# This worksheet contains the Maple commands from Chapter 18 of
# Introduction to Scientific Programming by Joseph L. Zachary.
# 
# The commands below create the animation produced by Example 18.1.
# 
> frame0 :=[[0,100],[2,0],[4,0],[6,0],[8,0],[10,50]]:
> 
> frame1 :=[[0,100],[2,50],[4,0],[6,0],[8,25],[10,50]]:
> 
> frame2 :=[[0,100],[2,50],[4,25],[6,12.5],[8,25],[10,50]]:
> 
> frame3 :=[[0,100],[2,62.5],[4,31.25],[6,25],[8,31.25],[10,50]]:
> 
> frame4 :=[[0,100],[2,65.625],[4,43.75],[6,31.25],[8,37.5],[10,50]]:
> 
> frame5
> :=[[0,100],[2,71.875],[4,48.4375],[6,40.625],[8,40.625],[10,50]]:
> 
> plots[display]([plot(frame0),plot(frame1),plot(frame2),plot(frame3),pl
> ot(frame4),plot(frame5)], insequence=true);
# 
# (18.1)  If you use the C program "heat11" with the appropriate input
# file, or if you copy the commands from above and put them into a file
# called "heat-output.txt", you can create the animation from above by
# evaluating
# 
> read(`heat-output.txt`);
# 
# The commands below create the animation produced by Example 18.2.
# 
> frame0 :=
> [[0,100],[0.1,0],[0.2,0],[0.3,0],[0.4,0],[0.5,0],[0.6,0],[0.7,0],[0.8,
> 0],[0.9,0],[1,0],[1.1,0],[1.2,0],[1.3,0],[1.4,0],[1.5,0],[1.6,0],[1.7,
> 0],[1.8,0],[1.9,0],[2,0],[2.1,0],[2.2,0],[2.3,0],[2.4,0],[2.5,0],[2.6,
> 0],[2.7,0],[2.8,0],[2.9,0],[3,0],[3.1,0],[3.2,0],[3.3,0],[3.4,0],[3.5,
> 0],[3.6,0],[3.7,0],[3.8,0],[3.9,0],[4,0],[4.1,0],[4.2,0],[4.3,0],[4.4,
> 0],[4.5,0],[4.6,0],[4.7,0],[4.8,0],[4.9,0],[5,0],[5.1,0],[5.2,0],[5.3,
> 0],[5.4,0],[5.5,0],[5.6,0],[5.7,0],[5.8,0],[5.9,0],[6,0],[6.1,0],[6.2,
> 0],[6.3,0],[6.4,0],[6.5,0],[6.6,0],[6.7,0],[6.8,0],[6.9,0],[7,0],[7.1,
> 0],[7.2,0],[7.3,0],[7.4,0],[7.5,0],[7.6,0],[7.7,0],[7.8,0],[7.9,0],[8,
> 0],[8.1,0],[8.2,0],[8.3,0],[8.4,0],[8.5,0],[8.6,0],[8.7,0],[8.8,0],[8.
> 9,0],[9,0],[9.1,0],[9.2,0],[9.3,0],[9.4,0],[9.5,0],[9.6,0],[9.7,0],[9.
> 8,0],[9.9,0],[10,50]]:
> 
> frame1 :=
> [[0,100],[0.1,95.7382],[0.2,91.5006],[0.3,87.263],[0.4,83.0972],[0.5,7
> 8.9314],[0.6,74.8826],[0.7,70.8339],[0.8,66.9434],[0.9,63.053],[1,59.3
> 571],[1.1,55.6612],[1.2,52.1899],[1.3,48.7187],[1.4,45.4953],[1.5,42.2
> 72],[1.6,39.313],[1.7,36.3539],[1.8,33.6683],[1.9,30.9827],[2,28.573],
> [2.1,26.1633],[2.2,24.0258],[2.3,21.8883],[2.4,20.014],[2.5,18.1396],[
> 2.6,16.5149],[2.7,14.8902],[2.8,13.4981],[2.9,12.106],[3,10.9272],[3.1
> ,9.74842],[3.2,8.76219],[3.3,7.77597],[3.4,6.96106],[3.5,6.14615],[3.6
> ,5.48166],[3.7,4.81717],[3.8,4.2832],[3.9,3.74923],[4,3.32744],[4.1,2.
