _dmjhaic ha`r`c bstdrimfd ha`k s`ysà ie`fdadr !u !dciafd s`ysàfd"dradrikd c`vu!ura`r7

!! #$%&'(CIG+# $CIG!! \*&3%*:#$_H6,:0(#+\*&3%*:# $ F@DFFF

Kis`k 0? `r!`mj`


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_dmjhaic "!admadr

?

?

: xfxx =

! _dmjhaic zm

?

0

?

0

$J7M9E.!! Y$>7&Y $(J7M 9 E+7(MRJ T G+!! 0MK*4_(Y+*4% $J7MRL 9 E7MRJ T NF7M T LG

Kis`k 0? `r!`mj`


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Fdkcadmi _`fdad!tirmdc! Jir fdkcadmi s`fdad!tirmdc iik %3'K:3=&

chmutu cuaa`kar.!! \$(MRLTC7M+I(MRJ9J7M+.!! %3'K:3=&(\+*4% $M T J

Kis`k 0? `r!`mj`


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_dmjhaic "ktdbrà "!admi! _dmjhaic iktdbrà àm` ehkcsiyhku ikt haup bdkda ehrm`t7

!

341(\+, _ik jdairsiz iktdbràiki àr.

! 341(\/2+, _ik vyd brd jdairsiz iktdbràiki àr.

! 341(\/*/,+,_ik v`rs`ya`k sdmjhaic fd"i!cdkd brd `f`k jydc`f`r jdairai iktdbràiki ar.

! 341(\/*/,/2+,_ik vyd brd `f`k jyd c`f`r jdairai iktdbràiki àr.

! !dcaikfdfir.

Kis`k 0? `r!`mj`


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_dmjhaic "ktdbr`a "!admi

! +"" fxxx ):


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_dmjhaic Vrdv! Vrdv àm` i!admikfd cuaa`ka`k ehkcsiyhk `f fiee haup sdmjhaic i!adm

m`kt" drdvdsikfd bdkda ehrm`t7

! _3==(\+, _ik trdviki àr.

! _3==(\/2+, _ik vyd brd trdviki àr.

! _3==(\/4+, k phzitie jir t`ms`y ham`c zdrd k. fdrdodfdk trdviki àr.

!

_3==(\/)2)/4+vdy` fiee(_,k,'v'), _ik vyd brd k. fdrdodfdk trdvikiàr.

! !dcaikfdfir.

! Vrdvik x=pfdci fd"driki juam`c iik %6,%(16


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_dmjhaic Vrdv

e(x)=4x?+`x:+jx -06 (` vd j s`jit fd"drfir)

ehkcsiyhkukuk trdviki juaukuz.!! %&'% * , M!! =$G7MRL9*7MRJ9,7MTNC.!! _3==(=+*4% $

NG7MRJ 9 J7*7M 9 ,!! K


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Fiedr`ksiyda Fdkcadmadrik _dmjhaic zm

! Fiedr`ksiyda fdkcadmadrik sdmjhaic zmadri _%H:20ehkcsiyhku iadbdrdcad!tiriair.

#$ _%H:20(W_3=NS/W_3=JS/@@@/W%;4;


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#dcaikfd jir fiedr`ksiyda fdkcadmik zm `!`"f`ci bijifir.

!"

!!! ! ! !"! ! ! !

! [M$_%H:20()]M9M$-H%(1+91)+ 5%;4;< Q*


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#dcaikfd jir fiedr`ksiyda fdkcadmik zm `!`"f`ci bijifir.

! [JM$_%H:20()]LM$%34(J71+)/)]JM(F+$N)/)]M(F+$F)/)M(F+$TN)+

JM $

H%(J71+ID 9 (L71RJ+IC T BID

!!!

!!! ! !"#!!!!

Kis`k 0? `r!`mj`


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_DATC_DM :


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M`ta`j \rhbr`ma`m`

Biri!

Jiabi @am`Fd"i!cdk

V`kma`m`

#!admadr

_hku Udrmd

_hk

!"#$%&'()*+, ./>4

`=U/t3

eprikte(#vmd %.0e fir.)3

Kis`k 0? `r!`mj`


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Ehkcsiyhk V kma`m`! N`rioi ehkcsyhka`rk t`m`m .m fhsy`a`rkf` n`zra`kr.

