CE00998 Coding and Transformations

Assignment 1 : Fourier Series

ABBAS Thomas - Group1 - EFREI For Monday 19th October 2009

1. a) f(x) = -1 for -1 <x< 0 T=2

-1+2*sin(x*Pi) for 0 <x< 1

restart:with(plots):alias(u=Heaviside):assume(n,integer):T:=2:

f:=x->(-1)*(u(x+1)-u(x))+(2*sin(Pi*x)-1)*(u(x)-u(x-1));

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgtSSJ1R0YlNiMsJjkkIiIiRi9GLyEiIi1GKzYjRi5GLyomLCYtSSRzaW5HRiU2IyomSSNQaUclKnByb3RlY3RlZEdGL0YuRi8iIiNGMEYvRi8sJkYxRi8tRis2IywmRi5GL0YwRi9GMEYvRi9GJUYlRiU=

N:=25:a:=array([],0..N):b:=array([],0..N):

a[0] := factor(2*integrate(f(x), x = -1 .. 1)/T);

LCQqJiwmISIjIiIiSSNQaUclKnByb3RlY3RlZEdGJkYmRichIiJGJQ==

for n from 1 to N do a[n]:=2/T*int(f(x)*cos(2*n*Pi*x/T),x=-1..1); b[n]:=2/T*int(f(x)*sin(2*n*Pi*x/T),x=-1..1); end do:n:='n':

F:=x->a[0]/2+sum(a[n]*cos(2*n*Pi*x/T)+b[n]*sin(2*n*x*Pi/T),n=1..M);plot([subs(f(x)),subs(M=2,F(x))],x=-1..1,thickness=2);plot([subs(f(x)),subs(M=5,F(x))],x=-1..1,thickness=2);plot([subs(f(x)),subs(M=25,F(x))],x=-1..1,thickness=2);

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYmSSJhR0YlNiMiIiEjIiIiIiIjLUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQsJiomJkYrNiNJIm5HRiVGLy1JJGNvc0dGMzYjLCQqKkY7Ri9JI1BpR0Y0Ri85JEYvSSJUR0YlISIiRjBGL0YvKiYmSSJiR0YlRjpGLy1JJHNpbkdGM0Y+Ri9GLy9GOztGL0kiTUdGJUYvRiVGJUYl

