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0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "" -1 225 "Times" 1 14 0 0 255 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 226 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 227 "Times" 1 14 0 128 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 228 "Times" 1 14 0 128 0 1 2 2 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 210 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 8 2 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT 229 10 " " }{TEXT 210 32 " Quick Introduction to Maple" }}{PARA 4 "" 0 "" {TEXT 230 19 " (Please, read also " }{TEXT 211 15 "New User's Tour" }{TEXT 230 39 " ( click \"Help\" and \"New User's Tour\" ))" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 231 87 "Learning basics of Maple is very easy. Every Maple work sheet consists of parts, called " }{TEXT 212 16 "execution groups" } {TEXT 213 1 "," }{TEXT 231 146 " marked by vertical lines on the left. Some execution groups contain text, like this one. Some, displayed in red with the prompt [> in front, are " }{TEXT 214 13 "command lines" }{TEXT 231 25 ". In general, you should " }{TEXT 215 20 "execute all c ommands" }{TEXT 231 79 " by placing a cursor on the command line and \+ pressing ENTER. For example, the " }{TEXT 216 8 "restart;" }{TEXT 231 180 " command above clears all prior Maple assignments and starts a fr esh Maple session for you. As with every mathematical software, Maple \+ has its own way of entering commands, called " }{TEXT 217 6 "syntax" } {TEXT 231 41 ". The syntax must be strictly followed. \n" }}{PARA 4 "" 0 "" {TEXT 230 48 "Basics: precise arithmetics, use of the command " }{TEXT 209 6 "evalf " }{TEXT 230 26 "to obtain numerical value\n" }} {PARA 206 "" 0 "" {TEXT 231 108 "The way to enter arithmetical operati ons is very similar in Maple as it is in most of graphing calculators: " }{TEXT 218 1 "+" }{TEXT 231 2 ", " }{TEXT 219 1 "-" }{TEXT 231 32 " , for addition and subtraction, " }{TEXT 220 1 "*" }{TEXT 231 47 " for multiplication, (don't forget this one!), " }{TEXT 221 1 "/" }{TEXT 231 15 " for division, " }{TEXT 222 1 "^" }{TEXT 231 77 " for power. F or example, if you want to calculate the value of the expression" }} {PARA 207 "" 0 "" {TEXT 232 0 "" }{XPPEDIT 18 0 "Typesetting:-mrow(Typ esetting:-mfrac(Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:- mrow(Typesetting:-mn(\"2\", mathvariant = \"normal\"), Typesetting:-mo (\"+\", mathvariant = \"normal\", fence = \"false\", separator = \"fal se\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\" , movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222e m\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-msup(Ty pesetting:-mn(\"3\", mathvariant = \"normal\"), Typesetting:-mn(\"5\", mathvariant = \"normal\"), superscriptshift = \"0\")), Typesetting:-m i(\"\")), Typesetting:-mi(\"\")), Typesetting:-mrow(Typesetting:-mi(\" \"), Typesetting:-mrow(Typesetting:-mn(\"7\", mathvariant = \"normal\" ), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fen ce = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mfen ced(Typesetting:-mrow(Typesetting:-mn(\"31\", mathvariant = \"normal\" ), Typesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", l argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp ace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn(\"16 \", mathvariant = \"normal\")), mathvariant = \"normal\")), Typesettin g:-mi(\"\")), linethickness = \"1\", denomalign = \"center\", numalign = \"center\", bevelled = \"false\"));" "-I%mrowG6#/I+modulenameG6\"I, TypesettingGI(_syslibGF'6#-I&mfracGF$6(-F#6%-I#miGF$6#Q!F'-F#6&-I#mnGF $6$Q\"2F'/%,mathvariantGQ'normalF'-I#moGF$6-Q\"+F'F:/%&fenceGQ&falseF' /%*separatorGFC/%)stretchyGFC/%*symmetricGFC/%(largeopGFC/%.movablelim itsGFC/%'accentGFC/%'lspaceGQ,0.2222222emF'/%'rspaceGFR-F#6#-I%msupGF$ 6%-F76$Q\"3F'F:-F76$Q\"5F'F:/%1superscriptshiftGQ\"0F'F0F0-F#6%F0-F#6% -F76$Q\"7F'F:-F>6-Q1⁢F'F:FAFDFFFHFJFLFN/FQQ&0.0emF'/FTF ho-I(mfencedGF$6$-F#6%-F76$Q#31F'F:F=-F76$Q#16F'F:F:F0/%.linethickness GQ\"1F'/%+denomalignGQ'centerF'/%)numalignGFjp/%)bevelledGFC" }{TEXT 232 3 " " }}{PARA 0 "" 0 "" {TEXT 223 0 "" }{TEXT 209 10 "you enter: " }}{PARA 0 "" 0 "" {TEXT 233 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "(2+3^5)/(7*(31+16));" }{TEXT 233 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 231 130 "Execute the command above, by placing the cursor on the red line and pressing ENTER, to see the result, th e output, displayed in " }{TEXT 224 4 "blue" }{TEXT 231 1 "." }}{PARA 209 "" 0 "" {TEXT 225 5 "Note:" }{TEXT 226 1 " " }{TEXT 227 12 "Observ e that" }{TEXT 209 1 " " }{TEXT 228 227 "every Maple command has to en d with a semicolon! Observe also, that because of the rules of associa ting operations, you must enclose the denominator in parentheses. This applies to Maple as well as to your graphing calculators." }{TEXT 209 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " a:=32/5;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "b:=14/7;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 4 "a+b;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a*b;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a-b;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "12!;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "127!;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Pi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(Pi/3);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "cos(Pi/4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sin(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(sin(1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalf(sin(1),120);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(Pi, 340);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf(exp(1)); e:= exp(1);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 