Approximating Fourier's Solution This notebook provides explorations of the general solution to the heat-flow problem. Click on the formula given below and then press the ENTER key. When you are asked if you want to evaluate all the initialization cells, answer YES. When Mathematica warns that there might be a problem, proceed and answer EVALUATE. z :=(x,w) -> Sum(a[i]*exp((1/2*(2*i-1)*(-Pi)*w))*(cos(1/2*(2*i-1)*Pi*x)),i = 1 .. nops(a));

NiM+SSJ6RzYiZio2JEkieEdGJUkid0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkU3VtRzYkSSpwcm90ZWN0ZWRHRjBJKF9zeXNsaWJHRiU2JCooJkkiYUdGJTYjSSJpR0YlIiIiLUkkZXhwR0YvNiMsJCooLCZGNyIiIyEiIkY4RjhJI1BpR0YwRjg5JUY4I0ZARj9GOC1JJGNvc0dGLzYjLCQqKEY+RjhGQUY4OSRGOCNGOEY/RjgvRjc7RjgtSSVub3BzR0YwNiNGNUYlRiVGJQ==

The variable a is a list of the coefficients. For example, we might have a = {1,-1/2,1/3,-1/4,1/5}. This definition of z uses the length of the list to determine the number of summands. The following input enters these values and returns the resulting function z.a := [1, -1/2, 1/3, -1/4, 1/5]: z(x,w);

NiMtSSRTdW1HNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiYmNyciIiIjISIiIiIjI0YtIiIkI0YvIiIlI0YtIiImNiNJImlHRihGLS1JJGV4cEdGJTYjLCQqKiwmRjhGMEYvRi1GLUkjUGlHRiZGLUkid0dGKEYtLUkkY29zR0YlNiMsJCooRj5GLUY/Ri1JInhHRihGLSNGLUYwRi1GLkYtL0Y4O0YtRjY=

The first command produces a 3-dimensional plot of z(x,w), the second produces the cross-section parallel to the w-axis at x=0, and the third produces the cross-section above the x-axis.plot3d(z(x, w), x= -1.. 1, w= 0.. 2);plot(z(0, w), w= 0.. 2);plot(z(x, 0), x= -1.. 1);

The first line enters the function FS(n,x), the first n terms of Fourier's approximation to the constant function 1. The second line graphs this truncated Fourier series. It is set up to use 6 terms. This value can be changed. The third line intrdouces the solution to the heat equation, a function of both x and w. The fourth line graphs the resulting surface that shows the solution of the heat equation. Again, this has been set up to use the first 6 terms, but this parameter can be varied.FS := (n, x) -> 4/Pi*sum((-1)^(i-1)/(2*i-1)*cos(1/2*(2*i-1)*Pi*x),i = 1 .. n) ;

NiM+SSNGU0c2ImYqNiRJIm5HRiVJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwkKiZJI1BpR0kqcHJvdGVjdGVkR0YwISIiLUkkc3VtR0YlNiQqKClGMSwmSSJpR0YlIiIiRjFGOUY5LCZGOCIiI0YxRjlGMS1JJGNvc0c2JEYwSShfc3lzbGliR0YlNiMsJCooRjpGOUYvRjk5JUY5I0Y5RjtGOS9GODtGOTkkRjkiIiVGJUYlRiU=

plot(FS(6,x), x=-1..1);