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

-%%PLOTG6(-%'CURVESG6$7dp7$$!#5!""%*undefinedG7$$!1MekynP')**!#;$!#5!""7$$!1n;HdNvs**!#;$!#5!""7$$!/v$fLI"f**!#9$!#5!""7$$!1MLe9r]X**!#;$!#5!""7$$!1,](=ng#=**!#;$!#5!""7$$!1nm;HU,"*)*!#;$!#5!""7$$!-vV8_O)*!#7$!#5!""7$$!1MLLe%G?y*!#;$!#5!""7$$!,voUIn*!#6$!#5!""7$$!1nmm;p0k&*!#;$!#5!""7$$!-vV5Su$*!#7$!#5!""7$$!1LL$3<XZ=*!#;$!#5!""7$$!1nmmT%p"e()!#;$!#5!""7$$!1mmm"4m(G$)!#;$!#5!""7$$!1ML$3i.9!z!#;$!#5!""7$$!1nm;/R=0v!#;$!#5!""7$$!,vL@\4(!#6$!#5!""7$$!1nm;/siqm!#;$!#5!""7$$!,vy$pZi!#6$!#5!""7$$!1LLL$yaE"e!#;$!#5!""7$$!1nmm">s%Ha!#;$!#5!""7$$!2/+++N*4)*\!#<$!#5!""7$$!*Db\c%!"*$!#5!""7$$!*lSv9%!"*$!#5!""7$$!1nm;/#)[oP!#;$!#5!""7$$!2OLLL=exJ$!#<$!#5!""7$$!1MLLL2$f$H!#;$!#5!""7$$!20++vju<\#!#<$!#5!""7$$!2VLLLB@')4#!#<$!#5!""7$$!2'****\P'psm"!#<$!#5!""7$$!,D"4_c7!#6$!#5!""7$$!1JLL$3x%z#)!#<$!#5!""7$$!1MLL3s$QM%!#<$!#5!""7$$!29++Dcx7A#!#=$!#5!""7$$!1^omm;zr)*!#>$!#5!""7$$"2UKL3-Dg5#!#=$!1hH'ym5xn)!#;7$$"1<LLezw5V!#<$!1n73'HO(*H(!#;7$$"1`mmmJ+Ii!#<$!1l5p)G<06'!#;7$$"0****\PQ#\")!#;$!2vXK?&RVN\!#<7$$"2cm;z\1A-"!#<$!2(=d()3I6(o$!#<7$$"2BLL$e"*[H7!#<$!2i2(*e$HblC!#<7$$"2emm"HCjV9!#<$!2J@P[.jrB"!#<7$$"2$*******pvxl"!#<$!006*QN#=%[!#<7$$"2')***\7JFn=!#<$"2&=EpcX+r5!#<7$$"1)****\_qn2#!#;$"1dl=I&)[U@!#;7$$"2#)**\P/q%zA!#<$"2C)Rx;M?HJ!#<7$$"2%)***\i&p@[#!#<$"2c#[&oh&piS!#<7$$"1)****\2'HKH!#;$"16y>prlEf!#;7$$"1lmmmZvOL!#;$"1miw<oCJt!#;7$$"2'******\2goP!#<$"1%*)3g()**>_)!#;7$$"2CLLeR<*fT!#<$"1-M"*)Q(\2$*!#;7$$"1mm"HiBQP%!#;$"1_B&)yAE9'*!#;7$$"2(******\)Hxe%!#<$"1V5f%)R[K)*!#;7$$"1m;z%Rk$)o%!#;$"1rZgXhA/**!#;7$$"1KLeR*)**)y%!#;$"0Zb-=vg&**!#:7$$"2$)*\P%[L'*)[!#<$"/EUo#zz)**!#97$$"2Ymm"H!o-*\!#<$"19'4Q_1*****!#;7$$"1)****\7ga4&!#;$"18EMjo+"***!#;7$$"1KL$3A_1?&!#;$"0>sC$oFg**!#:7$$"1mmm;V%eI&!#;$"17bo))*\x!**!#;7$$"1****\7k.6a!#;$"1=wz"p$[L)*!#;7$$"1KLe9as;c!#;$"1J\,7AyD'*!#;7$$"1mmm;WTAe!#;$"1ZODi#fhL*!#;7$$"1****\i!*3`i!#;$"1fhX*Qa,Z)!#;7$$"1MLLL*zym'!#;$"1`Q&zA&p;t!#;7$$"1LLL3N1#4(!#;$"1'ykAf9O$e!#;7$$"1mm;HYt7v!#;$"20?x88Wa3%!#<7$$"1LLek6,1x!#;$"2YAV#)f#)y>$!#<7$$")xG**y!")$"1(*)f]6x;E#!#;7$$"1LL$3U/37)!#;$"2sD0C(QJL6!#<7$$"1mmmT6KU$)!#;$!1$p'pyTg%*[!#=7$$",vL[/a)!#6$!2Y5EPHht9"!#<7$$"1LLLLbdQ()!#;$!2al.C$G1!G#!#<7$$"1nm"zW?)\*)!#;$!101i6Ve?N!#;7$$",DOl5;*!#6$!2'3FZ0Bj*y%!#<7$$")PDj$*!")$!1c"zwBMe-'!#;7$$",v.Uac*!#6$!1WO!=Pl!ys!#;7$$".D"G:3u'*!#8$!1E+B%4qd&z!#;7$$"-v=5s#y*!#7$!1H`8Ne&ej)!#;7$$"/D1k2/P)*!#9$!1K(y)HTaw*)!#;7$$".v$40O"*)*!#8$!1b&)3k/`<$*!#;7$$"1^7.#Q?&=**!#;$!1"[()yO/")[*!#;7$$"/voa-oX**!#9$!1Fn]Rbre'*!#;7$$"1Cc,">g#f**!#;$!1%pO#>7.W(*!#;7$$"0vVt7SG(**!#:$!1()p%yb^$H)*!#;7$$"1v=nj+U')**!#;$!1"fCC+vY"**!#;7$$"#5!""%*undefinedG-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'CURVESG6$7ep7$$!#5!""$!1nH0"4_`u*!#;7$$!1MLe9r]X**!#;$!1mtk1>P$*)*!#;7$$!1nm;HU,"*)*!#;$!1#[$)py6k***!#;7$$!-vV8_O)*!#7$!2Yz'*3)y%e+"!#;7$$!1MLLe%G?y*!#;$!2eiA21!e35!#;7$$!1nm"HdNvs*!#;$!1%3G8S;'35!#:7$$!,voUIn*!#6$!2Q<1h*4"o+"!#;7$$!1ML3-)\&='*!#;$!1<)eO^3S+"!#:7$$!1nmm;p0k&*!#;$!1L1H&Ql4+"!#:7$$!1L$3-)*G#p%*!#;$!1s'*>qs(y'**!#;7$$!-vV5Su$*!#7$!1E3!R<*p`**!#;7$$!1n;H2Jdz#*!#;$!1"[;#Hg#o'**!#;7$$!1LL$3<XZ=*!#;$!1$o&[x)*R%***!#;7$$!1nmmT%p"e()!#;$!1')e,'ePi***!#;7$$!1mmm"4m(G$)!#;$!2tDXp-C3+"!#;7$$!1ML$3i.9!z!#;$!1*)H'fEe(*)**!#;7$$!1nm;/R=0v!#;$!2#*o0\G$)3+"!#;7$$!,vL@\4(!#6$!/zy%\\6***!#97$$!1nm;/siqm!#;$!28u$H*3m4+"!#;7$$!,vy$pZi!#6$!14ObZB#**)**!#;7$$!1LLL$yaE"e!#;$!22q")QRT5+"!#;7$$!1nmm">s%Ha!#;$!1Z$QQV`+***!#;7$$!2/+++N*4)*\!#<$!2/x5"f_,,5!#;7$$!*Db\c%!"*$!1Yq)Gdo,***!#;7$$!*lSv9%!"*$!1rkKg\&4+"!#:7$$!1nm;/#)[oP!#;$!1yCt=GZ*)**!#;7$$!2OLLL=exJ$!#<$!2y10uS.4+"!#;7$$!1MLLL2$f$H!#;$!1NPJsNE*)**!#;7$$!20++vju<\#!#<$!1P"Gz"o&3+"!#:7$$!2VLLLB@')4#!#<$!1y1gUev*)**!#;7$$!2'****\P'psm"!#<$!2*4Ui:"o2+"!#;7$$!,D"4_c7!#6$!1Ad3,UL$***!#;7$$!1JLL$3x%z#)!#<$!1;PrqRE)***!#;7$$!1KLe9rc&H(!#<$!18U,w#="p**!#;7$$!1LL$e9d;J'!#<$!1jEEelz`**!#;7$$!2NL$3xruF`!#=$!1O0GGSEn**!#;7$$!1MLL3s$QM%!#<$!1&)GPj)\5+"!#:7$$!1,](oH(>8Q!#<$!2P4*p'y:S+"!#;7$$!1omT&QdDG$!#<$!2pbJGe_n+"!#;7$$!2YLeRZ<>v#!#=$!2(e"y&=Ec35!#;7$$!29++Dcx7A#!#=$!2(Q%="[sm35!#;7$$!2#o;/^wj!p"!#=$!2y"Q*)[bF15!#;7$$!1NLeRx**f6!#<$!1)>'4K'e1+"!#:7$$!1<+D"GyNH'!#=$!1*R3AU4A"**!#;7$$!1^omm;zr)*!#>$!1<:*R:,cx*!#;7$$"2UKL3-Dg5#!#=$!1KPehmdh()!#;7$$"1<LLezw5V!#<$!1`!z=?O?J(!#;7$$"1`mmmJ+Ii!#<$!1#\p;R/U1'!#;7$$"0****\PQ#\")!#;$!17H$4EK(H\!#;7$$"2cm;z\1A-"!#<$!1-;(R4"y<P!#;7$$"2BLL$e"*[H7!#<$!2oi_@1?VY#!#<7$$"2emm"HCjV9!#<$!29rplaB\@"!#<7$$"2$*******pvxl"!#<$!1uF)o='3sa!#=7$$"2')***\7JFn=!#<$"1CFhfpTa5!#;7$$"1)****\_qn2#!#;$"2#oPxO3W]@!#<7$$"2#)**\P/q%zA!#<$"1A+.L)4C9$!#;7$$"2%)***\i&p@[#!#<$"1r;H]$)*\0%!#;7$$"1)****\2'HKH!#;$"0C>C$Q?Pf!#:7$$"1lmmmZvOL!#;$"1uv]k0B@t!#;7$$"2'******\2goP!#<$"1V"ekeHD`)!#;7$$"2CLLeR<*fT!#<$"1LHEFGd(H*!#;7$$"1mm"HiBQP%!#;$"12!H!3&*)>h*!#;7$$"2(******\)Hxe%!#<$"1sy,&=kE%)*!#;7$$"1m;z%Rk$)o%!#;$"1s*=+")=@"**!#;7$$"1KLeR*)**)y%!#;$"1PK%*>m+d**!#;7$$"2$)*\P%[L'*)[!#<$"1(=:NhC9)**!#;7$$"2Ymm"H!o-*\!#<$"1GQT$e#y*)**!#;7$$"1)****\7ga4&!#;$"1#)=(e)))e$)**!#;7$$"1KL$3A_1?&!#;$"0&y<P)z.'**!#:7$$"1mmm;V%eI&!#;$"0P`*\#Q`"**!#:7$$"1****\7k.6a!#;$"1LfL-NnV)*!#;7$$"1KLe9as;c!#;$"19YigzEC'*!#;7$$"1mmm;WTAe!#;$"1u7'HYkeK*!#;7$$"1****\i!*3`i!#;$"1\TCA\/![)!#;7$$"1MLLL*zym'!#;$"1Ns\)3)*oI(!#;7$$"1LLL3N1#4(!#;$"1'yJ:([mUe!#;7$$"1mm;HYt7v!#;$"1b#pBLys2%!#;7$$"1LLek6,1x!#;$"1&y.(zY/5K!#;7$$")xG**y!")$"2K)pmgN7sA!#<7$$"1LL$3U/37)!#;$"2V2!ol(pv6"!#<7$$"1mmmT6KU$)!#;$!1-$*Q,PVBb!#=7$$",vL[/a)!#6$!2D9ibSQg7"!#<7$$"1LLLLbdQ()!#;$!1'>=b')fCF#!#;7$$"1nm"zW?)\*)!#;$!1#y9sf$3]N!#;7$$",DOl5;*!#6$!2;mWlIt6z%!#<7$$")PDj$*!")$!1xF,.[#)zf!#;7$$",v.Uac*!#6$!1Eqtf%p%)G(!#;7$$"-v=5s#y*!#7$!08?9)f\@()!#:7$$"#5!""$!1lH0"4_`u*!#;-%&COLORG6&%$RGBG$"2'\_'eM%yg>!#<$"1ij9.e@R!)!#;$"2'\_'eM%yg>!#<-%%VIEWG6$;$!#5!""$"#5!""%(DEFAULTG-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%*THICKNESSG6#""#-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"$?"!""-%-BOUNDS_WIDTHG6#$"%!z$!""-%.BOUNDS_HEIGHTG6#$"%qP!""-%)CHILDRENG6"

b) f(x) = x+1 for -1 <x< 0 T=2

x-1 for 0 <x< 1

restart:with(plots):alias(u=Heaviside):assume(n,integer):T:=2:

f:=x->(x+1)*(u(x+1)-u(x)) + (x-1)*(u(x)-u(x-1));

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmOSQiIiJGLUYtRi0sJi1JInVHRiU2I0YrRi0tRjA2I0YsISIiRi1GLSomLCZGLEYtRjRGLUYtLCZGMkYtLUYwNiNGNkY0Ri1GLUYlRiVGJQ==

N:=25:a:=array([],0..N):b:=array([],0..N):

a[0] := factor(2*integrate(f(x), x = -1 .. 1)/T);

IiIh

for n from 1 to N do a[n]:=2/T*int(f(x)*cos(2*n*Pi*x/T),x=-1..1); b[n]:=2/T*int(f(x)*sin(2*n*Pi*x/T),x=-1..1); end do:n:='n':