21 "Symbolic Calculations " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand((c+d)^4);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "p:=x^2-4*x-5; factor(p); " } }}{EXCHG {PARA 4 "" 0 "" {TEXT 230 17 "Solving equations" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve(p,x); solve(p=3,x);" }}} {EXCHG {PARA 4 "" 0 "" {TEXT 230 22 "Defining an expression" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 233 0 "" }{MPLTEXT 1 0 18 "f:=ln(x^2+sin( x));" }{TEXT 233 0 "" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 37 "Differen tiation (finding derivatives)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g:= diff(f,x);" }{TEXT 233 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "gg:=diff(f,x,x,x);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 35 "Derivative of the previous function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(%,x);" }{TEXT 233 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }{TEXT 233 0 "" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 24 "Integration of functions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int(sin(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "int(x*ln(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "int(f,x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int (f,x=1..9);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(%);\n" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 4 "Sums" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "sum(k^2,'k'=1..r);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sum(q^k,k=0..r);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 19 "Limits of functions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "limit(x*(Pi/2-arctan(x)),x=infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "limit(ln(cos(x))/x^2,x=0);" }}}{EXCHG {PARA 4 "" 0 " " {TEXT 230 50 "Plotting graphs of functions (2-dimensional plots)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(g,x=1..4); " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(\{x*sin(x),x^2\},x=-1.. 1); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(sin(1/x), x=-0 .10..0.10);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 50 " Plotting graphs \+ of functions(3-dimensional plots)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "plot3d(2*x+y^2-x^3-1,x=-4..4, y=-4..4, axes=box);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot3d(x^2+y^2, x=-1..1, y= -1..1, axes=normal);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plo t3d(x^2-y^2,x=-2..2,y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot3d(cos(x^2+y^2), x=-3..3,y=-3..3);" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 229 28 "Plotting double-gabled roof " }}{PARA 0 "" 0 "" {TEXT 233 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot3d(1-abs(x), x=-1..1,y=-1..1,axes=box);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot3d(max(1-abs(x),1-abs(y)),x=-1..1,y=-1..1,axes=box);" }}}} {EXCHG {PARA 4 "" 0 "" {TEXT 230 33 "The plotting tools: package plots " }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 229 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }{TEXT 233 0 "" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 17 "Animated graphics" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "animate3d(cos(t*y*x),t=1..10,x=-1..1,y=-1..1,axes=nor mal,frames=10);\n" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 14 "Implicit pl ots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "implicitplot3d( x^2 \+ + y^2 - z^2 + 1,x=-2..2,y=-2..2,\n" }{MPLTEXT 1 0 19 "z=-4..4,axes=box );\n" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 20 "Space curves (helix)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "spacecurve([cos(t),sin(t),t ],t=0..20.2,thickness=5,axes=framed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "for k from 1 to 80 do q[k]:=spacecurve([cos(t),sin(t) ,t],t=0..k*0.2,thickness=5,axes=framed):\n" }{MPLTEXT 1 0 3 "od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "display([seq(q[k],k=1..80)],inseque nce=true);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 25 "Level sets: contou r plots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "contourplot(sin( x*y),x=-3..3,y=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "c ontourplot(x^4/2-x^2*y^2-6*sin(y),x=-3..3,y=-3..3);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 230 13 "Vector fields" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "fieldplot3d([-y, x, 0],x=-1..1,y=-1..1,z=-1..1,color= red, axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 210 "" 0 " " {TEXT 209 42 "Vector Calculus (Gradients, Hessians etc.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "? VectorCalculus;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "with(VectorCalculus):" }{MPLTEXT 1 233 12 " # Load the " }{MPLTEXT 1 233 15 "VectorCalculus " }{MPLTEXT 1 233 6 "packge" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "f:=x[1]*x[ 3]+(x[2]-3*x[3]^2)^2+2*x[1]^2+x[4]^4; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Gradien t(f,[x[1],x[2],x[3],x[4]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "BasisFormat(false); " }{TEXT 209 74 "The output of the Vector Cal culus operations is represented in vector form" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "gf:=Gradient(f,[x[1],x[2],x[3],x[4]]);" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "hf:=Hes sian(f," }{MPLTEXT 1 0 23 "[x[1],x[2],x[3],x[4]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ge:=eval(gf," }{MPLTEXT 1 0 32 "[x[1]=1,x[2 ]=-1,x[3]=3,x[4]=2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "M: =eval(hf,[x[1]=1,x[2]=-1,x[3]=3,x[4]=2]);" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "A:=Matrix(M);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "p:=-LinearSolve(A,ge);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 15 10 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }