{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 1 }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 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plo t" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f := proc(x) 1/2*x^2+2*x + 1; end: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "rando := rand(-10^5 .. \+ 10^5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "for i from 1 to \+ 10 do\n x[i] := i;\n if i = 3 then y[i] := f(i) + 0; else y[i] : = f(i) + rando()/(10.0^5)/2;\nfi;print(\"y[\",i,\"]\",y[i]);od;\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y[6\"\"\"\"Q\"]F$$\"I+++++++++++++++++u=O!#R" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y[6\"\"\"#Q\"]F$$\"I+++++++++++++++++I4m!#R" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y[6\"\"\"$Q\"]F$#\"#B\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"%F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y [6\"\"\"%Q\"]F$$\"I++++++++++++++++&[Lq\"!#Q" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y [6\"\"\"&Q\"]F$$\"I++++++++++++++++0')pB!#Q" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y [6\"\"\"'Q\"]F$$\"I++++++++++++++++!p#eI!#Q" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"(F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y [6\"\"\"(Q\"]F$$\"I++++++++++++++++lX4R!#Q" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\")F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y [6\"\"\")Q\"]F$$\"I++++++++++++++++b!p*[!#Q" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"*F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y [6\"\"\"*Q\"]F$$\"I++++++++++++++++qsOf!#Q" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"#5F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q#y[ 6\"\"#5Q\"]F$$\"I++++++++++++++++&3u5(!#Q" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 81 "points := []:for i from 1 to 10 do\n points := [ op(points), [x[i], y[i]]];\nod:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "points;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7,7$\"\"\"$ \"I+++++++++++++++++u=O!#R7$\"\"#$\"I+++++++++++++++++I4mF(7$\"\"$#\"# BF*7$\"\"%$\"I++++++++++++++++&[Lq\"!#Q7$\"\"&$\"I++++++++++++++++0')p BF57$\"\"'$\"I++++++++++++++++!p#eIF57$\"\"($\"I++++++++++++++++lX4RF5 7$\"\")$\"I++++++++++++++++b!p*[F57$\"\"*$\"I++++++++++++++++qsOfF57$ \"#5$\"I++++++++++++++++&3u5(F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "p1 := plot(points, style=point,color = blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "A := Matrix(10,2): b := Vector(10): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 194 "x_coords := []: y_coor ds:=[]: yw_coords:=[]:\nfor i from 1 to 10 do\n x_coords := [op(x_c oords), x[i]]; A[i,1] := 1; A[i,2] := x[i];\n y_coords := [op(y_coo rds), y[i]]; b[i] := y[i];\n od:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "A;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*% QoI:-%'MATRIXG6#7,7$\"\"\"F,7$F,\"\"#7$F,\"\"$7$F,\"\"%7$F,\"\"&7$F,\" \"'7$F,\"\"(7$F,\"\")7$F,\"\"*7$F,\"#5%'MatrixG" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 2 "b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLE G6%\"*3y1`\"-%'MATRIXG6#7,7#$\"I+++++++++++++++++u=O!#R7#$\"I+++++++++ ++++++++I4mF.7##\"#B\"\"#7#$\"I++++++++++++++++&[Lq\"!