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYmSSJhR0YlNiMiIiEjIiIiIiIjLUkkc3VtR0YlNiQsJiomJkYrNiNJIm5HRiVGLy1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqKkY4Ri9JI1BpR0Y8Ri85JEYvSSJUR0YlISIiRjBGL0YvKiYmSSJiR0YlRjdGLy1JJHNpbkdGO0Y+Ri9GLy9GODtGL0kiTUdGJUYvRiVGJUYl

-%%PLOTG6(-%'CURVESG6$7\p7$$!#5!""%*undefinedG7$$!1MekynP')**!#;$"2$\mTN@Ki8!#>7$$!1n;HdNvs**!#;$"2&)HL3FWYs#!#>7$$!/v$fLI"f**!#9$"1[*\iSmp3%!#=7$$!1MLe9r]X**!#;$"1(fm;a)G\a!#=7$$!1,](=ng#=**!#;$"1'*)*\7G$R<)!#=7$$!1nm;HU,"*)*!#;$"20LL$3x&)*3"!#=7$$!-vV8_O)*!#7$"28++Dc'yM;!#=7$$!1MLLe%G?y*!#;$"1hmm;arz@!#<7$$!,voUIn*!#6$"2E++]7t&pK!#=7$$!1nmm;p0k&*!#;$"1LLLL3VfV!#<7$$!-vV5Su$*!#7$"1(***\i&*)fD'!#<7$$!1LL$3<XZ=*!#;$"1smm"H[D:)!#<7$$!1nmmT%p"e()!#;$"2LLL$e0$=C"!#<7$$!1mmm"4m(G$)!#;$"2RLL$3RBr;!#<7$$!1ML$3i.9!z!#;$"2imm"zjf)4#!#<7$$!1nm;/R=0v!#;$"2KLLe4;[\#!#<7$$!,vL@\4(!#6$",Dmy]!H!#67$$!1nm;/siqm!#;$"1LL$ezs$HL!#;7$$!,vy$pZi!#6$"2&****\7iI_P!#<7$$!1LLL$yaE"e!#;$"1nmm;_M(=%!#;7$$!1nmm">s%Ha!#;$"2MLL$3y_qX!#<7$$!2/+++N*4)*\!#<$"*l+>+&!"*7$$!*Db\c%!"*$"*vW]V&!"*7$$!*lSv9%!"*$"*NfC&e!"*7$$!1nm;/#)[oP!#;$"1LL$ez6:B'!#;7$$!2OLLL=exJ$!#<$"1mmm;=C#o'!#;7$$!1MLLL2$f$H!#;$"1mmmm#pS1(!#;7$$!20++vju<\#!#<$",DOD#3v!#67$$!2VLLLB@')4#!#<$"1mmmm(y8!z!#;7$$!2'****\P'psm"!#<$",DOIFL)!#67$$!,D"4_c7!#6$",v3zMu)!#67$$!1JLL$3x%z#)!#<$"1nmm"H_?<*!#;7$$!1MLL3s$QM%!#<$"1nm;zihl&*!#;7$$!29++Dcx7A#!#=$"-vVA(yx*!#77$$!1^omm;zr)*!#>$"1LLL3#G,***!#;7$$"1."3Fp^y!R!#>$!1#H2$[@4'***!#;7$$"2eI3_]\(o<!#>$!1<z%\]7B)**!#;7$$"1,e9TQrYJ!#=$!1U&)ehG`o**!#;7$$"1(H$3x"yY_%!#=$!1m"H#=Kva**!#;7$$"1)Ge*[og!G(!#=$!1</^JR>F**!#;7$$"2yK$3_Nl.5!#=$!1n;zWYj**)*!#;7$$"1E$ekGR[b"!#<$!1oTNrg^W)*!#;7$$"2UKL3-Dg5#!#=$!1om"z\(R*y*!#;7$$"21K$e*['R3K!#=$!1o;/^.;z'*!#;7$$"1<LLezw5V!#<$!1om;/K#*o&*!#;7$$"1`mmmJ+Ii!#<$!1NLL$o**pP*!#;7$$"0****\PQ#\")!#;$!1,+]ih2&=*!#;7$$"2BLL$e"*[H7!#<$!1ommT3^q()!#;7$$"2$*******pvxl"!#<$!1,+++VAU$)!#;7$$"1)****\_qn2#!#;$!1-++v%HK#z!#;7$$"2%)***\i&p@[#!#<$!1-+]P/$y^(!#;7$$"1)****\2'HKH!#;$!1-++DRqnq!#;7$$"1lmmmZvOL!#;$!1NLLL_Cjm!#;7$$"2'******\2goP!#<$!*D*RJi!"*7$$"2CLLeR<*fT!#<$!1om;/E3Se!#;7$$"2(******\)Hxe%!#<$!*:qAT&!"*7$$"2Ymm"H!o-*\!#<$!1NL$3(>t4]!#;7$$"1****\7k.6a!#;$!1,+](ej*)e%!#;7$$"1mmm;WTAe!#;$!1MLL$e&exT!#;7$$"1****\i!*3`i!#;$!1,+]P4"pu$!#;7$$"1MLLL*zym'!#;$!1mmmm+7KL!#;7$$"1LLL3N1#4(!#;$!1nmm"\Oz!H!#;7$$"1mm;HYt7v!#;$!2PLL3Pls[#!#<7$$")xG**y!")$!20+++I725#!#<7$$"1mmmT6KU$)!#;$!2NLL$e)ywl"!#<7$$"1LLLLbdQ()!#;$!2ummmYC9E"!#<7$$",DOl5;*!#6$!1&****\PY$*Q)!#<7$$")PDj$*!")$!1&*******HYnj!#<7$$",v.Uac*!#6$!2c****\izbM%!#=7$$".D"G:3u'*!#8$!1(**\(=Z=fK!#<7$$"-v=5s#y*!#7$!2y***\7)*ys@!#=7$$"/D1k2/P)*!#9$!2%)*\PfBfH;!#=7$$".v$40O"*)*!#8$!2*)**\i!\R'3"!#=7$$"1^7.#Q?&=**!#;$!1O\(ozhz9)!#=7$$"/voa-oX**!#9$!2X**\7`u>V&!#>7$$"1Cc,">g#f**!#;$!1zvV)*3)R2%!#=7$$"0vVt7SG(**!#:$!2G0DcE()fr#!#>7$$"1v=nj+U')**!#;$!2k_7Gj$*zN"!#>7$$"#5!""%*undefinedG-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'CURVESG6$7_z7$$!#5!""$!1n`\&4ss!f!#K7$$!1nmm;p0k&*!#;$"2b!)=rcu!GR!#=7$$!1LL$3<XZ=*!#;$"1wBLT7Gk%)!#<7$$!1nmmT%p"e()!#;$"1Qfh=,"y<"!#;7$$!1nm"H-%\/()!#;$"2'zLuQ$48>"!#<7$$!1mm;/'=3l)!#;$"2'[w@w0oB7!#<7$$!1mmT&=Vrf)!#;$"22jaIOv)y7!#<7$$!1mmmmxYV&)!#;$"2z["pA8qc8!#<7$$!1mm;Hp6O%)!#;$"2pvt'Hgif:!#<7$$!1mmm"4m(G$)!#;$"2(QVn'zMjw"!#<7$$!/D"GyX`F)!#9$"2=`Sthix%=!#<7$$!1M$eRZD>A)!#;$"2$\PLjX02>!#<7$$!1nT5l^]o")!#;$"1Tg&)GV/V>!#;7$$!-Dc[3:")!#7$"2$=I'o>o(e>!#<7$$!1m;aQUC3!)!#;$"2(R@2uque>!#<7$$!1ML$3i.9!z!#;$"1L*)4orV!)>!#;7$$!1,+]iPH.x!#;$"2#\jCB)H&RA!#<7$$!1nm;/R=0v!#;$"2b>!oUVu<E!#<7$$!1MLL$3,RX(!#;$"1E*[ezR:o#!#;7$$!,DE=ES(!#6$"1z-(R\"zAF!#;7$$!1nmmTaL^t!#;$"1'=+"4#=Iu#!#;7$$!1LL$3i_+I(!#;$"1iG!)=iDZF!#;7$$!1*******zp([s!#;$"1@z)>$[CVF!#;7$$!1mm;zp[(>(!#;$"2tR1K.c,u#!#<7$$!1MLLeT?Yr!