Download - Práctica 2 Series Exponenciales de Fourier
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7/23/2019 Prctica 2 Series Exponenciales de Fourier
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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=
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lkgap 5 jaz gap $ k zhg gap /2m(
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c/p( 5ja
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^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;
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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
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pmebhlg lz ~azhbfl abplglrfaz `l c/p(' ^mrm mjfmrmr lzpa& zl jmfj|fm `l fm zhi|hlgpl emglrm;
ja 5=
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ja 5=
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c/p(zhg gap `p
ja 5 =P
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c/p(/jaz gap k zhg gap `p( |phfh{mg`a fm h`lgph`m` `l L|flr /2b(
jg 5=
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c/p( lkgap `p /0(
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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>
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Aprm lx~fhjmjhag m fa mgplrhar zlrm omjlr fm zhi|hlgpl hi|mf`m`;
jg 5=
2/mg kbg( /
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:
Chi|rm = Zlmf @hlgpl `l Zhlrrm
Chi|rm 2 Zlmf Zlgah`mf jag Rljphchjmjhg `l Ag`m Jae~flpm
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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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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
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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((
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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'
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^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
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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'