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^rmjphjm Ga'>2^rmjphjm Ga'>2^rmjphjm Ga'>2Fm Zlrhl Jae~flkm `l Ca|rhlrFm Zlrhl Jae~flkm `l Ca|rhlrFm Zlrhl Jae~flkm `l Ca|rhlr

Zlgmflz ^lrha`hjmz rl~rlzlgpm`mz jag Zlrhlz Lx~aglgjhmflzZlgmflz ^lrha`hjmz rl~rlzlgpm`mz jag Zlrhlz Lx~aglgjhmflzZlgmflz ^lrha`hjmz rl~rlzlgpm`mz jag Zlrhlz Lx~aglgjhmflz

C\G@MELGPAZ PL ARHJAZ

@l mj|lr`a m fm ~rmjphjm mgplrhar& zmbleaz }|l fmz zlgmflz zl ~|l`lg lx~rlzmr el`hmgpl z| m~raxhemjhag jag

fm zlrhl prhiagaelprhjm `l Ca|rhlr;

c/p( 5=

2ma $

g5=

/mg jaz gap $ bg zhg gap( /=(

^lra& pmebhlg ~a`leaz lx~rlzmrfm `l carem emz jae~mjpm rl~rlzlgpmg`a fmz c|gjhaglz zlga jazlga lgcarem lx~aglgjhmf |phfh{mg`a fm h`lgph`m` `l L|flr'

lkgap 5 jaz gap $ k zhg gap /2m(

lkgap 5 jaz gapk zhg gap /2b(

jaz gap 5=

2 lkgap $ lkgap

/2j(

zhg gap 5 =k2

lkgap

lkgap

/2`(

Z|zphp|lg`a /2j( /2`( lg /=( mir|~mg`a plrehgaz `mg f|imr m;

Z|zphp|lg`a /2j( /2`( lg /=(

c/p( 5=

2ma $

g5=

mg

2

lkgap $ lkgap

$

bg

k2

lkgap lkgap

zl cmjparh{m =

2

5=

2ma $

=

2

g5= mg lkgap $ lkgapkbg l

kgap lkgap `lzmrraffa mir|~mjhag `l plrehgaz

5=

2ma $

=

2

g5=

/mg kbg( l

kgap $ /mg $ kbg( lkgap

@l lzpm |fphem lj|mjhag& ~a`leaz `lghr |g g|lsa jaljhlgpl jg `l emglrm }|l;

ja

25

ma

2

jg 5mg kbg

2

jg 5 j

g 5mg $ kbg

2

Lgpagjlz c/p( zl jagshlrpl lg;

c/p( 5ja

2$

g5=

jgl

kgap $ jglkgap

^lra zh e|fph~fhjmeaz m g ~ar %='

c/p( 5ja

2$

g5=

jglkgap $

g5=

jglkgap

Moarm plgleaz `az plrehgaz hi|mflz lg fmz z|emparhmz& ~ar pmgpa fmz ~a`leaz |ghr ~mrm caremr |gm g|lsmz|emparhm jag g|lsaz fehplz;

=

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c/p( 5ja

2$

g5

jglkgap z|emparhm hg`lgh`m ~mrm g 5 >

^lra lg lzpm lj|mjhag fm z|emparhm lz hg`lgh`m ~mrm g 5 >& ~ar pmgpa zh fm z|emparhm hgjf|l mf smfar~rael`ha ja fm lj|mjhag zl `lghrm `l fm zhi|hlgpl emglrm;

c/p( 5

g5 j

gl

kgap

/:(

Jaea ~a`leaz slr moarm fm lj|mjhag /=( lzpm rl~rlzlgpm`m lg plrehgaz `l |gm zafm lx~aglgjhmf' ^ar pmgpa&fmz zlgmflz }|l`mrmg rl~rlzlgpm`mz `l fm carem eazprm`m lg fm lj|mjhag /:(& `hjom lj|mjhag zl jagajl jaeaZlrhl Lx~aglgjhmf a Jae~flkm `l Ca|rhlr' Zhlg`a lzpm emz jae~mjpm }|l /=(& m|g}|l faz jaljhlgplz `lfm zlrhl lx~aglgjhmf `l Ca|rhlr& jg& pmebhlg ~|l`lg abplglrzl `l mg bg |zmg`a `lghjhaglz ~mrm ja& jg& j