#Q7#$\"I++++++++ ++++++++0')pBF97#$\"I++++++++++++++++!p#eIF97#$\"I++++++++++++++++lX4R F97#$\"I++++++++++++++++b!p*[F97#$\"I++++++++++++++++qsOfF97#$\"I+++++ +++++++++++&3u5(F9&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "x_coords;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"\"\" \"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "y_coords;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7,$ \"I+++++++++++++++++u=O!#R$\"I+++++++++++++++++I4mF&#\"#B\"\"#$\"I++++ ++++++++++++&[Lq\"!#Q$\"I++++++++++++++++0')pBF.$\"I++++++++++++++++!p #eIF.$\"I++++++++++++++++lX4RF.$\"I++++++++++++++++b!p*[F.$\"I++++++++ ++++++++qsOfF.$\"I++++++++++++++++&3u5(F." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "Digits:=40;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'D igitsG\"#S" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "model := stat s[fit,leastsquare[[x,y],y= 'c'[2]*x^2 \n+ 'c'[1]*x + 'c'[0]]]([x_coord s, y_coords]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&modelG/%\"yG,(*&$ \"I_^^^^^^^^^^^^^^,ku!3&!#S\"\"\")%\"xG\"\"#F,F,*&$\"Izyyyyyyyyyyyyyy. l.2>!#RF,F.F,F,$\"ILLLLLLLLLLLLLLL$30_5\"F3F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "sum((y[k]-subs('x'='x'[k], op(2,model)))^2,k=1.. 10)^(1/2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"I*4))3$QjLnwg\"*)>07 q'\\uem!#S" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "xhat := Linea rSolve(Transpose(A) . A, Transpose(A) . b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%xhatG-%'RTABLEG6%\"*wqYq\"-%'MATRIXG6#7$7#$!I+++++++ +++++++++PC25!#Q7#$\"IXXXXXXXXXXXXXXXXv&e\\(!#R&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Norm(A . xhat - b, 2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"In(po(4cg7)z0=$4wwLSOp6!#Q" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "oldres:=%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'oldresG$\"In(po(4cg7)z0=$4wwLSOp6!#Q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "p2 := plot(op(2, model), x=0..10, c olor = red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plots[displ ay](\{p1, p2\});" }}{PARA 13 "" 1 "" {GLPLOT2D 492 492 492 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"!F)$\"ILLLLLLLLLLLLLLL$30_5\"!#R7$$\"Immmmmm mmmmmmmmm;arz@!#S$\"IUv3Uv3ncmfI#)pJe0U-X:F,7$$\"ILLLLLLLLLLLLLL$e9ui2 %F0$\"I[\"[\"[1'4`!4k'4:0P0=()p'>F,7$$\"Immmmmmmmmmmmmmm\"z_\"4iF0$\"I w4Vw4odUa&[#F,7$$\"IlmmmmmmmmmmmmmmT&phN)F0$\"I)=_&)=-)pH&=_ 0v7A'GJ_`IF,7$$\"ILLLLLLLLLLLLLLe*=)H\\5F,$\"I0St1l/-#fDS13.$)Qxecm$F, 7$$\"Immmmmmmmmmmmmm\"z/3uC\"F,$\"IHl)>.*zk,r[sCRehTbjuUF,7$$\"I++++++ ++++++++DJ$RDX\"F,$\"IGFFF_3NK/#Hdt*Qv5BAZ\\F,7$$\"Immmmmmmmmmmmmm\"zR 'ok;F,$\"I-Pq.i^6#*4f')pmi+,&*y(o&F,7$$\"I++++++++++++++D1J:w=F,$\"I21 11JPE*QQ]ymgah6&\\rkF,7$$\"ILLLLLLLLLLLLLLL3En$4#F,$\"Ia)=_&)=-)pzZ%)R (fmAdU]K(F,7$$\"Immmmmmmmmmmmmm;/RE&G#F,$\"IQt1StJr='p&RrfW:x:n;\")F,7 $$\"I+++++++++++++++D.&4]#F,$\"I>=====V*f2^^YiGsy*[_!*F,7$$\"I++++++++ +++++++vB_E>\"zyMm,9(R+\"!#Q7$$\"I+++++++++++++++v'H i#HF,$\"Ihgggg5tQO#4o_#G&QO=O5\"Fio7$$\"Immmmmmmmmmmmmm\"z*ev:JF,$\"Iy 6XGCB/w.s#)Ry-b!3Uz>\"Fio7$$\"ILLLLLLLLLLLLLLL347TLF,$\"Ik(4Vw4o2b2lu$ ['=2q_[J\"Fio7$$\"ILLLLLLLLLLLLLLLLY.KNF,$\"Il)>`')>`'[WBE)RpU#p\"HzT \"Fio7$$\"I***************************\\7o7Tv$F,$\"ILLL$e9;#)3dP)[2OW% [\"\\U:Fio7$$\"ILLLLLLLLLLLLLLL$Q*o]RF,$\"I!Rs0Rs0k`j>]ulf1eJpl\"Fio7$ $\"I***************************\\7=lj;%F,$\"ILLL$e9mW*fjuef))GUz+(y\"F io7$$\"I***************************\\PaRFio7$$\"ILLLLLLLLLLLLLL$e9Ege%F,$\"Iz7Yzie2^QEc$GA'o9ll`?Fio7$$\"ILLL LLLLLLLLLLLeR\"3Gy%F,$\"Iv3UD@XKV'*R0CZn\")3J&[=#Fio7$$\"Immmmmmmmmmmm mm;/T1&*\\F,$\"I`(3UvLtq&eS!=E4z:]x2L#Fio7$$\"Immmmmmmmmmmmmm\"zRQb@&F ,$\"I\"[\"[JFEKg90/!4y*3m#*>([#Fio7$$\"I***************************\\( =>Y2aF,$\"I011c=MW)zd8!eh[zBiQFEFio7$$\"Immmmmmmmmmmmmm;zXu9cF,$\"I')> `')plkXnxQ97/3@i*Hy#Fio7$$\"I******************************\\y))GeF,$ \"I::::::lF=U:j=!36sT$[HFio7$$\"I****************************\\i_QQgF, $\"IKLLL$ek./ezpqV3,G4Y6$Fio7$$\"I***************************\\7y%3TiF ,$\"ILLL$e9m%pGt%))>jpSwE(zKFio7$$\"I****************************\\P![ hY'F,$\"ILLLL$eky(*oDrC0N***H&zY$Fio7$$\"IKLLLLLLLLLLLLLL$Qx$omF,$\"I5 Xy6Xyhdcn'zEh'etHZTOFio7$$\"I*****************************\\P+V)oF,$\" IUUUUU#\\bpj`dJ\"*>E#*H8$QFio7$$\"Immmmmmmmmmmmmm\"zpe*zqF,$\"ISu2\"pe oO,19uqhUn-gu+%Fio7$$\"I*****************************\\#\\'QH(F,$\"IFF FFFxRb:P@N0Ti8zY/UFio7$$\"IKLLLLLLLLLLLLLe9S8&\\(F,$\"IWy6&4*RLLu$4*H? -<`D3%R%Fio7$$\"I***************************\\i?=bq(F,$\"I011c=48`j7$z ?%)4Vo%o'f%Fio7$$\"IKLLLLLLLLLLLLLL3s?6zF,$\"Iy7Yz7'>4%fl]v+Y#z[8\"*z% Fio7$$\"I***************************\\7`Wl7)F,$\"I!===V*fKxN(H;yFAh-Wc ,&Fio7$$\"Ilmmmmmmmmmmmmmmm*RRL)F,$\"I=`')>`')>.*zAGAbiX5V'G_Fio7$$\"I lmmmmmmmmmmmmm;a<.Y&)F,$\"IRu2TC?>Dy$[ouAhgv&)4X&Fio7$$\"IKLLLLLLLLLLL LLe9tOc()F,$\"IHj'*zvCVCtK\"poLyrh,gn&Fio7$$\"I*********************** *******\\Qk\\*)F,$\"I011111c=4eJz2\\$4DJn)eFio7$$\"IKLLLLLLLLLLLLL$3dg 6<*F,$\"I'3Uv3n1acBqkqxyoc>H8'Fio7$$\"IlmmmmmmmmmmmmmmmxGp$*F,$\"Io.Pq .Pq`\\=$GVq\"**4wLdjFio7$$\"I)**************************\\7oK0e*F,$\"I egg5t))[lg$\\trWKyw25g'Fio7$$\"I)**************************\\(=5s#y*F, $\"I&ppp%4Dg?k.].ldim#y%QoFio7$$\"#5F)$\"Ikjjjjjjjjjjjjjj8MI)4(Fio-%'C OLOURG6&%$RGBG$\"*++++\"!\")F(F(-F$6%7,7$$\"\"\"F)$\"I++++++++++++++++ +u=OF,7$$\"\"#F)$\"I+++++++++++++++++I4mF,7$$\"\"$F)$\"I++++++++++++++ ++++]6Fio7$$\"\"%F)$\"I++++++++++++++++&[Lq\"Fio7$$\"\"&F)$\"I++++++++ ++++++++0')pBFio7$$\"\"'F)$\"I++++++++++++++++!p#eIFio7$$\"\"(F)$\"I++ ++++++++++++++lX4RFio7$$\"\")F)$\"I++++++++++++++++b!p*[Fio7$$\"\"*F)$ \"I++++++++++++++++qsOfFio7$Fez$\"I++++++++++++++++&3u5(Fio-Fjz6&F\\[l F(F(F][l-%&STYLEG6#%&POINTG-%+AXESLABELSG6%Q\"x6\"Q!F]_l-%%FONTG6#%(DE FAULTG-%%VIEWG6$;F(FezFb_l" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?stats" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "21 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 153068384 153067808 170467076 }{RTABLE M7R0 I6RTABLE_SAVE/153068384X,%)anythingG6"6"[gl!"%!!!#5"+"#"""F'F'F'F'F'F'F'F'F'F'" "#""$""%""&""'""("")""*"#5F& } {RTABLE M7R0 I6RTABLE_SAVE/153067808X*%)anythingG6"6"[gl!#%!!!"+"+$"I+++++++++++++++++u=O!#R $"I+++++++++++++++++I4mF)#"#B""#$"I++++++++++++++++&[Lq"!#Q$"I++++++++++++++++0 ')pBF1$"I++++++++++++++++!p#eIF1$"I++++++++++++++++lX4RF1$"I++++++++++++++++b!p *[F1$"I++++++++++++++++qsOfF1$"I++++++++++++++++&3u5(F1F& } {RTABLE M7R0 I6RTABLE_SAVE/170467076X*%'sfloatG6"6"[gl!#%!!!"#"#$!I++++++++++++++++PC25!#Q$" IXXXXXXXXXXXXXXXXv&e\(!#RF& }