#;$"1VK$)3j2ZF!#;7$$!,vL@\4(!#6$"2XbsaT"\rF!#<7$$!1ML$3FuF)o!#;$"1oMw7f4'4$!#;7$$!1nm;/siqm!#;$"1iLGSlMtM!#;7$$!1ML$e\g"fk!#;$"2XD<CLKc_$!#<7$$!,vy$pZi!#6$"21+L;"y61O!#<7$$!1nmT&Gu,.'!#;$"2WK(RW%e(HS!#<7$$!1LLL$yaE"e!#;$"1*fZ81^(>V!#;7$$!1mmTN"for&!#;$"1#)\\eET>V!#;7$$!,v[j5i&!#6$"0pX!o^9'H%!#:7$$!1m;ajc;tb!#;$"20b8Gu^tH%!#<7$$!1LLeRyEDb!#;$"20y,;3PpJ%!#<7$$!.Dc,qtZ&!#8$"2Z<vcox#fV!#<7$$!1nmm">s%Ha!#;$"1\H^a4[DW!#;7$$!-D")*G;K&!#7$"1WUf*GCXk%!#;7$$!1LL$3x&y8_!#;$"2V[qDrV6*[!#<7$$!1,]ilT')f^!#;$"1iY@^b0$*\!#;7$$!1nmTgD%f5&!#;$"0)\V^PRn]!#:7$$!1M$3_&4-_]!#;$"1v"Q(\j#*4^!#;7$$!2/+++N*4)*\!#<$"1yew2CBA^!#;7$$!2.++]K8)*)[!#<$"1st#)Qo8*3&!#;7$$!)t_"y%!")$"18IY\!Qh1&!#;7$$!20++vG%QFZ!#<$"1Qs^*>/.4&!#;7$$!+v7CtY!#5$"1[JJ+V.[^!#;7$$!,DE)4>Y!#6$"1"zOTG"HR_!#;7$$!*Db\c%!"*$"1B5?+:yd`!#;7$$!2/+++g,1Y%!#<$"1,(*49!zxh&!#;7$$!*&zCcV!"*$"1A%H^Nu6$e!#;7$$!2(*****\7rSI%!#<$"1t$)3:R8%*e!#;7$$!)V*=D%!")$"1R>gG:yAf!#;7$$!+vur*>%!#5$"1s9sT]\?f!#;7$$!*lSv9%!"*$"1_K)3U$4'*e!#;7$$!1nm;/#)[oP!#;$"1Xh(Gx?A;'!#;7$$!2OLLL=exJ$!#<$"1&=;&z0qUm!#;7$$!1ML3_(H+F$!#;$"1UpUD*z#*f'!#;7$$!1ML$3K,BA$!#;$"1YxumDfsl!#;7$$!2OL$e*)GduJ!#<$"1e))z(>$)Rd'!#;7$$!1MLLeW%o7$!#;$"1*f%o/9,6m!#;7$$!2OLLef(QJI!#<$"12$HDlgnz'!#;7$$!1MLLL2$f$H!#;$"1uo8)=_n3(!#;7$$!2.+v$4<*[#G!#<$"0twuSmYT(!#:7$$!1nmT&o_Qr#!#;$"1CT$)))*fUd(!#;7$$!2/]PM<L$eE!#<$"1hH-UYZov!#;7$$!1M$e9m8Gg#!#;$"1K5!p-U]^(!#;7$$!2t;z%\THZD!#<$"1#*zK(H_OV(!#;7$$!20++vju<\#!#<$"1n_)z6H.N(!#;7$$!2s;z>YIEW#!#<$"19Eo684(H(!#;7$$!1M$ekG'[$R#!#;$"1crPl(z1G(!#;7$$!22]P46UVM#!#<$"1(*)>h@sFJ(!#;7$$!2um;a$z>&H#!#<$"1"*[9js)zR(!#;7$$!23+vVe4p>#!#<$"0ZP*fJ=1x!#:7$$!2VLLLB@')4#!#<$"1\HzXl,$4)!#;7$$!2t;aQG-Z/#!#<$"1"RX(*G,nF)!#;7$$!21+vVL$y!*>!#<$"1Z^Rn#>hS)!#;7$$!1Me*[Qko$>!#;$"1p#\7%)fTY)!#;7$$!1nmTNa%H)=!#;$"1i&4VaYhW)!#;7$$!2KLek`2^x"!#<$"1A+=[.>K#)!#;7$$!2'****\P'psm"!#<$"1fx\'*Rssz!#;7$$!2(**\(o/Efh"!#<$"1k#p0l4R"z!#;7$$!2'***\iX#ek:!#<$"1W$*R(p=*Hz!#;7$$!2&**\il)QK^"!#<$"1/_'[8B<.)!#;7$$!2(*****\F&*=Y"!#<$"1j2+3pU;#)!#;7$$!2)***\P43#f8!#<$"1W$GFb$H`()!#;7$$!,D"4_c7!#6$"1Y&>*zc&*z#*!#;7$$!2KeRs3N(H7!#<$"12YV(3GoP*!#;7$$!2l;z>E\H?"!#<$"1a2\>+xZ%*!#;7$$!2)\(=nVjh<"!#<$"1nS3h#e&*[*!#;7$$!2KLe9hx$\6!#<$"1(35M'=;+&*!#;7$$!2l"z>'y"fA6!#<$"133u;h))y%*!#;7$$!2)*\P4'f!e4"!#<$"1ThyXWYE%*!#;7$$!2J3xc8?!p5!#<$"1M[!eF#4X$*!#;7$$!2lm;/JMA/"!#<$"0dA%="*RQ#*!#:7$$!1)**\P454N*!#<$"1or$)H=Su')!#;7$$!1JLL$3x%z#)!#<$"1i(y6(e(pD)!#;7$$!1LL$e9d;J'!#<$"1^y"eKir;*!#;7$$!1MLL3s$QM%!#<$"26]_X(*Q\7"!#;7$$!1^(o/Bx6@%!#<$"2eL[KA;=8"!#;7$$!1oTg_s^yS!#<$"2*>c(e\jn8"!#;7$$!2WeRZFde%R!#=$"1"3jN76'R6!#:7$$!1,](oH(>8Q!#<$"2'=uXAz>S6!#;7$$!2X$e9Tt(ya$!#=$"2)QIr%4&*R8"!#;7$$!1omT&QdDG$!#<$"2xkdW3(3<6!#;7$$!2YLeRZ<>v#!#=$"2F7G,W5![5!#;7$$!29++Dcx7A#!#=$"18<eux\$H*!#;7$$!2#o;/^wj!p"!#=$"17t/Vdm@w!#;7$$!1NLeRx**f6!#<$"1'3S;k5N_&!#;7$$!1%oT&QyxY*)!#=$"1T?%*[e?XV!#;7$$!1<+D"GyNH'!#=$"1(y@;)=#=5$!#;7$$!28NeRsy.k$!#>$"2A`KbnU9"=!#<7$$!1^omm;zr)*!#>$"1DG!z_ZT$\!#<7$$"2eI3_]\(o<!#>$!1Uy"*>cpL))!#<7$$"1(H$3x"yY_%!#=$!2$*[QM*ycXA!#<7$$"1)Ge*[og!G(!#=$!29"=!*[o'3d$!#<7$$"2yK$3_Nl.5!#=$!1A_Y?\-Q[!#;7$$"1F3F>kCz7!#<$!1lRD#o#[Fg!#;7$$"1E$ekGR[b"!#<$!0N"yJ\">7(!#:7$$"1Dek`@VI=!#<$!1.<r")fq1")!#;7$$"2UKL3-Dg5#!#=$!1aJI#>K.(*)!#;7$$"2CK3_v5sl#!#=$!26"**)fg+0."!#;7$$"21K$e*['R3K!#=$!2p0#Q.aK56!#;7$$"0#3xc$*)R[$!#;$!2,91RDQ48"!#;7$$"1>$eRA#efP!#<$!1CdA1)e(R6!#:7$$"1o?bd'yt*Q!#<$!24MDj!f4S6!#;7$$"1=e9"4v^.%!#<$!2n83/#G$z8"!#;7$$"2ucRZ_rH<%!#=$!2")\EK^YM8"!#;7$$"1<LLezw5V!#<$!1xH1nV#o7"!#:7$$"1`mmmJ+Ii!#<$!1,CLX!eVD*!#;7$$"0****\PQ#\")!#;$!1-yW8qOS#)!#;7$$"1BL3x;l&=*!#<$!1Z$oo!GU(e)!#;7$$"2cm;z\1A-"!#<$!1*)fiM#4]9*!#;7$$"2B$3-jr-u5!#<$!1:mu)RbBO*!#;7$$"1**\7Gy%e7"!#;$!0BL#)fjJ[*!#:7$$"2B3x1;e<:"!#<$!1>lMF)40]*!#;7$$"2c;HK\ow<"!#<$!1-v$=+C!)[*!#;7$$"1\7yD)yN?"!#;$!10o7RnUY%*!