-%%PLOTG6%-%'CURVESG6$7iv7$$!""""!$"3bOqtcB#Rt'!#L7$$!3.MLe9r]X**!#=$"3Gvy)o7T``'!#>7$$!3%pmm"HU,"*)*F3$"3m,!RO*zy/8F37$$!3')***\PM@l$)*F3$"3prSS*f&\^>F37$$!3!RLL$e%G?y*F3$"3s'R(**e">9f#F37$$!3#om;HdNvs*F3$"3NIrj]IOAKF37$$!3t****\(oUIn*F3$"3qv)4%pt=UQF37$$!3wLL3-)\&='*F3$"3UfBk'3@)[WF37$$!3ommm;p0k&*F3$"3YK#**\qu-/&F37$$!3#HL3-)*G#p%*F3$"30Iqr&3Xx-'F37$$!3E++vV5Su$*F3$"3:_iJAPNapF37$$!3^m;H2Jdz#*F3$"3)4^;>))>?"yF37$$!3vKL$3<XZ=*F3$"3_pbl&HERf)F37$$!3&fmT&Q75y!*F3$"3J#p<![$QgP*F37$$!39***\iId9(*)F3$"3=MQB%y&*\+"!#<7$$!3YL$eRP8['))F3$"3gB;m*\c71"Fbp7$$!3mmmmT%p"e()F3$"3gD'G(pvJ16Fbp7$$!3qlm;/'=3l)F3$"3T(e.4HR09"Fbp7$$!3%emmmwnMa)F3$"3\*)ym4N*R;"Fbp7$$!3#fm;zM#z*[)F3$"3#[hlDDq=<"Fbp7$$!3+mm;Hp6O%)F3$"3y06!pK0t<"Fbp7$$!32mmT5:W#Q)F3$"3?l,OnqS!="Fbp7$$!3:mmm"4m(G$)F3$"3.tWnhUH"="Fbp7$$!3))*\7GyX`F)F3$"3hbQT2c5!="Fbp7$$!3iL$eRZD>A)F3$"31Oc6\_)p<"Fbp7$$!3NnT5l^]o")F3$"3JRc7X_2s6Fbp7$$!3)****\i&[3:")F3$"3jX$*3ZQ_l6Fbp7$$!3Mm;aQUC3!)F3$"3mSHQ)=9"[6Fbp7$$!3"QLL3i.9!zF3$"3Z'3N;qBg7"Fbp7$$!3"ommT!R=0vF3$"3U4)ReD/X-"Fbp7$$!3tKL$3i_+I(F3$"378J&ec0%R(*F37$$!3u****\P8#\4(F3$"3ISt7;'ofL*F37$$!3$ommT!y%)))pF3$"3jaxGY`I#=*F37$$!3#RLL3FuF)oF3$"3:.UuBa0r!*F37$$!3Znm;/vtHoF3$"3!HU(R(z:>.*F37$$!3,,+]P2qwnF3$"3w"yP3`iQ+*F37$$!3WLL$3(RmBnF3$"3(y%>&4FQo)*)F37$$!3*pmmT?F1n'F3$"3gHc#>+'o!)*)F37$$!3&RL$3F0w<mF3$"3,^,Tz@7&)*)F37$$!3")******\Q*[c'F3$"3cHX3U)p(***)F37$$!3xmm"H<F?^'F3$"39**Rk"o/U-*F37$$!3tLL$e\g"fkF3$"3n(R[(4R#z0*F37$$!3mnmmTrU`jF3$"3\Be@g1&3:*F37$$!3[++](y$pZiF3$"3xAHto5@t#*F37$$!3MnmT&Gu,.'F3$"3s:X$=#*R2f*F37$$!33LLL$yaE"eF3$"3uMp&\jBr%**F37$$!3%)****\([j5i&F3$"3,b/1f#oX-"Fbp7$$!3hmmm">s%HaF3$"3ud3mF]B\5Fbp7$$!3]***\7)*G;K&F3$"3-99:'3z(f5Fbp7$$!3]LL$3x&y8_F3$"3S)R&ynZZn5Fbp7$$!30,]ilT')f^F3$"3q:twp^=q5Fbp7$$!3]nmTgD%f5&F3$"33blU%4;@2"Fbp7$$!3%RL3