{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 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" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "Courier" 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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Problem 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 369 "resis := proc( r1, r2, r3 )\n local s;\n\n if r1<0 or r2<0 or r3 <0 then\n return \+ \"input must be positive\";\n else\n if r1 = 0 or r2 = 0 or r3 \+ = 0 then\n return 0;\n else\n # could be (not rec ommended)\n # return 1/(1/r1+1/r2+1/r3);\n #\n \+ s := 1/r1 + 1/r2 + 1/r3;\n return 1/s;\n end if;\n end if;\n\nend proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "read( \"e:/resis.txt\");" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&resisGf*6%%#r 1G%#r2G%#r3G6#%\"sG6\"F,@%5529$\"\"!29%F229&F2OQ7input~must~be~positiv eF,@%55/F1F2/F4F2/F6F2OF2C$>8$,(*&\"\"\"FEF1!\"\"FE*&FEFEF4FFFE*&FEFEF 6FFFEO-%&evalfG6#*&FEFEFBFFF,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "resis(3,4,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\" !" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "resis(-5,4,-2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#Q7input~must~be~positive6\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "resis(6,7,9);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+\"\\etP#!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 59 "The nested if structure for the in-class project on Sept. 3" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 182 "QuaRoo f := proc( x )\n local ;\n\n if x <= 0 then\n return \"input \+ number must be a positive integer\";\n else\n if x mod 2 = 0 th en\n if x/2 mod 2 = 0\n\n else\n" }}{PARA 258 "" 0 "" {TEXT -1 142 " end if\n else\n if (x+1)/2 mod 2 = 0 then\n\n else\n\n end if\n end if\n end if; \n\n return ...\nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 31 "Ex ample: Problem #10, page 31." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 62 "The classical quadratic formula (as it is ) may not be accurate" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "a, b, c := 10.0^(-20), 1, -1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6%%\"a G%\"bG%\"cG6%$\"+++++5!#H\"\"\"!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 " We want to solve " }{XPPEDIT 18 0 "a*x^2+b*x+c = 0;" "6#/ ,(*&%\"aG\"\"\"*$)%\"xG\"\"#F'F'F'*&%\"bGF'F*F'F'%\"cGF'\"\"!" }{TEXT -1 25 " for that set of a, b, c" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "(-b+sqrt(b^2+4*a*c))/(2*a); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"!F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "(-b-sqrt(b^2+4*a*c))/(2*a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+++++5\"#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 34 "The accurate quadratic formula is " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 " " } {XPPEDIT 18 0 "x[1] = (-b+sqrt(b^2-4*a*c))/(2*a);" "6#/&%\"xG6#\"\"\"* &,&%\"bG!\"\"-%%sqrtG6#,&*$)F*\"\"#F'F'*(\"\"%F'%\"aGF'%\"cGF'F+F'F'*& F2F'F5F'F+" }{TEXT -1 7 " if " }{XPPEDIT 18 0 "b < 0;" "6#2%\"bG\" \"!" }{TEXT -1 16 ", otherwise " }{XPPEDIT 18 0 "" "6#%#%?G" } {XPPEDIT 18 0 "2*c/(-b-sqrt(b^2-4*a*c));" "6#*(\"\"#\"\"\"%\"cGF%,&%\" bG!\"\"-%%sqrtG6#,&*$)F(F$F%F%*(\"\"%F%%\"aGF%F&F%F)F)F)" }{TEXT -1 1 "," }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "The other solution is " }{XPPEDIT 18 0 "x[2] = c/(a*x[1]);" "6#/&%\"xG6# \"\"#*&%\"cG\"\"\"*&%\"aGF*&F%6#F*F*!\"\"" }{TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 114 "Suppose that we want only real solution. We k now that the number of real solutions depends on the discriminant " }{XPPEDIT 18 0 "b^2-4*a*c;" "6#,&*$)%\"bG\"\"#\"\"\"F(*(\"\"%F(%\"aGF( %\"cGF(!\"\"" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "There are two questions to ask in the program: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "1. \+ is discriminant > 0, = 0, or < 0" }}{PARA 0 "" 0 "" {TEXT -1 58 "2. is b > 0 (ask this question only if discriminant > 0.)" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 489 "AccuQuad := pro c( a, b, c)\n local disc, x1, x2;\n\n disc := evalf(b^2 - 4*a*c); \n\n if disc > 0 then\n if evalf(b) > 0 then\n x1 := ev alf(2*c/(-b-sqrt(disc)));\n x2 := evalf(c/(a*x1));\n r eturn x1, x2;\n else\n x1 := evalf((-b+sqrt(disc))/(2*a)) ;\n x2 := evalf(c/(a*x1));\n return x1, x2;\n end if\n elif disc = 0 then\n x1 := evalf(-b/(2*a));\n return x1, x1;\n else\n return \"no real solutions\";\n end if;\n\n end proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 24 "read(\"e:/accuquad.txt\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "AccuQuad(a,b,c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+++++5!\"*$!+++++5\"#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Digits := 10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"# 5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a, b, c := 2, sqrt(2), -3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6%%\"aG%\"bG%\"cG6%\"\"#*$F)# \"\"\"F)!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "AccuQuad(a, b,c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+y[,7#*!#5$!+p#3$G;!\"*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "AccuQuad(0,4,-5);" }} {PARA 8 "" 1 "" {TEXT -1 57 "Error, (in AccuQuad) numeric exception: d ivision by zero\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 57 "In-class project: Real solutions of a quadratic e quation" }}{PARA 0 "" 0 "" {TEXT -1 46 "(Combination of problem 12 and 13 on page 32) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 "Input: a, b, c (for solving " }{XPPEDIT 18 0 "a*x^2+b*x +c = 0;" "6#/,(*&%\"aG\"\"\"*$)%\"xG\"\"#F'F'F'*&%\"bGF'F*F'F'%\"cGF' \"\"!" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "The program needs to ask the following questions:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "1. if a= 0 or not (if so, there is one solution " }{XPPEDIT 18 0 "-c/b;" "6#,$ *&%\"cG\"\"\"%\"bG!\"\"F(" }{TEXT -1 21 " unless b = 0 too)" }} {PARA 0 "" 0 "" {TEXT -1 65 "2. if a = 0, ask if b=0 or not, if so, o utput \"invalid equation\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "3. if a <> 0 then check the discriminant (>0, =0 , <0)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 53 "Homework: the file \"homework03a.do c\" on the website" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 14 0" 53 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }