{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 "" -1 256 "" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 } {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 "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 1" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 1 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 "T imes" 1 12 0 0 0 1 1 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 1" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 24 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Basic Types" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "Expression Sequences" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1,2/6,3,4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x,y,z,w;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "S:=1,x=2,3,4 ;" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 5 "Lists" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "data_list:=[1,2,3,4,5];" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 36 "polynominals:=[x^2+3,x^2+3*x-1,2*x];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "participants:=[Kathy,Frank,R ene,Nilaus,Liz];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "empty_l ist:=[];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "[a,b,c],[b,c,a] ,[a,a,b,c,a];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "letters:=[ a,b,c];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "letters[2];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "nops(letters);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "[letters[],d];" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 16 "[op(letters),d];" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "letters[5];" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 4 "Sets" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "data_set:=\{0,-1, 0,10,2\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "unknowns:=\{x, y,z\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "empty_set:=\{\}; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "\{a,b,c\},\{c,b,a\},\{a ,a,b,c,a\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "\{1,2,2.0\}; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "\{a,b,c\} union \{c,d,e \};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "\{1,2,3\} intersect \+ \{0,1,y,a\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "\{1,2,4,5\} minus \{2,5\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nops(%); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "op(\{1,2,3,a,b\});" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 6 "Arrays" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "squares:=array(1..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "squares[1]:=1; squares[2]:=2^2; squares[3]:=3^2; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "cubes:=array(1..3,[1,8,27 ]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "squares[2];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "squares;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 15 "print(squares);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "pwrs:=array(1..3,1..3);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "pwrs[1,1]:=1; pwrs[1,2]:=1; pwrs[1,3]:=1;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "pwrs[2,1]:=2: pwrs[2,2]:=4: \+ pwrs[2,3]:=8:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "pwrs[3,1]: =3: pwrs[3,2]:=9: pwrs[3,3]:=27:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "print(pwrs);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "pwrs[2,3];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "pwrs:=a rray(1..3,1..3,[[1,1,1],[2,4,8],[3,9,27]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "array3:=array(1..2,1..2,1..2,[[[1,2],[3,4]],[[5,6] ,[7,8]]]);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Expression Manip ulation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "The simplify Command" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "expr:=cos(x)^5+sin(x)^4+2*cos(x)^2- 2*sin(x)^2 - cos(2*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "s implify(expr);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "simplify( sin(x)^2+ln(2*y)+cos(x)^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "simplify(sin(x)^2+ln(2*y)+cos(x)^2,'trig');" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 41 "simplify(sin(x)^2+ln(2*y)+cos(x)^2,'ln');" }}} {EXCHG }{EXCHG }{EXCHG }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "The fact or Command" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "big_poly:=x^5- x^4-7*x^3+x^2+6*x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "facto r(big_poly);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "rat_expr:=( x^3-y^3)/(x^4-y^4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fact or(rat_expr);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "The expand Com mand" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "expand((x+1)*(x+2)); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(sin(x+y));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "expand(exp(a+ln(b)));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "expand((x+1)*(y+z),x+1);" }} }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "The convert Command" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "convert(cos(x),exp);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "convert(1/2*exp(x)+1/2*exp(-x),trig );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "A:=array(1..2,1..2,[[ a,b],[c,d]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "convert(A, 'listlist');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "convert(A,' set');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "convert(%,'list') ;" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "The combine Command" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "combine(exp(x)^2*exp(y),exp) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "combine((x^a)^2,power) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "expr:=(x+1)^(1/2)*(x+2 )^(1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "combine(expr); " }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "The map Command" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "map(f,[a,b,c]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "data_list:=[0,Pi/2,3*Pi/2,2*Pi];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "map(sin,data_list);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "map(f,[a,b,c],x,y);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fcn_list:=[sin(x),ln(x),x^2] ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "map(Diff,fcn_list,x); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "map(value,%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "map(x->x^2,[1,0,1,2,3]);" }} }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 24 "The lhs and rhs commands" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eqn1:=x+y=z+3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "lhs(eqn1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "rhs(eqn1);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 28 "The numer and denom Commands" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "numer(3/4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "denom(1/(1+x));" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 24 "The no ps and op Commands" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "nops([ 1,2,3,4,5]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "op([1,2,3,4 ,5]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nops(x^2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nops(x+y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "op(x^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op(1,x^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op(2,x^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op(0,x^2) ;" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 12 "Substitution" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "L:=3*x*(x-x^3);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(x=2,L);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "subs(x=sqrt(t),L);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 25 "simplify(%) assuming t>0;" }}}{EXCHG }{EXCHG } {EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "L:=( a+b+c)^2;" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG } {EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(a=1,L);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(a+b=p,L);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sub s(a+b+c=p,L);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "algsubs(a+ b=p,L);" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "L:=z*sin(x^2)+Pi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L:=x*(y-1);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "subs(x=y,y=x,L);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "subs(y=x,x=y,L);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "subs(\{x=y,y=x\},L);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Simple sol ve" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG } {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(\{x^2=4\},\{x\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(\{a*x^2+b*x+c=0\},\{x \});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(sin(x)=cos(x) ,x);" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sol ve(sin(x)=cos(x),x,AllSolutions);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "about(_Z10);" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solve(x^4+x^3+2=0,x); # Explicit" }}}{EXCHG } {EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "allvalues(\{%%\});" }}} {EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "solve(\{sin( x)=cos(x),x>0,x<2*Pi\},x,AllSolutions); # Explicit" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "about(_Z13);" }}}{EXCHG }{EXCHG }{EXCHG } {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(\{x^2+3*x>0\},x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^2+3*x>0,x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(\{x^2+b*x>0\},x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "solve(\{x^2+b*x>0\},x) assum ing b>0;" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve(\{x^2+y^2=1,x-y=a\},\{x,y\}); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "allvalues(\{%\});" }}} {EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "eqns:=\{x+2*y=3,y+1/ x=1\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "soln:=solve(eqns, \{x,y\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "soln[1];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "soln[2];" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "Verifying Solutions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs(soln[1],eqns);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs(soln[2],eqns);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "map(evalb,%);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "map(subs,[soln],eqns);" }}}{EXCHG }{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "map2(map,evalb,%);" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "x1:=subs(soln[1],x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "y1:=subs(soln[1],y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }}{EXCHG }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "The unapply Com mand" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "sol:=solve(\{x^2+y^2 =r,p*x-y=0,x>0,y>0\},\{x,y\},Explicit) assuming r>0,p>0;" }}}{EXCHG } {EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(sol,x);" }}} {EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=(p,q)->su bs(sol,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(p,q);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(1,2);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f:=unapply(subs(sol,x),p,r);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(1,2);" }}}{EXCHG }{EXCHG } {EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "The assign Command" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "sol;" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f:=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(g=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "g;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g:=2;" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(sol) ;" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x; y;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 27 "Solving Numerically: fsolve" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "solve(\{cos(x^2)=sin(x)\},x,AllSolutions);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "fsolve(\{cos(x^2)=sin(x)\},x );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "poly:=3*x^8-16*x^5-3* x^2+13*x+16;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fsolve(\{po ly\},x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "fsolve(\{poly\} ,x,complex);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fsolve(\{si n(x)=0\},x);" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG } {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fsolve(\{sin(x)=0\},x=2);" } }}{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "fs olve(\{sin(x)=0\},\{x\},Pi..