#;7$$"2BLL$e"*[H7!#<$!1NJ1KJgx$*!#;7$$"1***\PzglL"!#;$!1,r3j^Y")))!#;7$$"2emm"HCjV9!#<$!1:R<onE*H)!#;7$$"2#**\(oCor\"!#<$!1E<j(4c63)!#;7$$"2DL$ekSq]:!#<$!1p=CUS$)[z!#;7$$"1m;H#))RUg"!#;$!12'=X9x."z!#;7$$"2$*******pvxl"!#<$!1[M5G65dz!#;7$$"1***\iSCDw"!#;$!0J.q<T*)>)!#:7$$"2')***\7JFn=!#<$!1;ah.biF%)!#;7$$"2%)*\iluk>>!#<$!02%o*G6lY)!#:7$$"2$)**\(==-s>!#<$!124>Hy$\V)!#;7$$"1)*\(=<'RC?!#;$!0>")*)pqHL)!#:7$$"1)****\_qn2#!#;$!1p"\1#*yC<)!#;7$$"1)*\P%G?"y@!#;$!1*)GbSD-zx!#;7$$"2#)**\P/q%zA!#<$!13)pCCXhV(!#;7$$"2#[Pf$[2[I#!#<$!1"[L%pH>xt!#;7$$"2#)\PM#\9IB!#<$!1Q`Nz(H>L(!#;7$$"2$[7GjB[bB!#<$!1OxZA?)3I(!#;7$$"2$)*\7.)>3Q#!#<$!1Tr6+7*RG(!#;7$$"2%)\7Go%\JC!#<$!1%Q%>0+j*G(!#;7$$"2%)***\i&p@[#!#<$!1'z+bWoxL(!#;7$$"2%)\ilPN%QD!#<$!1fnk0Uw>u!#;7$$"2%)*\i!>,Zf#!#<$!1<;%p`AV](!#;7$$"2%)\(o/q'4l#!#<$!1**4/Isyjv!#;7$$"2$)**\(=GB2F!#<$!1PQxj(*\wv!#;7$$"1[7yDdONF!#;$!1Qb%)\<@hv!#;7$$"2$)\7Gj)\jF!#<$!1Jua&oi2`(!#;7$$"2'[P%)R:j"z#!#<$!1/TpVlb&[(!#;7$$"1)*\(oWk(>G!#;$!1"3"ekbsEu!#;7$$"1)\P4EIg(G!#;$!1*4b_/4fF(!#;7$$"1)****\2'HKH!#;$!1Zm*[$fa)4(!#;7$$"1lm"zu5M.$!#;$!1e&)y#)=X"z'!#;7$$"1KL$3UDX8$!#;$!1;@))>YZ-m!#;7$$"1l;HdF3&=$!#;$!1XTo`+"3d'!#;7$$"2&)**\P4ScB$!#<$!19$[C/awd'!#;7$$"1K$3-V(>'G$!#;$!1%\jr]gFh'!#;7$$"1lmmmZvOL!#;$!1i(**3Ky;m'!#;7$$"2'******\2goP!#<$!1n%esS=>;'!#;7$$"2l;H2L:v"Q!#<$!1>"y)>-wQg!#;7$$"1L$e9"*Hk'Q!#;$!1lgN&HQ)Qf!#;7$$"1*\(=#\W`"R!#;$!1vtc(4&Gpe!#;7$$"1mm"H2fU'R!#;$!1#RKldND$e!#;7$$"1Lek`O<8S!#;$!18UEMb1Ee!#;7$$"1**\PM#)3iS!#;$!0JtL1uG%e!#:7$$"2b;/^"G+6T!#<$!1KZ#)yEise!#;7$$"2CLLeR<*fT!#<$!1e5Jn"[K!f!#;7$$"1mTg_RR8U!#;$!1z5(=\xO#f!#;7$$"1**\P40(oE%!#;$!1.8&Qd#)z"f!#;7$$"2E$e9mqM?V!#<$!1`Oi7T<ye!#;7$$"1mm"HiBQP%!#;$!1\n-Zw^-e!#;7$$"1L$ektw2[%!#;$!1=)=dyBzc&!#;7$$"2(******\)Hxe%!#<$!1,cjW1E0`!#;7$$"1LeRAr/QY!#;$!1/9y-$3Q?&!#;7$$"1m;z%Rk$)o%!#;$!1ZJFQSTG^!#;7$$"1*\(=n;oQZ!#;$!1zY=]sg#3&!#;7$$"1KLeR*)**)y%!#;$!1Bd+2R;l]!#;7$$"2$)*\P%[L'*)[!#<$!1(*Rwm!f!*3&!#;7$$"2Ymm"H!o-*\!#<$!1<85W*p=7&!#;7$$"1JL3xS'G/&!#;$!1mo]qa,9^!#;7$$"1)****\7ga4&!#;$!1&4zl<(=y]!#;7$$"1km"H<c![^!#;$!1YyV[^#>,&!#;7$$"1KL$3A_1?&!#;$!1uv6d/3=\!#;7$$"1mmm;V%eI&!#;$!1B"*4,?L"o%!#;7$$"1****\7k.6a!#;$!1>>Mv1$pX%!#;7$$"1L3-j'eCY&!#;$!216nAestP%!#<7$$"1m;a84)Q^&!#;$!1*4_xhU[K%!#;7$$"1)\iS;.`c&!#;$!2'*>t5,`"*H%!#<7$$"1KLe9as;c!#;$!1Uy2$olcH%!#;7$$"1**\i:*p&>d!#;$!1FK2)\a+K%!#;7$$"1mmm;WTAe!#;$!2v(y:_i5;V!#<7$$"1KLeR<vPg!#;$!1H2_CzV8S!#;7$$"1****\i!*3`i!#;$!2;<ERsw%*f$!#<7$$"1mm"z\%[gk!#;$!2'))4=:9'e_$!#<7$$"1MLLL*zym'!#;$!1*>=*H&fhZ$!#;7$$"1LL$3sr*zo!#;$!2d]B"y"R?5$!#<7$$"1LLL3N1#4(!#;$!2/pu.IwMx#!#<7$$"1*\P%)RZY9(!#;$!1`!36TGvu#!#;7$$"1m;a)GJs>(!#;$!1,&Gjee,u#!#;7$$"1Leky^")\s!#;$!1CgPj%\Lu#!#;7$$"-vo!*R-t!#7$!1()pN;)3tu#!#;7$$"1mT&)eH)\N(!#;$!2L6kz.&=UF!#<7$$"1M$e*[oc2u!#;$!2B-B([*z(>F!#<7$$"/D1R2:gu!#9$!2d#>'Hxh\n#!#<7$$"1mm;HYt7v!#;$!2Z@8tGNlg#!#<7$$"1LLek6,1x!#;$!2_,wt+7UB#!#<7$$")xG**y!")$!02)HPOc")>!#:7$$"1nmTgg/5!)!#;$!1Uh9@Uye>!#;7$$"1LL$3U/37)!#;$!2)o'y%))o(y&>!#<7$$"1n;/,O=w")!#;$!1.khiPBR>!#;7$$"1***\7yi:B)!#;$!2H)4ZTJ5)*=!#<7$$"1L$e9'>%pG)!#;$!2`ddYHZ=$=!#<7$$"1mmmT6KU$)!#;$!2cw!4p&)oU<!#<7$$"1LLeRZQT%)!#;$!1)4"39y$*[:!#;7$$",vL[/a)!#6$!1JuQq>oh8!#;7$$"1L$ek8!)**e)!#;$!12#[**)o+)G"!#;7$$"1mmTN>^R')!#;$!2Klf]x^LB"!#<7$$"1**\PMP/*o)!#;$!28QX<!eW)>"!#<7$$"1LLLLbdQ()!#;$!2ZWclPb4="!#<7$$".D1*z>W))!#8$!2'z%f.$=Ew6!#<7$$"1nm"zW?)\*)!#;$!2D:"R/g>d6!#<7$$"1L$3_!HWb!*!#;$!2Q.j!p>ml5!#<7$$",DOl5;*!#6$!1%*4a$4kc#*)!#<7$$",v.Uac*!#6$!1:C+(y(GFR!#<7$$"#5!""$"1n`\&4ss!f!#K-%&COLORG6&%$RGBG$"2'\_'eM%yg>!#<$"1ij9.e@R!)!#;$"2'\_'eM%yg>!#<-%%VIEWG6$;$!#5!""$"#5!""%(DEFAULTG-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%*THICKNESSG6#""#-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"#q!""-%-BOUNDS_WIDTHG6#$"%!z$!""-%.BOUNDS_HEIGHTG6#$"%]Q!""-%)CHILDRENG6"

