Sayısal Analiz (MATLAB) - Emre Özbay Ders Notları
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Transcript of Sayısal Analiz (MATLAB) - Emre Özbay Ders Notları
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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 :
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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 :#"!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`"a`o`! 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 `ap e`ctryda nds`j y`pp cuaa`koy` `ca`yo jiabi vdrdk jir prhbr`my`zkz.
K=ikput('E`ctriydai `ak`o`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
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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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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
fshavd iad Fiedr`ksiyda Fdkcadmadrik zm
! !"#$%&chmutu `fi fiedr`ksiyda fdkcadmadrik zm bdrdcad"tiriair.
! Ju chmut "=>6#$42 ?##$6#;idrisikfd juaukur.
! f/ft "dcaikfdci fiedr`ksiyda ie`fdyi F n`rff tdmsia dfdr.
! D!dr skr "`rta`r jdairtiamdmi"isd rdtiadodc ha`k sdmjhaic fdkcadmfd obiji s`jitadr ha`o`ctr.
!!!!
!!!
!
!! ! !
!!!
!!!! !
!!!
!!! ! !! !
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
fshavd iad Fiedr`ksiyda Fdkcadmadrik zm
!!!!! !!
!! ! ! !
!!!
!!!! !
!!!
!!!! ! ! !
WW ;E?@!"#$%&JO_-;\
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
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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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
fshavd iad Fiedr`ksiyda Fdkcadmadrik zm - _hru
!!!! !
!! !!
Kis`k 0? `r!`mj`
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_DATC_DM :
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
_dmjhaic V kma`m`! _dmjhaic i!admadrfd c`r`ctdradr m`ta`j hrt`mk` s`ys`a fd"drmi!biji
t`kma`kr.
! _trikb jir fd"i!cdk fd"ia s`ys`a jir fd"i!cdkmi!biji `aba`kr.
! #u !dciafd t`kma`m`a`r mmckfr7
!! #$%&'()*)+# $*
%&'% *,-.
!! #$%&'()*)/)
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
_dmjhaic Jiimd Fk!trmd!! 5 10=0
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
_dmjhaic Jiimfdk _`ys`a Jiimd Fk!trmd
! _dmjhaic ha`r`c bstdrimfd ha`k s`ys`a ie`fdadr !u !dciafd s`ys`afd"dradrikd c`vu!ura`r7
!! #$%&'(CIG+# $CIG!! \*&3%*:#$_H6,:0(#+\*&3%*:# $ F@DFFF
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
_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
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
Fdkcadmi _`fdad!tirmdc! Jir fdkcadmi s`fdad!tirmdc iik %3'K:3=&
chmutu cuaa`kar.!! \$(MRLTC7M+I(MRJ9J7M+.!! %3'K:3=&(\+*4% $M T J
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
_dmjhaic "ktdbr`a "!admi! _dmjhaic iktdbr`a `am` ehkcsiyhku ikt haup bdkda ehrm`t7
!
341(\+, _ik jdairsiz iktdbr`aiki `ar.
! 341(\/2+, _ik vyd brd jdairsiz iktdbr`aiki `ar.
! 341(\/*/,+,_ik v`rs`ya`k sdmjhaic fd"i!cdkd brd `f`k jydc`f`r jdairai iktdbr`aiki ar.
! 341(\/*/,/2+,_ik vyd brd `f`k jyd c`f`r jdairai iktdbr`aiki `ar.
! !dcaikfdfir.
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
_dmjhaic "ktdbr`a "!admi
! +"" fxxx ):
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
_dmjhaic Vrdv! Vrdv `am` i!admikfd cuaa`ka`k ehkcsiyhk `f fiee haup sdmjhaic i!adm
m`kt" drdvdsikfd bdkda ehrm`t7
! _3==(\+, _ik trdviki `ar.
! _3==(\/2+, _ik vyd brd trdviki `ar.
! _3==(\/4+, k phzitie jir t`ms`y ham`c zdrd k. fdrdodfdk trdviki `ar.
!
_3==(\/)2)/4+vdy` fiee(_,k,'v'), _ik vyd brd k. fdrdodfdk trdviki`ar.
! !dcaikfdfir.
! Vrdvik x=pfdci fd"driki juam`c iik %6,%(16
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
_dmjhaic Vrdv
e(x)=4x?+`x:+jx -06 (` vd j s`jit fd"drfir)
ehkcsiyhkukuk trdviki juaukuz.!! %&'% * , M!! =$G7MRL9*7MRJ9,7MTNC.!! _3==(=+*4% $
NG7MRJ 9 J7*7M 9 ,!! K
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
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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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
Fiedr`ksiyda Fdkcadmadrik _dmjhaic zm
#dcaikfd jir fiedr`ksiyda fdkcadmik zm `!`"f`ci bijifir.
!"
!!! ! ! !"! ! ! !
! [M$_%H:20()]M9M$-H%(1+91)+ 5%;4;< Q*
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_dauc kivdrsitdsi | Dmrd zj`y | shruLdmrdhzj`y.kdt
Fiedr`ksiyda Fdkcadmadrik _dmjhaic zm
#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
!!!
!!! ! !"#!!!!
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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
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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`m`a
! Ndfde ca`sradrfdk jirikfd ha`k fhsy`a`r iad `yk isimfd ham`m`a
! 9&$7'#3$ ie`fdsi iad j`!a`m`a
! Ehkcsiyhk `f iad fhsy` `f `yk ham`a
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Ehkcsiyhk V kma`m`
#fd`a b`z fdkcadmikfd n`omi jua`k jir ehkcsiyhk y`z`am.
Bifiadr7J`sk (\), Mha s`ys (k), _o`cac (V)
cta`r7N`oim (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
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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.
!
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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>
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M`ktcs`a !"`rdtiadr
"!`rdt @ka`m
& vd
! vdy`
~ fd"ia
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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
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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