{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 88 " Quick Maple worksheet \+ to produce graphs of ellipse, for solutions for Homework No. 1" }} {PARA 0 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 96 " First, we define the ellipse as a parame tric equation; below is the syntax to do this:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "nm:=[cos(t),B*sin(t),t=0..2* Pi];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nmG7%-%$cosG6#%\"tG*&%\"BG \"\"\"-%$sinGF(F,/F);\"\"!,$*&\"\"#F,%#PiGF,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 " The equation above has an arbitrary parameter \+ in it, the ratio of the semiaxes in the two directions." }}{PARA 0 "" 0 "" {TEXT -1 101 " The syntax below creates a collection of ellipses with 4 different, specific values for this ratio." }{MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "nms:=seq(subs(B=j/2,nm) ,j=1..4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$nmsG6&7%-%$cosG6#%\"tG ,$*&#\"\"\"\"\"#F.-%$sinGF)F.F./F*;\"\"!,$*&F/F.%#PiGF.F.7%F'F0F27%F', $*&#\"\"$F/F.F0F.F.F27%F',$*&F/F.F0F.F.F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 " The command below then produces a plot with all these \+ distinct, specific ellipses." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 " Note the use of the \"character\" \\n , which gi ves a carriage return inside the title name." }}{PARA 0 "" 0 "" {TEXT -1 56 " Also note one may use Greek characters for labelling." }} {PARA 0 "" 0 "" {TEXT -1 110 " Also note the use of the command scal ing=constrained, which insists on the same length scale for both axes. " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "plo t([nms],x=-1.5..1.5,-2.5..2.5,scaling=constrained, labelfont=[SYMBOL,1 2], labels=[\"x\",\"h\"], title=`Ellipses \\n with axis ratios: 1/2, \+ 1, 3/2, 2`);" }}{PARA 13 "" 1 "" {GLPLOT2D 495 495 495 {PLOTDATA 2 "6* -%'CURVESG6$7S7$$\"\"\"\"\"!$F*F*7$$\"3w\"4hRPij!**!#=$\"3b@$)y74REo!# >7$$\"3E8J#))4-Qn*F/$\"3UiuzzWkm7F/7$$\"3-N5')yke[#*F/$\"3!o;GC;b:!>F/ 7$$\"3?goz=42`')F/$\"3Kdnsp/@1DF/7$$\"3Sb](G._U!zF/$\"3Ow9,NGziIF/7$$ \"3_\\$R'oTd#3(F/$\"3S\"=Y/Nr(HNF/7$$\"3?H$>jubk6'F/$\"3W21wC&fc&RF/7$ $\"3VGuIc:x5]F/$\"3^'f%QpI,FVF/7$$\"37C3nW'R,#QF/$\"3F;+`bFy?YF/7$$\"3 $oY@iF'QDDF/$\"3'GpSs1Mz$[F/7$$\"3OB^hAo8X8F/$\"3/*zr=oeX&\\F/7$$!3+qB /u(p5(f!#@$\"3uk!e'3\"*****\\F/7$$!33)\\T#fB[i8F/$\"3yM(4QktL&\\F/7$$! 3)e:d.:#=YEF/$\"3>h4fuiw@[F/7$$!3%*yV1J*3Jx$F/$\"3l*Q6zEL/j%F/7$$!3V( \\AOF:B/&F/$\"3P@$Rl`UyJ%F/7$$!3[igNw%*[RgF/$\"3S\"3*>>]6&)RF/7$$!3/XU wYjJ*3(F/$\"3hzP=IgQENF/7$$!3&=e_b?/U!zF/$\"3Qae:#pBG1$F/7$$!3w!G5)RnI f')F/$\"37Zmu/-#3]#F/7$$!3/`k8ti$4B*F/$\"3lLV(*fk(G#>F/7$$!3!p!RS4Nij' *F/$\"3%oM2L\">#fG\"F/7$$!3#p(pT>+.2**F/$\"3H:-ED]7-oF27$$!3/gKG4>&*** **F/$\"3Q7hC=Zl]:!#?7$$!3__Is=!Q%3**F/$!3aja*4Gf1v'F27$$!3)>b`sYlSn*F/ $!3snx89:9m7F/7$$!37_J.8AEj#*F/$!3%[Df\"oMl*47e\\F/7$$!3EzyOHMQdIFas$!3A.='4jw***\\F/7$$ \"3GIAj`Ks(G\"F/$!3KtBaA4Pe\\F/7$$\"3EKRqX8/bDF/$!3rTUt9)RS$[F/7$$\"3@ %)yb&Q)zNQF/$!3b^`3'fQvh%F/7$$\"3O7w4w0I.]F/$!3)[,y_!Qa1$F/7$$\"3%*R,@;vLu')F/$!3y4**G'[jx[#F/7$$\"3!G$e@`4 +D#*F/$!3\"yf`$)G%)*H>F/7$$\"31mGAp))oa'*F/$!3#*Hv$)>>f-8F/7$$\"3@zb'f `bp!**F/$!3;q[tIl$[!oF27$F($\"30BmIq&o?5%!#F-%'COLOURG6&%$RGBG$\"#5!\" \"F+F+-F$6$7SF'7$F-$\"3Ikwb#=y_O\"F/7$F4$\"3%[#\\ff*)GLDF/7$F9$\"3gLj& [K5J!QF/7$F>$\"3j9NXR4U7]F/7$FC$\"3t_H-qceDhF/7$FH$\"3!GO#*3qU&fqF/7$F M$\"3!\\@@&\\!>8\"zF/7$FR$\"3-$>p(Qh-a')F/7$FW$\"3aK+16bcT#*F/7$Ffn$\" 3s&Q\"[M\"oen*F/7$F[o$\"33)fVPO<\"4**F/7$F`o$\"2%HhJ<#)******!#<7$Ffo$ \"3ap%>wGZn!**F/7$F[p$\"3PA>=\\D`V'*F/7$F`p$\"3IzF#e`m3E*F/7$Fep$\"3vU 'yI2&oN')F/7$Fjp$\"3!G;)RQ+BqzF/7$F_q$\"3AfvOg?x_qF/7$Fdq$\"3u3HvXQF/7$Fcr$\"3o$p9m#Q%=d#F/7$ Fhr$\"31V?00]Ug8F/7$F]s$\"3vCA\\O%485$Fas7$Fcs$!3q#4*>c=8]8F/7$Fhs$!3U NbFGIGKDF/7$F]t$!3q4&=j`Bsw$F/7$Fbt$!3kENX')3zv\\F/7$Fgt$!37W(H!pUCrgF /7$F\\u$!3Y?#o?\"yMJqF/7$Fau$!3)4j2yeGL'zF/7$Ffu$!3I_Mh6Mil')F/7$F[v$! 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