c) f(x) = x(x^2-1) for -1 <x< 1 T=1

restart:with(plots):alias(u=Heaviside):assume(n,integer):T:=2:

f:=x->x*((x^2)-1)*(u(x+1)-u(x-1));

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKig5JCIiIiwmKiRGKiIiI0YrISIiRitGKywmLUkidUdGJTYjLCZGKkYrRitGK0YrLUYyNiMsJkYqRitGL0YrRi9GK0YlRiVGJQ==

N:=25:a:=array([],0..N):b:=array([],0..N):

a[0] := factor(2*integrate(f(x), x = -1 .. 1)/T);

IiIh

for n from 1 to N do a[n]:=2/T*int(f(x)*cos(2*n*Pi*x/T),x=-1..1); b[n]:=2/T*int(f(x)*sin(2*n*Pi*x/T),x=-1..1); end do:n:='n':

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

d) f(x) = -2(x+1) for -1 <x< -1/2 T=1

-1 for -1/2 <x< 0

1 for 0 <x< 1/2

-2(x-1) for 1/2 <x< 1

restart:with(plots):alias(u=Heaviside):assume(n,integer):T:=2:

f:=x->(-2*(x+1))*(u(x+1)-u(x+1/2)) + (-1)*(u(x+1/2)-u(x)) + (1)*(u(x)-u(x-1/2)) + (-2*(x-1))*(u(x-1/2)-u(x-1));

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCwqJiwmOSQhIiNGLSIiIkYuLCYtSSJ1R0YlNiMsJkYsRi5GLkYuRi4tRjE2IywmRixGLiNGLiIiI0YuISIiRi5GLkY0RjktRjE2I0YsRjgtRjE2IywmRixGLiNGOUY4Ri5GOSomLCZGLEYtRjhGLkYuLCZGPEYuLUYxNiMsJkYsRi5GOUYuRjlGLkYuRiVGJUYl

N:=25:a:=array([],0..N):b:=array([],0..N):

a[0] := factor(2*integrate(f(x), x = -1 .. 1)/T);

IiIh

for n from 1 to N do a[n]:=2/T*int(f(x)*cos(2*n*Pi*x/T),x=-1..1); b[n]:=2/T*int(f(x)*sin(2*n*Pi*x/T),x=-1..1); end do:n:='n':