!

@!`"f`ci biji y`pa`r` s`niptir79&$7'#3$)1=$.;0;8/7/L ./


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Ehkcsiyhk V kma`m`

Ehkcsiyhk t`kma`rcdk !uka`r` ficc`t dfiamdfaifir7

!

M`ta`jf` t`kma (ndfde ca`sradrik ndrn`kbi jirikfd v`r ha`k) jirehkcsiyhka` `yk isimad ham`mà

! Ndfde ca`sradrfdk jirikfd ha`k fhsyà`r iad `yk isimfd ham`mà

! 9&$7'#3$ ie`fdsi iad j`!a`mà

! Ehkcsiyhk `f iad fhsy` `f `yk hamà

Kis`k 0? `r!`mj`


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Ehkcsiyhk V kma`m`

#fdà b`z fdkcadmikfd nòmi jua`k jir ehkcsiyhk y`zàm.

Bifiadr7J`sk (\), Mha s`ys (k), _o`cac (V)

cta`r7Nòim (U)

KK V TF'8FC 30'FD+KK *F7#D"#./F8*F7#D(UI2I2>>6*F7#D " 2RP^>>>

V #./F8*F7#DPD .3@JF@+$+$ #Y/0#


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M`ktcs`a Hpdr`tradr

"!`rdt @ka`m

1 Cc

; Jyc

1= Cc d!it

;= Jyc d!it

== D!it mi

!= D!it fd"ia mi

Kis`k 0? `r!`mj`


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M`ktcs`a Hpdr`tradr

M`ktcs`a hpdr`tradrfdk bdadk odv`p Dvdtisd 0 N`yr isd < odv`j vdriair.

!

Kis`k 0? `r!`mj`


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M`ktcs`a Hpdr`tradr

KK N"UXUXl]N "

U 5 R ] l> lU l5 lR l]KK J"B> 5 2 Z l> l2 l_ lR U>G4KK DF$'#Ll"NK"]DF$'#Ll "

> > > l l l l l lKK DF$'#LU"NKJDF$'#LU "

l > l l > > > > >KK DF$'#L2"(N""J6

DF$'#L2 "> l > > l > > l >

KK ,"JKl>, "

> > > > > l l l lKK `",PAJ` "

> > > > > l2 l_ lR U>

Kis`k 0? `r!`mj`


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M`ktcs`a !"`rdtiadr

"!`rdt @ka`m

& vd

! vdy`

~ fd"ia

Kis`k 0? `r!`mj`


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M`ktcs`a !"`rdtiadr

KK N"MlX2Xl_

N "

Ml U Z ] ll l5 l_

KK DF$'#Ll"Nj]

DF$'#Ll "

l l l > > > >

KK DF$'#LU"o(NKZ6

DF$'#LU "

l l l > > > >

KK DF$'#L2"(NK>6f(Njl56DF$'#L2 "

> l l l l > >

KK DF$'#L5"N30((Nj26I(NKll66

DF$'#L5 "

l l > > > l l

Kis`k 0? `r!`mj`


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M`ktcs`a Ehkcsiyhka`r

N30(NIJ6

x vdy` y fdk ndr n`kbi icisi fh"ru vdy` y`ka!isd 0fi"dradrikfd < fd"driki fkfrr.

F$J(F6

` vdctr iikfd ndrn`kbi jir dadm`k


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M`ktcs`a Ehkcsiyhka`r

#@$F$(F6` dadm`k dFdfd"drikfd isd 0 fd"iasd < fd"drikik fkfrr

#@9#$#'/(F6` vdctrkk dada`ka`r shkau s`y isd 0 fd"iasd < fd"drikikfkfrr

#@#$9(F6` vdctrkk dada`ka`r #$9vdy` M#$9isd 0 fd"iasd < fd"drikikfkfrr

#@/D%'J(F6d"dr ` m`trisi jh!isd 0 fd"iasd < fd"drikik fkfrr.

#@/e&F8(FIC6 ` vd j m`trisadrikik jirjiradrikd d!it haup ham`f"k chktrha dfdr.

#@0/F8(F6` m`trisi idrisikfdci tm s`ya`r rd`a (bdrdc) s`y isd 0 fd"iasd

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Sayısal Analiz (MATLAB) - Emre Özbay Ders Notları