g

pmebhlg lz ~azhbfl abplglrfaz `l c/p(' ^mrm mjfmrmr lzpa& zl jmfj|fm `l fm zhi|hlgpl emglrm;

ja 5=

2/mg kbg( |phfh{mg`a fmz lj|mjhaglz l mg bg `l fm Z'P'C'

ja 5=

P

P!2P!2

c/p(jaz gap `pk

P!2P!2

c/p(zhg gap `p

ja 5 =P

P!2P!2

c/p(/jaz gap k zhg gap `p( |phfh{mg`a fm h`lgph`m` `l L|flr /2b(

jg 5=

P

P!2P!2

c/p( lkgap `p /0(

`ag`l a 52

P'

Fmz zlrhlz lx~aglgjhmflz prhiagaelprhjmz `l Ca|rhlr ga zag `az ph~az `hclrlgplz `l zlrhlz& zhga `az caremz`hzphgpmz `l lx~rlzmr fm ehzem zlrhl' Zl ~|l`lg abplglr faz jaljhlgplz `l |gm `l fmz zlrhlz m ~mrphr `l fm aprm'Lz `ljhr& zh }|lrleaz omffmr faz jaljhlgplz mg bg omffmr fm zlrhl prhiagaelprhjm `l Ca|rhlr ~mrphlg`a `lfjaljhlgpl jg `l fm zlrhl jae~flkm `l Ca|rhlr& zafa bmzpm mjfmrmr fa zhi|hlgpl;

ma 5 j>

mg 5 jg $ jg 5 jg $ j

g 5 2Rl TjgU

bg 5 k /jg jg( 5 k /jg j

g( 5 2He TjgU

Aprm lx~fhjmjhag m fa mgplrhar zlrm omjlr fm zhi|hlgpl hi|mf`m`;

jg 5=

2/mg kbg( /

7/23/2019 Prctica 2 Series Exponenciales de Fourier

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:

Chi|rm = Zlmf @hlgpl `l Zhlrrm

Chi|rm 2 Zlmf Zlgah`mf jag Rljphchjmjhg `l Ag`m Jae~flpm

7/23/2019 Prctica 2 Series Exponenciales de Fourier

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0

J@HIA LG EMPFMB Lklrjhjha =

,Jae|ghjmjhaglz = ^mrjhmf =,[lrg Olrgg`l{ Mflkmg`ra Rmf Ir|~a; 0BS2,Mgfhzhz l Zlmflz el`hmgpl Zlrhlz Jae~flkmz a Lx~aglgjhmflz l Ca|rhlr,Cljom fphem Ea`hjmjhg;

jflmr mff& jfjjfazl mffcaremp fagic~rhgpc/)VpVpZLRHLZ PRHIAGAEPRHJM X L_^AGLGJHMF @L CA\RHLR /^MRPL =(VgVg[lrg O`l{' Mflkmg`ra R'VgVg)(4

d5hg~|p/)Hgpra`|jl lf Ga' `l Mreghjaz }|l m~raxhelg m fm zlmf; )(4P524 ya52+~h!P4pa5>;~h!=>>;0';~h!=>>;24 p252;~h!=>>;04=5='>=;=4car g5=;d

jg5:!/2+g+~h(4i5jg+rlmf/lx~/h+~h+/g+p%/~h!2((((4JC5mj|e $ i4mj|e5JC4

lg`JC5='

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'>?239::

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Chi|rm 8 L= \phfh{mg`a mreghjaz `l fm ZPC

LRRAR 5 >'>>8>2?:2=0

Chi|rm => LK = \phfh{mg`a mreghjaz l fm ZJC

Chi|rm == L= \phfh{mg`a =>> mreghjaz l fm ZPC

LRRAR 5 >'>>0 mreghjaz l fm ZJC

7/23/2019 Prctica 2 Series Exponenciales de Fourier

8/9

?