_&4-_]F3$"3iNLgp:Et5Fbp7$$!3Q+++]$*4)*\F3$"3c6esxMit5Fbp7$$!3j++]Pj&R%\F3$"3c'eF*R"3K2"Fbp7$$!3K+++DL")*)[F3$"3M3LGf(H?2"Fbp7$$!3,++]7.nN[F3$"3<jiXbH6q5Fbp7$$!3E++++t_"y%F3$"3me&Q=J*[n5Fbp7$$!3>+++v7CtYF3$"3*=I`r5!Gg5Fbp7$$!38+++]_&\c%F3$"3W8quOpx]5Fbp7$$!33+++]zCcVF3$"3AYe8,%=x-"Fbp7$$!30+++]1aZTF3$"3JV<=O"[;+"Fbp7$$!3RLL3FW,eRF3$"35c9^>)oty*F37$$!3umm;/#)[oPF3$"3Ii3Z/[I%f*F37$$!3=L$e*)p0el$F3$"3z`fsnU/1&*F37$$!3<++v$>BJa$F3$"3U->i;w'>W*F37$$!3RLe9T>y'[$F3$"3Ce5%*e0w>%*F37$$!3<n;a)oS/V$F3$"3J')pE*HmVS*F37$$!3R+v$fV*4uLF3$"3qJr$)\P)eR*F37$$!3hLLL$=exJ$F3$"3'[1&\-`L%R*F37$$!3)RLL3K,BA$F3$"35_)*z)4^tS*F37$$!3!QLL$eW%o7$F3$"3$**zN)R%R$R%*F37$$!3hLL$ef(QJIF3$"3[A(eDWv*)[*F37$$!3)RLLLtIf$HF3$"3:FuCJRSa&*F37$$!3CnmT&o_Qr#F3$"3:_6BSg2a(*F37$$!3]++]PYx"\#F3$"3D2KHRH$)*)**F37$$!3QnmTNz>&H#F3$"3i;&f.'pd>5Fbp7$$!3EMLLL7i)4#F3$"3Yd'**>;`q."Fbp7$$!3g+]PMLy!*>F3$"39blY#erW/"Fbp7$$!3#pm;aVXH)=F3$"3VWLavS(*\5Fbp7$$!3CL$ek`2^x"F3$"3tJ2upqN`5Fbp7$$!3c****\P'psm"F3$"3Y:C$G,/X0"Fbp7$$!3k***\iX#ek:F3$"3=h%f()=$\`5Fbp7$$!3r*****\F&*=Y"F3$"3=$Hs4B&[]5Fbp7$$!3z***\P43#f8F3$"3u4[HPogX5Fbp7$$!3')****\74_c7F3$"3qLT[j=0R5Fbp7$$!3ZmmT5VBU5F3$"3o#R`bRX6-"Fbp7$$!3)3LLL3x%z#)F6$"3)*3D-`Y-+5Fbp7$$!3gKL$e9d;J'F6$"3?zwp!*G/2)*F37$$!3KMLL3s$QM%F6$"3QY+li2OT'*F37$$!3'ym;aQdDG$F6$"3ahK&>ro9d*F37$$!3T,+]ivF@AF6$"3oqK8C-*)=&*F37$$!3'\L$eRx**f6F6$"3aHK[G<o&[*F37$$!3\^omm;zr)*!#@$"3i:gvR59t%*F37$$"3&yK$3_Nl.5F6$"3Ot/,t_^#[*F37$$"3@CL$3-Dg5#F6$"3X"\"H`kJ9&*F37$$"3e?Le*['R3KF6$"3C//\*3/sc*F37$$"3%pJL$ezw5VF6$"3?6./Br%*Q'*F37$$"3K`mmmJ+IiF6$"35O?7/,X*z*F37$$"3s*)***\PQ#\")F6$"3u72([6<r)**F37$$"3ilm"z\1A-"F3$"3p?uedqD>5Fbp7$$"3GKLLe"*[H7F3$"3<-MT0"yq."Fbp7$$"3.