> 90564],[4.2,2.57963],[4.3,2.25362],[4.4,2.00925],[4.5,1.76488],[4.6,1.
> 59042],[4.7,1.41596],[4.8,1.30219],[4.9,1.18842],[5,1.12862],[5.1,1.06
> 883],[5.2,1.05878],[5.3,1.04873],[5.4,1.08659],[5.5,1.12445],[5.6,1.21
> 064],[5.7,1.29682],[5.8,1.43389],[5.9,1.57096],[6,1.76338],[6.1,1.9558
> 1],[6.2,2.20979],[6.3,2.46377],[6.4,2.78697],[6.5,3.11017],[6.6,3.5114
> ],[6.7,3.91264],[6.8,4.40153],[6.9,4.89042],[7,5.47697],[7.1,6.06353],
> [7.2,6.75769],[7.3,7.45185],[7.4,8.26298],[7.5,9.07412],[7.6,10.0105],
> [7.7,10.9469],[7.8,12.0151],[7.9,13.0833],[8,14.2879],[8.1,15.4924],[8
> .2,16.835],[8.3,18.1776],[8.4,19.657],[8.5,21.1364],[8.6,22.748],[8.7,
> 24.3595],[8.8,26.0951],[8.9,27.8307],[9,29.6787],[9.1,31.5266],[9.2,33
> .4718],[9.3,35.417],[9.4,37.4413],[9.5,39.4657],[9.6,41.5486],[9.7,43.
> 6315],[9.8,45.7503],[9.9,47.8691],[10,50]]:
> 
> frame2 :=
> [[0,100],[0.1,96.992],[0.2,93.9841],[0.3,90.9934],[0.4,88.0028],[0.5,8
> 5.0464],[0.6,82.09],[0.7,79.1844],[0.8,76.2788],[0.9,73.4395],[1,70.60
> 03],[1.1,67.842],[1.2,65.0838],[1.3,62.4199],[1.4,59.756],[1.5,57.1984
> ],[1.6,54.6408],[1.7,52.1999],[1.8,49.7589],[1.9,47.4435],[2,45.1281],
> [2.1,42.9453],[2.2,40.7625],[2.3,38.7178],[2.4,36.6731],[2.5,34.7703],
> [2.6,32.8675],[2.7,31.109],[2.8,29.3505],[2.9,27.7371],[3,26.1238],[3.
> 1,24.6552],[3.2,23.1866],[3.3,21.8613],[3.4,20.536],[3.5,19.3515],[3.6
> ,18.167],[3.7,17.1202],[3.8,16.0733],[3.9,15.1603],[4,14.2472],[4.1,13
> .4639],[4.2,12.6806],[4.3,12.0226],[4.4,11.3645],[4.5,10.8274],[4.6,10
> .2903],[4.7,9.86972],[4.8,9.44913],[4.9,9.14094],[5,8.83275],[5.1,8.63
> 308],[5.2,8.4334],[5.3,8.33872],[5.4,8.24404],[5.5,8.25119],[5.6,8.258
> 35],[5.7,8.36457],[5.8,8.4708],[5.9,8.67368],[6,8.87657],[6.1,9.17403]
> ,[6.2,9.47149],[6.3,9.86169],[6.4,10.2519],[6.5,10.7332],[6.6,11.2144]
> ,[6.7,11.7852],[6.8,12.3559],[6.9,13.0145],[7,13.6732],[7.1,14.4179],[
> 7.2,15.1626],[7.3,15.9914],[7.4,16.8202],[7.5,17.7308],[7.6,18.6413],[
> 7.7,19.6308],[7.8,20.6203],[7.9,21.6853],[8,22.7504],[8.1,23.8872],[8.
> 2,25.0239],[8.3,26.2277],[8.4,27.4315],[8.5,28.6971],[8.6,29.9628],[8.