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "S1:=fsolve(\{cos(x^2)=sin(x)\},\{x\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "S2:=fsolve(\{cos(x^2)=sin(x)\},\{x \},avoid=\{S1\});" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "S3:=fsolve(\{cos(x^2)=sin(x)\},\{x\},avoid=\{S1,S2\});" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=30;" }}} {EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fsolve(\{cos(x)=0\}, \{x\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Other Solver" }}{SECT 1 {PARA 4 " " 0 "" {TEXT -1 25 "Finding Integer Solutions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "isolve(\{3*x-4*y=7\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "about(_Z1);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Finding Solutions Modulo m" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "msolve(\{3*x-4*y=1,7*x+y=2\},17);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "msolve(\{2^n=3\},19);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "2^(13+18*5) mod 19;" }}}{EXCHG } {EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 28 "Solving Recurrence Relations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "rsolve(\{g(n)=g(n-1)+g(n-2),g(0)=1,g(1)=1\} ,\{g(n)\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 30 "Differential Equations: dsolve" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "y:=t->sin(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D(y)(t);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "ode1:=\{diff(y(t),t,t)+5*diff(y(t),t)+6*y(t)=0\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "ic:=\{y(0)=0,D(y)(0)=1\};" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "soln:=dsolve(ode1 union ic, \+ \{y(t)\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "subs(soln,y(t ));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "y1:=unapply(%,t);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "y1(a);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 16 "subs(y=y1,ode1);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "eval(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(y=y1,ic);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "eval(% );" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 36 "Another method for solutio n checking" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "y:=unapply(sub s(soln,y(t)),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "ode1;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "ic;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 7 "y:='y';" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Solving ODE Numerically" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 24 "Numeric dsolve + \+ odeplot" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "ode := (t+1)^2*d iff(y(t),t,t) + (t+1)*diff(y(t),t) + ((t+1)^2-0.25)*y(t) = 0;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "ic := y(0) = 0.67139670714 18030, D(y)(0) = 0.09540051444747446:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "nsoln := dsolve(\{ode,ic\}, type=numeric);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "nsoln(0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "nsoln(0.5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "nsoln(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "odeplot(nsoln,0..5);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 6 "DEplot" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "DEplot(cos(x)*diff(y(x),x$3)-diff(y(x),x$2)+Pi*diff(y(x),x)=y (x)-x,y(x),\nx=-2.5..1.4,[[y(0)=1,D(y)(0)=2,(D@@2)(y)(0)=1]],y=-4..5,s tepsize=.05);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 199 "dfieldplo t([diff(x(t),t)=x(t)*(1-y(t)), diff(y(t),t)=.3*y(t)*(x(t)-1)],\n[x(t), y(t)],t=-2..2, x=-1..2, y=-1..2, arrows=MEDIUM,\ntitle=`Lotka-Volterra model`, color=[.3*y(t)*(x(t)-1),x(t)*(1-y(t)),.1]);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 "Maple packages" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "?package" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "matrix (2,2,[5,4,6,3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "matrix( [[5,4],[6,3]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f := (i, j) -> x^(i+j-1):\nA := matrix(2,2,f);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "map(diff,A,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "B := matr ix([[5,4],[6,3]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalm (A&*B+2*B);" }}}}{PAGEBK }{PARA 260 "" 0 "" {TEXT -1 4 "Grap" }{TEXT 256 0 "" }{TEXT -1 4 "hics" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{SECT 1 {PARA 259 "" 0 "" {TEXT -1 26 "Graphing in Two D imensions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(sin(x),x=- 2*Pi..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:=x->7*sin (x)+sin(7*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f(x), x=0..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(f(x),x=0. .10,y=4..8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(sin(x) /x,x=0..infinity);" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 16 "Parametric Plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot([cos(t),sin(t ),t=0..2*Pi],scaling=constrained);" }{TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 17 "Polar Coordinates" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "polarplot(1,theta=0..2*Pi,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "polarplot(sin(3*theta),theta=0..2*P i);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "polarplot(theta,thet a=0..4*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "polarplot([s in(t),cos(t),t=0..2*Pi]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "polarplot([r,sin(3*r),r=0..7]);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 30 "Functions with Discontinuities" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "f:=x->piecewise(x<1,-1,x<2,1,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(f(x),x=0..3);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 31 "plot(f(x),x=0..3,discont=true);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(1/(x-1)^2,x=-5..6);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot(1/(x-1)^2,x=-5..6,y=-1. .7);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(tan(x),x=-2*Pi ..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(tan(x),x=- 2*Pi..2*Pi,y=-4..4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plo t(tan(x),x=-2*Pi..2*Pi,y=-4..4,discont=true);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "Multiple Plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot([x,x^2,x^3,x^4],x=-10..10,y=-10..