***\PzglL"F3$"3]AfcpsHW5Fbp7$$"3ylm;HCjV9F3$"3OY7'ej\(\5Fbp7$$"3aKLekSq]:F3$"3q;)f7I,K0"Fbp7$$"3H*******pvxl"F3$"3H3IPPj\a5Fbp7$$"3&*)**\iSCDw"F3$"3s5f=eug`5Fbp7$$"3g)***\7JFn=F3$"38+rr66g]5Fbp7$$"3F)**\(==-s>F3$"36Yz$pOtb/"Fbp7$$"3#z****\_qn2#F3$"3%)RR`p%)pQ5Fbp7$$"3=)**\P/q%zAF3$"3q%>;[yB6-"Fbp7$$"3U)***\i&p@[#F3$"3r@9>M<-+5Fbp7$$"3L)**\(=GB2FF3$"3D&f.+()z2w*F37$$"3A)****\2'HKHF3$"3RF`zEv<d&*F37$$"3)\m;zu5M.$F3$"3;kao8Av([*F37$$"3uJL$3UDX8$F3$"3eI8l694O%*F37$$"37l;HdF3&=$F3$"3V*==!\ti<%*F37$$"3])**\P4ScB$F3$"3&36UIioVS*F37$$"3)=L3-V(>'G$F3$"3i%G;13"['R*F37$$"3ElmmmZvOLF3$"3;%[j4J%3%R*F37$$"3yJLe9bt!R$F3$"3#R]pn^mwR*F37$$"3%))***\iirWMF3$"3)[du'och2%*F37$$"3#fm;/,(p)\$F3$"3w@*>:j$*QU*F37$$"3VKLLexn_NF3$"3a.dIsxRY%*F37$$"3-mm;a#R1m$F3$"3*=2WJQa$4&*F37$$"3h******\2goPF3$"3Kmb%o*RS%f*F37$$"3,mm"H2fU'RF3$"3%y7NC6%[%z*F37$$"3UKL$eR<*fTF3$"35/))Gn_?.5Fbp7$$"3.mm"HiBQP%F3$"39Ct1_@$)H5Fbp7$$"3l******\)Hxe%F3$"3hGH3dY%H0"Fbp7$$"3*em"z%Rk$)o%F3$"3:kd%[BM91"Fbp7$$"36KLeR*)**)y%F3$"3T%Hn$p?*y1"Fbp7$$"3]l"z>@;$R[F3$"3)e%R8:YEq5Fbp7$$"3M)*\P%[L'*)[F3$"3?/x9*fC?2"Fbp7$$"3=J3xc2&*R\F3$"3/\\WRo9t5Fbp7$$"3ckm;H!o-*\F3$"3NX*)e[8ht5Fbp7$$"31JL3xS'G/&F3$"398)oU4yL2"Fbp7$$"3c(****\7ga4&F3$"3SNi&>L+C2"Fbp7$$"31km"H<c![^F3$"3GS$p#**\nq5Fbp7$$"3nJL$3A_1?&F3$"3%f[ML71#o5Fbp7$$"3ylmm;V%eI&F3$"3n@\#es*3h5Fbp7$$"3y)***\7k.6aF3$"3CzN)\nE70"Fbp7$$"3IKLe9as;cF3$"3kP?pKi>D5Fbp7$$"3#emmmT9C#eF3$"3a#>">?1:J**F37$$"3WKLeR<vPgF3$"3?]bDI1ny&*F37$$"32****\i!*3`iF3$"33_`"*e'[jE*F37$$"3@K$3-y'ycjF3$"3H&z.!zXTZ"*F37$$"3Xmm"z\%[gkF3$"3%*\$G:dqp0*F37$$"39M3xcLL7lF3$"32^t&G"f.C!*F37$$"3q+]i:A=klF3$"3LW2A:[.+!*F37$$"3Fn"zW2Jgh'F3$"3>!)[*Q)=W&)*)F37$$"3%QLLL$*zym'F3$"39lI&*)=f1)*)F37$$"3qL$3-)G!4s'F3$"3BoT65:D')*)F37$$"3dLL3Fe#Rx'F3$"3d=6"pL*p-!*F37$$"3WL$eRx[p#oF3$"3QD8#Qlk,.*F37$$"3ILL$3sr*zoF3$"3+U'3H35(o!*F37$$"3-LLe9w,')pF3$"3!yEP!Q_xy"*F37$$"3wKLL3N1#4(F3$"33h%*=5zHJ$*F37$$"3c***\(o!