> 7,31.2843],[8.8,32.6059],[8.9,33.9768],[9,35.3477],[9.1,36.7607],[9.2,
> 38.1738],[9.3,39.6213],[9.4,41.0688],[9.5,42.5425],[9.6,44.0163],[9.7,
> 45.5078],[9.8,46.9992],[9.9,48.4996],[10,50]]:
> 
> frame3 :=
> [[0,100],[0.1,97.5618],[0.2,95.1235],[0.3,92.6953],[0.4,90.2671],[0.5,
> 87.8588],[0.6,85.4506],[0.7,83.072],[0.8,80.6934],[0.9,78.354],[1,76.0
> 145],[1.1,73.7233],[1.2,71.4322],[1.3,69.1979],[1.4,66.9636],[1.5,64.7
> 944],[1.6,62.6252],[1.7,60.5286],[1.8,58.4321],[1.9,56.4152],[2,54.398
> 3],[2.1,52.4673],[2.2,50.5364],[2.3,48.6971],[2.4,46.8578],[2.5,45.115
> ],[2.6,43.3723],[2.7,41.7304],[2.8,40.0885],[2.9,38.5511],[3,37.0136],
> [3.1,35.5835],[3.2,34.1534],[3.3,32.8329],[3.4,31.5123],[3.5,30.303],[
> 3.6,29.0937],[3.7,27.9967],[3.8,26.8997],[3.9,25.9154],[4,24.9312],[4.
> 1,24.0597],[4.2,23.1883],[4.3,22.4292],[4.4,21.6702],[4.5,21.0226],[4.
> 6,20.375],[4.7,19.8378],[4.8,19.3005],[4.9,18.872],[5,18.4435],[5.1,18
> .1219],[5.2,17.8003],[5.3,17.5835],[5.4,17.3668],[5.5,17.2525],[5.6,17
> .1383],[5.7,17.1241],[5.8,17.1098],[5.9,17.1929],[6,17.2759],[6.1,17.4
> 534],[6.2,17.6308],[6.3,17.8996],[6.4,18.1684],[6.5,18.5253],[6.6,18.8
> 822],[6.7,19.3239],[6.8,19.7655],[6.9,20.2884],[7,20.8112],[7.1,21.411
> 5],[7.2,22.0117],[7.3,22.6855],[7.4,23.3593],[7.5,24.1025],[7.6,24.845
> 8],[7.7,25.6541],[7.8,26.4625],[7.9,27.3314],[8,28.2004],[8.1,29.1253]
> ,[8.2,30.0502],[8.3,31.0262],[8.4,32.0021],[8.5,33.024],[8.6,34.0459],
> [8.7,35.1085],[8.8,36.1711],[8.9,37.2689],[9,38.3666],[9.1,39.4941],[9
> .2,40.6215],[9.3,41.7727],[9.4,42.924],[9.5,44.0933],[9.6,45.2626],[9.
> 7,46.4439],[9.8,47.6252],[9.9,48.8126],[10,50]]:
> 
> frame4 :=
> [[0,100],[0.1,97.9296],[0.2,95.8628],[0.3,93.796],[0.4,91.7399],[0.5,8
> 9.6838],[0.6,87.6453],[0.7,85.6069],[0.8,83.5931],[0.9,81.5793],[1,79.
> 5968],[1.1,77.6144],[1.2,75.6698],[1.3,73.7253],[1.4,71.8251],[1.5,69.
> 9248],[1.6,68.0748],[1.7,66.2249],[1.8,64.4309],[1.9,62.637],[2,60.904
> 5],[2.1,59.172],[2.2,57.506],[2.3,55.8399],[2.4,54.245],[2.5,52.6501],
> [2.6,51.1305],[2.7,49.611],[2.8,48.1706],[2.9,46.7303],[3,45.3726],[3.
> 1,44.0148],[3.2,42.7427],[3.3,41.4705],[3.4,40.2865],[3.5,39.1025],[3.
> 6,38.0088],[3.7,36.915],[3.8,35.9132],[3.9,34.9114],[4,34.0028],[4.1,3
> 3.0942],[4.2,32.2797],[4.3,31.4652],[4.4,30.7452],[4.5,30.0253],[4.6,2
> 9.3999],[4.7,28.7746],[4.8,28.2436],[4.9,27.7126],[5,27.2753],[5.1,26.
> 838],[5.2,26.4934],[5.3,26.1488],[5.4,25.8956],[5.5,25.6423],[5.6,25.4
> 789],[5.7,25.3154],[5.8,25.2398],[5.9,25.1642],[6,25.1743],[6.1,25.184
> 3],[6.2,25.2776],[6.3,25.3708],[6.4,25.5445],[6.5,25.7182],[6.6,25.969
> 4],[6.7,26.2206],[6.8,26.5462],[6.9,26.8718],[7,27.2683],[7.1,27.6648]
> ,[7.2,28.1287],[7.3,28.5926],[7.4,29.12],[7.5,29.6475],[7.6,30.2345],[
> 7.7,30.8216],[7.8,31.4642],[7.9,32.1067],[8,32.8005],[8.1,33.4943],[8.
> 2,34.2348],[8.3,34.9754],[8.4,35.7582],[8.5,36.5409],[8.6,37.3613],[8.
> 7,38.1816],[8.8,39.0347],[8.9,39.8878],[9,40.7688],[9.1,41.6497],[9.2,
> 42.5536],[9.3,43.4575],[9.4,44.3793],[9.5,45.3012],[9.6,46.2358],[9.7,
> 47.1704],[9.8,48.1127],[9.9,49.0551],[10,50]]:
> 
> frame5 :=
> [[0,100],[0.1,98.2038],[0.2,96.4104],[0.3,94.617],[0.4,92.8319],[0.5,9
> 1.0468],[0.6,89.2754],[0.7,87.504],[0.8,85.7518],[0.9,83.9996],[1,82.2
> 717],[1.1,80.5439],[1.2,78.8457],[1.3,77.1475],[1.4,75.4839],[1.5,73.8
> 204],[1.6,72.1962],[1.7,70.5721],[1.8,68.9921],[1.9,67.412],[2,65.8805
> ],[2.1,64.349],[2.2,62.8701],[2.3,61.3913],[2.4,59.9691],[2.5,58.5468]
> ,[2.6,57.1848],[2.7,55.8228],[2.8,54.5244],[2.9,53.226],[3,51.9942],[3
> .1,50.7624],[3.2,49.6],[3.3,48.4376],[3.4,47.3469],[3.5,46.2563],[3.6,
> 45.2395],[3.7,44.2228],[3.8,43.2817],[3.9,42.3406],[4,41.4765],[4.1,40
> .6125],[4.2,39.8267],[4.3,39.0408],[4.4,38.3339],[4.5,37.627],[4.6,36.
> 9995],[4.7,36.3721],[4.8,35.8241],[4.9,35.2762],[5,34.8076],[5.1,34.33
> 9],[5.2,33.9493],[5.3,33.5595],[5.4,33.2479],[5.5,32.9362],[5.6,32.701
> 5],[5.7,32.4668],[5.8,32.3077],[5.9,32.1486],[6,32.0634],[6.1,31.9783]
> ,[6.2,31.9652],[6.3,31.9521],[6.4,32.0089],[6.5,32.0657],[6.6,32.19],[
> 6.7,32.3143],[6.8,32.5035],[6.9,32.6926],[7,32.9438],[7.1,33.195],[7.2
> ,33.5052],[7.3,33.8154],[7.4,34.1814],[7.5,34.5473],[7.6,34.9656],[7.7
> ,35.3839],[7.8,35.851],[7.9,36.3181],[8,36.8302],[8.1,37.3423],[8.2,37
> .8956],[8.3,38.4489],[8.4,39.0393],[8.5,39.6298],[8.6,40.2533],[8.7,40
> .8769],[8.8,41.5293],[8.9,42.1817],[9,42.8587],[9.1,43.5357],[9.2,44.2
> 329],[9.3,44.9301],[9.4,45.643],[9.5,46.356],[9.6,47.0803],[9.7,47.804
> 5],[9.8,48.5356],[9.9,49.2667],[10,50]]:
> 
> plots[display]([plot(frame0),plot(frame1),plot(frame2),plot(frame3),pl
> ot(frame4),plot(frame5)], insequence=true);
# 
# (18.2)  If you use the C program "heat11" with the appropriate input
# file, or if you copy the commands from above and put them into a file
# called "heat-output.txt", you can create the animation from above by
# evaluating this.
# 
> read(`heat-output.txt`);
>