-%%PLOTG6(-%'CURVESG6$7`p7$$!#5!""%*undefinedG7$$!1MekynP')**!#;$!2&)HL3FWYs#!#>7$$!1n;HdNvs**!#;$!1(fm;a)G\a!#=7$$!/v$fLI"f**!#9$!1'*)*\7G$R<)!#=7$$!1MLe9r]X**!#;$!2%>LL3x&)*3"!#=7$$!1,](=ng#=**!#;$!1z**\ilyM;!#<7$$!1nm;HU,"*)*!#;$!1hmm;arz@!#<7$$!-vV8_O)*!#7$!2E++]7t&pK!#=7$$!1MLLe%G?y*!#;$!1ALLL3VfV!#<7$$!,voUIn*!#6$!10++]i9Rl!#<7$$!1nmm;p0k&*!#;$!1mmmm;')=()!#<7$$!-vV5Su$*!#7$!2&****\7z>^7!#<7$$!1LL$3<XZ=*!#;$!2XLL$e'40j"!#<7$$!1nmmT%p"e()!#;$!2nmmm6hO[#!#<7$$!1mmm"4m(G$)!#;$!2xmmm"yYUL!#<7$$!1ML$3i.9!z!#;$!2CLL$eF>(>%!#<7$$!1nm;/R=0v!#;$!2kmm;>K'*)\!#<7$$!,vL@\4(!#6$!+Dt:5e!#57$$!1nm;/siqm!#;$!1mmm"fX(em!#;7$$!,vy$pZi!#6$!1*****\U7Y](!#;7$$!1LLL$yaE"e!#;$!1MLLL/pu$)!#;7$$!1nmm">s%Ha!#;$!1nmm;c0T"*!#;7$$!1LL$3x&y8_!#;$!1LLLe%GCd*!#;7$$!2/+++N*4)*\!#<$!#5!""7$$!)t_"y%!")$!#5!""7$$!*Db\c%!"*$!#5!""7$$!*lSv9%!"*$!#5!""7$$!1nm;/#)[oP!#;$!#5!""7$$!2OLLL=exJ$!#<$!#5!""7$$!1MLLL2$f$H!#;$!#5!""7$$!20++vju<\#!#<$!#5!""7$$!2VLLLB@')4#!#<$!#5!""7$$!2'****\P'psm"!#<$!#5!""7$$!,D"4_c7!#6$!#5!""7$$!1JLL$3x%z#)!#<$!#5!""7$$!1MLL3s$QM%!#<$!#5!""7$$!29++Dcx7A#!#=$!#5!""7$$!1^omm;zr)*!#>$!#5!""7$$"1."3Fp^y!R!#>$"#5!""7$$"2eI3_]\(o<!#>$"#5!""7$$"1,e9TQrYJ!#=$"#5!""7$$"1(H$3x"yY_%!#=$"#5!""7$$"1)Ge*[og!G(!#=$"#5!""7$$"2yK$3_Nl.5!#=$"#5!""7$$"1E$ekGR[b"!#<$"#5!""7$$"2UKL3-Dg5#!#=$"#5!""7$$"21K$e*['R3K!#=$"#5!""7$$"1<LLezw5V!#<$"#5!""7$$"1`mmmJ+Ii!#<$"#5!""7$$"0****\PQ#\")!#;$"#5!""7$$"2BLL$e"*[H7!#<$"#5!""7$$"2$*******pvxl"!#<$"#5!""7$$"1)****\_qn2#!#;$"#5!""7$$"2%)***\i&p@[#!#<$"#5!""7$$"1)****\2'HKH!#;$"#5!""7$$"1lmmmZvOL!#;$"#5!""7$$"2'******\2goP!#<$"#5!""7$$"2CLLeR<*fT!#<$"#5!""7$$"2(******\)Hxe%!#<$"#5!""7$$"1KLeR*)**)y%!#;$"#5!""7$$"2Ymm"H!o-*\!#<$"#5!""7$$"1KL$3A_1?&!#;$"1PLLebp)f*!#;7$$"1****\7k.6a!#;$"1-++vr#z<*!#;7$$"1mmm;WTAe!#;$"1ommm6<b$)!#;7$$"1****\i!*3`i!#;$"1-++v=#Q\(!#;7$$"1MLLL*zym'!#;$"1KLLL,Ckm!#;7$$"1LLL3N1#4(!#;$"1MLL$)H(e"e!#;7$$"1mm;HYt7v!#;$"2tmm;uIX(\!#<7$$")xG**y!")$"1,+++YU,U!#;7$$"1mmmT6KU$)!#;$"1nmm;xN:L!#;7$$"1LLLLbdQ()!#;$"1NLLL*[G_#!#;7$$",DOl5;*!#6$"1*****\Fpyn"!#;7$$")PDj$*!")$"1*******f#\t7!#;7$$",v.Uac*!#6$"1"*****\#f6p)!#<7$$".D"G:3u'*!#8$"1$***\P%p$=l!#<7$$"-v=5s#y*!#7$"2c****\izbM%!#=7$$"/D1k2/P)*!#9$"1(**\(=Z=fK!#<7$$".v$40O"*)*!#8$"2y***\7)*ys@!#=7$$"1^7.#Q?&=**!#;$"2t)\PfBfH;!#=7$$"/voa-oX**!#9$"2*)**\i!\R'3"!#=7$$"1Cc,">g#f**!#;$"1e^(ozhz9)!#=7$$"0vVt7SG(**!#:$"2b5]7`u>V&!#>7$$"1v=nj+U')**!#;$"2G0DcE()fr#!#>7$$"#5!""%*undefinedG-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'CURVESG6$7fw7$$!#5!""$"1yB!\PB=K'!#K7$$!1nmm;p0k&*!#;$!0e=laa\F)!#;7$$!1LL$3<XZ=*!#;$!2bY8k7sGm"!#<7$$!1nmmT%p"e()!#;$!2Xt0:JVuT#!#<7$$!1mmm"4m(G$)!#;$!2.**fR"*z1W$!#<7$$!1ML$3i.9!z!#;$!1oXiW?GvS!#;7$$!1nm;/R=0v!#;$!0#oya([n6&!#:7$$!,vL@\4(!#6$!1.nqwG!>n&!#;7$$!1ML$3FuF)o!#;$!1Zi9/^d:i!#;7$$!1nm;/siqm!#;$!1l/e4I\2o!#;7$$!1ML$e\g"fk!#;$!1hI-xIvhq!#;7$$!,vy$pZi!#6$!160<3c>at!#;7$$!1nmT&Gu,.'!#;$!1Y%p$>5.3!)!#;7$$!1LLL$yaE"e!#;$!13FH,,73&)!#;7$$!1mmTN"for&!#;$!116B#)3V%f)!#;7$$!,v[j5i&!#6$!0$fgIX=h')!#:7$$!1LLeRyEDb!#;$!0^R2,30y)!#:7$$!1nmm">s%Ha!#;$!1@Akz@@(**)!#;7$$!1LL$3x&y8_!#;$!1T\s,T(Qq*!#;7$$!2/+++N*4)*\!#<$!2vJz&*>KW+"!#;7$$!2.++]K8)*)[!#<$!1[7t_oO!)**!#;7$$!)t_"y%!")$!1`u.e6Vu)*!#;7$$!20++vG%QFZ!#<$!0wj0C!GV)*!#:7$$!+v7CtY!#5$!1GFa`ODS)*!#;7$$!,DE)4>Y!#6$!1X>5"R="o)*!#;7$$!*Db\c%!"*$!1=Ow,%=I#**!#;7$$!2/+++g,1Y%!#<$!2NiFiF<m+"!#;7$$!*&zCcV!"*$!2"f79otU<5!#;7$$!2(*****\7rSI%!#<$!1%**Hy>K)=5!#:7$$!)V*=D%!")$!2pox<RYp,"!#;7$$!+vur*>%!#5$!22#>cdy+75!#;7$$!*lSv9%!"*$!2D7,3j/[+"!#;7$$!2kmT&Qvx_S!#<$!1)>nL'R@+**!#;7$$!2ML$3FW,eR!#<$!1"yEyPw9!)*!#;7$$!1nTNrGj5R!#;$!1#\?ivw3z*!#;7$$!2.+DcJ^K'Q!#<$!1.!)fMwR5)*!#;7$$!2N$e*)f(pe"Q!#<$!1,g0(*)[z&)*!#;7$$!1nm;/#)[oP!#;$!1t*pj$RKF**!#;7$$!1L$e*)p0el$!#;$!2j-z;\L?,"!#;7$$!-v$>BJa$!#7$!1n'\&[B.B5!#:7$$!2M$e9T>y'[$!#<$!2P)G%p6e?-"!#;7$$!1n;a)oS/V$!#;$!2/)H*>uPl,"!#;7$$!2/]PfV*4uL!#<$!2t42/#\X25!#;7$$!2OLLL=exJ$!#<$!1O+g3d]l**!#;7$$!1ML3_(H+F$!#;$!1U=w9"\\()*!#;7$$!1ML$3K,BA$!#;$!1<A)H"eD+)*!#;7$$!2OL$e*)GduJ!#<$!19nctD&Gv*!#;7$$!1MLLeW%o7$!#;$!13^@_D\S(*!#;7$$!1ML3Fg6zI!#;$!1GK9V$=gw*!#;7$$!2OLLef(QJI!#<$!1->K7]!o#)*!#;7$$!1MLek"fO)H!#;$!10ZVPH)\"**!#;7$$!1MLLL2$f$H!#;$!2uFtY.V=+"!#;7$$!1nTN@7T!)G!#;$!2G*=;"3QQ,"!#;7$$!2.+v$4<*[#G!#<$!1)))*H^K_B5!#:7$$!1MeR(>s$pF!#;$!2=R?c_'))G5!#;7$$!1nmT&o_Qr#!#;$!26p/'QYpG5!#;7$$!1M$e9m8Gg#!#;$!2j65CB[?,"!#;7$$!20++vju<\#!#<$!0')p4I!HY)*!#:7$$!2s;z>YIEW#!#<$!1%=<)yz_V(*!#;7$$!1M$ekG'[$R#!#;$!1O6L23+x'*!#;7$$!22]P46UVM#!#<$!1w!f`Pc&e'*!#;7$$!2um;a$z>&H#!#<$!1$4k_BWIp*!#;7$$!23+vVe4p>#!#<$!18=P%\:-!**!#;7$$!2VLLLB@')4#!#<$!2(30T>')y=5!#;7$$!2t;aQG-Z/#!#<$!2oT`r-==."!#;7$$!21+vVL$y!*>!#<$!2`1+$p1[R5!#;7$$!1Me*[Qko$>!#;$!2YGD[pU+/"!#;7$$!1nmTNa%H)=!#;$!2BJg'Hs+L5!#;7$$!2KLek`2^x"!#<$!2"*)\LW<0,5!#;7$$!2'****\P'psm"!