*R-tF3$"3g-)\BB9Zu*F37$$"3Mmm;HYt7vF3$"3:sqE'y$[E5Fbp7$$"3Y*******p(G**yF3$"3hLp&\tZb7"Fbp7$$"3ymmTgg/5!)F3$"3l.O#)=-X[6Fbp7$$"3)HLL3U/37)F3$"3'fht4;*Hm6Fbp7$$"3jm;/,O=w")F3$"3x!3ux`&)G<"Fbp7$$"3=***\7yi:B)F3$"3V(RAnq%ox6Fbp7$$"3%GLe9'>%pG)F3$"3IFJ$*[D`!="Fbp7$$"3]mmmT6KU$)F3$"3)*f:4DBF"="Fbp7$$"3w**\iSH&=R)F3$"3P3;#*3o-!="Fbp7$$"3-LLeRZQT%)F3$"3/?PS=q(o<"Fbp7$$"3Gm;aQl"4\)F3$"3*Qz+FnI<<"Fbp7$$"3a****\P$[/a)F3$"3LUMbQJ]k6Fbp7$$"31mmTN>^R')F3$"3,%4+gx2N9"Fbp7$$"3fKLLLbdQ()F3$"3N(zoId)Q86Fbp7$$"36+]i!*z>W))F3$"3,"yP`_Q32"Fbp7$$"3`mm"zW?)\*)F3$"3]&\5)3jJ<5Fbp7$$"3&HL3_!HWb!*F3$"38x$H%z!=%G&*F37$$"3Z++]i`1h"*F3$"3z/5mo$*ow()F37$$"3Y++DJ&f@E*F3$"33TZtSEYhzF37$$"3X++++PDj$*F3$"3zbE'G#[*)eqF37$$"3X++voyMk%*F3$"37;0Dt0+xgF37$$"3W++]P?Wl&*F3$"3yG"H=gWa-&F37$$"3Q+D"Gyh(>'*F3$"3_DuWWn[NWF37$$"3K+]7G:3u'*F3$"3%4#o8\!)[IQF37$$"3G+vVt7SG(*F3$"3G)[L+"4U7KF37$$"3A++v=5s#y*F3$"3_eS)*))zL$e#F37$$"3;+D1k2/P)*F3$"3oUmj](f`%>F37$$"35+]P40O"*)*F3$"3L%QcU]h1I"F37$$"30+voa-oX**F3$"3o!4Z=Y+Y^'F67$$"""F,F--%&COLORG6&%$RGBG$"#5F+$F,F+F^gn-%+AXESLABELSG6$Q"x6"Q!Fcgn-%%VIEWG6$;$!#5F+F\gn;$!1x)[L_)eiBFbp$"2A'z!p9?\?"!#;

FSS := (n,x,w) -> 4/Pi*sum((-1)^(i-1)/(2*i-1)*exp(1/2*(-2*i+1)*Pi*w)*cos(1/2*(2*i-1)*Pi*x),i = 1 .. n);

NiM+SSRGU1NHNiJmKjYlSSJuR0YlSSJ4R0YlSSJ3R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJComSSNQaUdJKnByb3RlY3RlZEdGMSEiIi1JJHN1bUc2JEYxSShfc3lzbGliR0YlNiQqKilGMiwmSSJpR0YlIiIiRjJGPEY8LCZGOyIiI0YyRjxGMi1JJGV4cEdGNTYjLCQqKCwmRjshIiNGPEY8RjxGMEY8OSZGPCNGPEY+RjwtSSRjb3NHRjU2IywkKihGPUY8RjBGPDklRjxGR0Y8L0Y7O0Y8OSRGPCIiJUYlRiVGJQ==

plot3d(FSS(6,x,w), x=-1..1, w=0..2);

-%'PLOT3DG6$-%%GRIDG6%;$!""""!$"""F+;$F+F+$""#F+X,6"F3I)anythingGI*protectedGF5[gl'!%"!!#\bm":":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%+AXESLABELSG6%Q"xF3Q"wF3Q!F3