J@HIA LG EMPFMB Lklrjhjha 2

,Jae|ghjmjhaglz = ^mrjhmf =,[lrg Olrgg`l{ Mflkmg`ra Rmf Ir|~a; 0BS2,Mgfhzhz `l Zlmflz el`hmgpl Zlrhlz Jae~flkmz a Lx~aglgjhmflz `l Ca|rhlr,Cljom fphem Ea`hjmjhg;

jflmr mff& jfjjfazl mffcaremp fagic~rhgpc/)VpVpZLRHLZ PRHIAGAEPRHJM X L_^AGLGJHMF @L CA\RHLR /^MRPL 2(VgVg[lrg O`l{' Mflkmg`raR'VgVg)(4d5hg~|p/)Hgpra`|jl lf Ga' `l Mreghjaz }|l m~raxhelg m fm zlmf; )(4P5=4 ya52+~h!P4M 5 hg~|p/)Hgpra`|jl fm me~fhp|` `l fm zlmf; )(4

,Irchjm `l c/p( arhihgmfx5%:;'>>=;:45mbz/M+zhg/x((4~fap/x&&)d)&)FhglYh`po)&2(oaf` ag

,Mj|e|fm`arlzmj|e5>4 mj|eQL5>4zez p

,@lzmrraffa `l fm Zlrhl Prhiagaeprhjm `l Ca|rhlrcar g5=;dmg5/M!/~h+/0+gW2%=(((4c5mg+jaz/2+g+~h+p(4C5mj|e $ c4mj|e5C4l5mj|eQL$mgW24mj|eQL5l4

lg`

,Irchjm `l fm Zlrhl Prhiagaeprhjm `l Ca|rhlrC5/M!2(%C4C5z|bz/C&x(4~fap/x&C&)%%r)&)FhglYh`po)&2(

mj|e5>4car g5=;d

jg52+M!/~h+/0+/gW2(%=((4{5h+2+g+~h4z5jg+rlmf/lx~/%{((4Z5mj|e$z4mj|e5Z4

lg`

,Irchjm `l fm c|gjhg lx~aglgjhmf `l Ca|rhlrZ5M!2 % Z4Z5z|bz/Z&x(4chi|rl/2(~fap/x&Z(

, Lrrar j|m`rphja el`hac~rhgpc/)VgLf lrrar j|m`rphja el`ha lz;)(4L^Z5/=!P(+/MW2%l+/P!2((

7/23/2019 Prctica 2 Series Exponenciales de Fourier

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8

ABZLRSMJHAGLZ X JAELGPMRHAZ

Ol `l omjlr gcmzhz `l j|rhazh`m` mf jmfj|fmr lf lrrar j|m`rphja' Zh j|e~fheaz fm cre|fm `lf lrrar j|m`rphja el`ha& fmzlrhl zl hbm m~raxhemg`a /jaea zl sha lg fmz irchjmz( mf hr m|elgpmg`a faz mreghjaz `l fm Zlrhl Prhiagaeprhjm `lCa|rhlr& ~lra lf lrrar& lg sl{ `l hr `hzehg|lg`a& hbm m|elgpmg`a' ^ar fa }|l lf lrrar zl jmfj|f `l aprm emglrm&GAREMFH[MG@A FM C\GJHG'

JAGJF\ZHAGLZ

^a`leaz `ljhr }|l fm zlrhl jae~flkm `l Ca|rhlr a lx~aglgjhmf lz fm emglrm ez zlgjhffm r~h`m ~mrm omjlr lf mgfhzhz`l |gm zlmf ~lrh`hjm' X zh lz gljlzmrha lx~rlzmr lzpm zlrhl lg prehgaz `l c|gjhaglz zhg|zah`mflz& zfa bmzpm lg omjlrfm a~lrmjhg elgjhagm`m lg lf C\G@MELGPA PLRHJA

RLCLRLGJHMZ

T=U MFL_MG@LR& JOMRFLZ # ZM@HD\& EMPOLY G'A'4 C|g`melgpaz `l Jhrj|hpaz Lfjprhjaz& :rm' L`'&

EjIrmyOhff& Exhja& 2>>9' Jm~p|fa =9 Fmz zlrhlz `l Ca|rhlr& ~iz' Jagz|fpm`mz' 9?= m 9?9'

T2U FMPOH& B' '& Ea`lrg @hihpmf mg` Mgmfai Jaee|ghjmphag Zzplez& :rm' L`'& Axcar` \ghslrzhp rlzz& Gly

Xard& =88?' Jom~plr 2; Hgpra`|jphag pa Zhigmfz& ~milz'