#<$!1TEEOJ0V'*!#;7$$!2(*\(=UyfT;!#<$!1BmF)z#Qz&*!#;7$$!2(**\(o/Efh"!#<$!0xE5/m>`*!#:7$$!2'*\i:Da-f"!#<$!1KEclfM.&*!#;7$$!2'***\iX#ek:!#<$!1G^`X/N&\*!#;7$$!2(*\P4m5*Q:!#<$!13%ok:$**3&*!#;7$$!2&**\il)QK^"!#<$!1&\WI50Wa*!#;7$$!2'*\7.2nv["!#<$!1p#*))Q.!3g*!#;7$$!2(*****\F&*=Y"!#<$!16#HhIykn*!#;7$$!2)***\P43#f8!#<$!2ag:g"f#4,"!#;7$$!,D"4_c7!#6$!2iSdNr+M0"!#;7$$!2KeRs3N(H7!#<$!2=)=&oIh/1"!#;7$$!2l;z>E\H?"!#<$!2/(e!y"y$\1"!#;7$$!2)\(=nVjh<"!#<$!2&o_5l\]m5!#;7$$!2KLe9hx$\6!#<$!2JC)zGk&\1"!#;7$$!2)*\P4'f!e4"!#<$!2C?!>QRO_5!#;7$$!2lm;/JMA/"!#<$!1$e#)QG2$G5!#:7$$!1)**\P454N*!#<$!1l77Y9b7'*!#;7$$!1JLL$3x%z#)!#<$!1'zXNE.k3*!#;7$$!1LL$e9d;J'!#<$!0Vn>r)f&z*!#:7$$!1MLL3s$QM%!#<$!2wQ?[Nb#o6!#;7$$!1oTg_s^yS!#<$!1TKi1!*[x6!#:7$$!1,](oH(>8Q!#<$!2&RL'=BN$y6!#;7$$!2X$e9Tt(ya$!#=$!2E!G4BQap6!#;7$$!1omT&QdDG$!#<$!2zd$4GQ/]6!#;7$$!2YLeRZ<>v#!#=$!1O4Di=wv5!#:7$$!29++Dcx7A#!#=$!18=?j]_=&*!#;7$$!2#o;/^wj!p"!#=$!0ogRvmOz(!#:7$$!1NLeRx**f6!#<$!1\I)H:S>k&!#;7$$!1%oT&QyxY*)!#=$!22wLe>rmV%!#<7$$!1<+D"GyNH'!#=$!2u.WBUHi;$!#<7$$!28NeRsy.k$!#>$!1y'GlVB([=!#;7$$!1^omm;zr)*!#>$!034<Uw_.&!#;7$$"2eI3_]\(o<!#>$"1z-g4+)[,*!#<7$$"1(H$3x"yY_%!#=$"2vOpC)e*=H#!#<7$$"1)Ge*[og!G(!#=$"1\idT(\`k$!#;7$$"2yK$3_Nl.5!#=$"1xW,[zdS\!#;7$$"1F3F>kCz7!#<$"1M(=Q@&*z:'!#;7$$"1E$ekGR[b"!#<$"1*R)HOgD!G(!#;7$$"1Dek`@VI=!#<$"1;iX85t#H)!#;7$$"2UKL3-Dg5#!#=$"1=F!32!*Q=*!#;7$$"2CK3_v5sl#!#=$"2v7(3l)=t0"!#;7$$"21K$e*['R3K!#=$"2B,/^kcD9"!#;7$$"0#3xc$*)R[$!#;$"288:dEje;"!#;7$$"1>$eRA#efP!#<$"2<f#Q_JPx6!#;7$$"1=e9"4v^.%!#<$"2w7k_UN#y6!#;7$$"1<LLezw5V!#<$"2#)HFid<)p6!#;7$$"1`mmmJ+Ii!#<$"1N5$*Qlau)*!#;7$$"0****\PQ#\")!#;$"1aU&4Fsk0*!#;7$$"2cm;z\1A-"!#<$"2)*HGbA%*p,"!#;7$$"2BLL$e"*[H7!#<$"2QP\5u901"!#;7$$"1***\PzglL"!#;$"225ARWw9-"!#;7$$"2emm"HCjV9!#<$"11@(3Zp1u*!#;7$$"2D$3-Q.Sq9!#<$"1Wi@u;T\'*!#;7$$"2#**\(oCor\"!#<$"1EZ%ofStd*!#;7$$"2f;Hd:OR_"!#<$"1jH_hH.F&*!#;7$$"2DL$ekSq]:!#<$"1)QfbS4+]*!#;7$$"2#*\PM(>Zx:!#<$"1H#oAd.n\*!#;7$$"1m;H#))RUg"!#;$"1^,x@#zk^*!#;7$$"2E$e9"z25j"!#<$"1<2sYJpd&*!#;7$$"2$*******pvxl"!#<$"1&pMO!)*z<'*!#;7$$"1***\iSCDw"!#;$"18+?tQ!['**!#;7$$"2')***\7JFn=!#<$"2o3F4&3jH5!#;7$$"2%)*\iluk>>!#<$"2#f(*)y82'Q5!#;7$$"2$)**\(==-s>!#<$"1-P$erN0/"!#:7$$"2#)\7`**3#)*>!#<$"2/S(G['>)Q5!#;7$$"1)*\(=<'RC?!#;$"2$eqX43XN5!#;7$$"1)\P%[Le]?!#;$"2:)HyJmhI5!#;7$$"1)****\_qn2#!#;$"2<a.0$HcC5!#;7$$"1)*\P%G?"y@!#;$"1ozbx3#R&**!#;7$$"2#)**\P/q%zA!#<$"1))4%p:p\r*!#;7$$"2#)\PM#\9IB!#<$"0'>a^y1j'*!#:7$$"2$)*\7.)>3Q#!#<$"1Ux%ei=tm*!#;7$$"2%)\7Go%\JC!#<$"0=*HVxvC(*!#:7$$"2%)***\i&p@[#!#<$"1;wd/>5C)*!#;7$$"2%)*\i!>,Zf#!#<$"2O"HP$o'=55!#;7$$"2$)**\(=GB2F!#<$"2_@7Pn!GG5!#;7$$"2$)\7Gj)\jF!#<$"2#4[?i99H5!#;7$$"1)*\(oWk(>G!#;$"2Y]C%e_AC5!#;7$$"1)\P4EIg(G!#;$"1yVelgr95!#:7$$"1)****\2'HKH!#;$"2$y4f;Dl-5!#;7$$"2;Le9T`G)H!#<$"1_"GI]Tm"**!#;7$$"1lm"zu5M.$!#;$"1[SVG.gB)*!#;7$$"2%)*\P%3oR3$!#<$"1a%46^D<w*!#;7$$"1KL$3UDX8$!#;$"1ikr"QL*R(*!#;7$$"1l;HdF3&=$!#;$"1cp0$=$[g(*!#;7$$"2&)**\P4ScB$!#<$"12?k^(=)=)*!#;7$$"1K$3-V(>'G$!#;$"1zY^1X\/**!#;7$$"1lmmmZvOL!#;$"20y#4G3I+5!#;7$$"1KLe9bt!R$!#;$"2-bRD;;/,"!#;7$$"1****\iirWM!#;$"0QD&etK=5!#97$$"1mmT5qp)\$!#;$"2\ZE*=&fE-"!#;7$$"2CLL$exn_N!#<$"1XRmQ&GF-"!#:7$$"1mm;a#R1m$!#;$"2A"pzhOF65!#;7$$"2'******\2goP!#<$"19Tu&GSr#**!#;7$$"2l;H2L:v"Q!#<$"1EjNy])e&)*!#;7$$"1L$e9"*Hk'Q!#;$"1e.N-W;3)*!#;7$$"1*\(=#\W`"R!#;$"1%RSFT&e!z*!#;7$$"1mm"H2fU'R!#;$"1dp?3(\]!)*!#;7$$"1**\PM#)3iS!#;$"1CD*=LlQ"**!#;7$$"2CLLeR<*fT!#<$"2AdpP5fm+"!#;7$$"1mTg_RR8U!#;$"2F.+0BiN,"!#;7$$"1**\P40(oE%!#;$"1)=<"o9#y,"!#:7$$"2E$e9mqM?V!#<$"2=iaDJU(=5!#;7$$"1mm"HiBQP%!#;$"2[ljD9di,"!#;7$$"1L$ektw2[%!#;$"2K[&)*)\0Q+"!#;7$$"2(******\)Hxe%!#<$"1$[rhoNr*)*!#;7$$"1LeRAr/QY!#;$"1G`\a"e\&)*!#;7$$"1m;z%Rk$)o%!#;$"11B)pz%)z$)*!#;7$$"1*\(=n;oQZ!#;$"1pt$ynrw%)*!#;7$$"1KLeR*)**)y%!#;$"1jjyr-]!))*!#;7$$"2$)*\P%[L'*)[!#<$"1sxv$[!>!)**!#;7$$"2Ymm"H!o-*\!#<$"1tw$=FsV+"!#:7$$"1JL3xS'G/&!#;$"2:'Hzf`8.5!#;7$$"1)****\7ga4&!#;$"1%=>B/))p(**!#;7$$"1km"H<c![^!#;$"1K#HMHw#z)*!#;7$$"1KL$3A_1?&!#;$"1V>Hxb*Gu*!#;7$$"1mmm;V%eI&!#;$"1d'[20"[(R*!#;7$$"1****\7k.6a!#;$"1DOne]D]!*!#;7$$"1mmm;WTAe!#;$"1pX56)*f&\)!#;7$$"1KLeR<vPg!#;$"1$yPD,oQ)z!#;7$$"1****\i!*3`i!#;$"1#3?zd)*=M(!#;7$$"1mm"z\%[gk!#;$"1[,&\w721(!#;7$$"1MLLL*zym'!#;$"1iDL9;)H"o!#;7$$"1LL$3sr*zo!#;$"1U0w'zLWA'!#;7$$"1LLL3N1#4(!#;$"1W(zlJrnn&!#;7$$"1mm;HYt7v!#;$"1eAy)yzz4&!#;7$$")xG**y!")$"2%='*Qwz^yS!#<7$$"1mmmT6KU$)!#;$"2(pk=?*)G.M!#<7$$"1LLLLbdQ()!#;$"2Nf)f4r#)RC!#<7$$",DOl5;*!#6$"2P41X*)>Kt"!#<7$$",v.Uac*!#6$"1[(Rv$)G1E)!#<7$$"#5!""$!1yB!\PB=K'!#K-%&COLORG6&%$RGBG$"2'\_'eM%yg>!#<$"1ij9.e@R!)!#;$"2'\_'eM%yg>!#<-%%VIEWG6$;$!#5!""$"#5!""%(DEFAULTG-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%*THICKNESSG6#""#-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"#q!""-%-BOUNDS_WIDTHG6#$"%!z$!""-%.BOUNDS_HEIGHTG6#$"%]Q!""-%)CHILDRENG6"