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "f:=x->piecewise(x<0,cos(x),x>=0,1+x^2);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([f(x),diff(f(x),x),dif f(f(x),x,x)],x=-2..2,discont=true);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plot([[2*cos(t),sin(t),t=0..2*Pi],[t^2,t^3,t=-1..1]]) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([sin(x)/x,cos(x)/ x],x=0..8*Pi,y=-0.5..2,linestyle=[1,2]);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "Refining Plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot(sum((-1)^(i)*abs(x-i/10),i=0..30),x=-1..4,y=1.5..1.6);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "plot(sum((-1)^(i)*abs(x-i/10 ),i=0..30),x=-1..4,y=1.5..1.6,numpoints=3000);" }}}}{SECT 1 {PARA 4 " " 0 "" {TEXT -1 20 "Plotting Data Points" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "data_list:=[[-2,4],[-1,1],[0,0],[1,1],[2,4],[3,9],[4, 16]];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(data_list);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(data_list,style=poin t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pointplot(data_list);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "x_data:=[seq(i,i=1..10)];" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "y_data:=[seq(x_data[i]^2,i =1..nops(x_data))];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "[seq ([x_data[i],y_data[i]],i=1..nops(x_data))];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "zip((x,y)->[x,y],x_data,y_data);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "pointplot(%);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 28 "Graphing in Three Dimensions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot3d(sin(x*y),x=-2..2,y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:=(x,y)->sin(x)*cos(y);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 26 "plot3d(f,0..2*Pi,0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot3d(f(x,y),x=0..2*Pi,y=0..2*Pi,style=patch); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot3d(sqrt(x-y),x=0..9 ,y=-x..x);" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 16 "Parametric Plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot3d([sin(s),cos(s)*sin( t),sin(t)],s=-Pi..Pi,t=-Pi..Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "plot3d([s*sin(s)*cos(t),s*cos(s)*cos(t),s*sin(t)],s=0 ..2*Pi,t=0..Pi,style=patch);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Spherical Coordinates" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "wi th(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "sphereplot((4 /3)^theta*sin(phi),theta=-1..2*Pi,phi=0..Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "sphereplot(1,theta=0..2*Pi,phi=0..Pi,scaling=con strained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "sphereplot([e xp(s)+t,cos(s+t),t^2],s=0..2*Pi,t=-2..2);" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 23 "Cylindrical Coordinates" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "cylinderplot(theta,theta=0..4*Pi,z=-1..1);" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "Refining plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plot3d(sin(x)*cos(y),x=0..3*Pi,y=0..3*Pi,gr id=[50,50]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "cylinderplo t(theta,theta=0..4*Pi,z=-1..1,grid=[100,5]);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 28 "Shading and Lighting Schemes" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "plot3d(x*y^2/(x^2+y^4),x=-5..5,y=-5..5,style=pat ch,shading=zgrayscale,lightmodel=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "plot3d(x*y^2/(x^2+y^4),x=-5..5,y=-5..5,style=patch,sh ading=none,lightmodel=light1);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Animation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: wit h(plots):" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 27 "Animation in Two Di mensions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "animate(plot,[si n(x*t),x=-10..10],t=1..2,frames=50);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "animate(plot,[[a*cos(u),sin(u),u=0..2*Pi]],a=0..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "animate(polarplot,[theta* t,theta=0..8*Pi],t=1..4);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "An imation in Three Dimensions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "animate3d(cos(t*x)*cos(t*y),x=-Pi..Pi,y=-Pi..Pi,t=1..2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "animate(plot3d,[cos(t*x)*cos (t*y),x=-Pi..Pi,y=-Pi..Pi],t=1..2);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "Annotating Plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "?plotoptions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "plot (sin(x),x=-2*Pi..2*Pi,\ntitle=\"Plot of Sine\",titlefont=[HELVETICA,BO LD,16],\nlabels=[\"abscissa\",\"ordinate\"],labeldirections=[horizonta l,vertical]);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Composite Plot s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "my_plot:=plot(sin(x),x=-1 0..10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "my_plot;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(my_plot);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "a:=plot([sin(t),exp(t)/20,t= -Pi..Pi],color=green):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "b :=polarplot([sin(t),exp(t),t=-Pi..Pi]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display([a,b]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "c:=sphereplot(1,theta=0..2*Pi,phi=0..Pi):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "d:=cylinderplot(0.5,theta=0..2*Pi,z =-2..2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "display([c,d],s caling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "f:= animate3d(sin(x+y+t),x=0..2*Pi,y=0..2*Pi,t=0..5,frames=20):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "g:=animate3d(t,x=0..2*Pi,y=0 ..2*Pi,t=-1.5..1.5,frames=20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display([f,g]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "GD:=seq(plot([[cos(2*Pi /100*i),sin(2*Pi/100*i)]],symbol=circle,style=point),i=0..100):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "display(GD);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "display(GD,insequence=true);" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 "Low-level Graphics" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 48 "a:=plot(x^2,x=0..10,numpoints=5,adaptive=false);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?PLOT" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 480 "PLOT(POINTS([0,0], SYMBOL(DIAMOND)),\n T EXT([0,0],'`Origin`', ALIGNBELOW, ALIGNRIGHT, FONT(HELVETICA,OBLIQUE,1 0)),\n CURVES([[-3,0.5],[3,0.5]], THICKNESS(3), LINESTYLE(2)),\n \+ TEXT([0,0.5], '`Dotted`', ALIGNBELOW),\n TEXT([3.1415,0], 'p', \+ FONT(SYMBOL,12)),\n TEXT([-3.1415,0], 'P', FONT(SYMBOL,12)),\n \+ POLYGONS([[-2,-0.25],[-2,-0.5],[2,-0.5],[2,-0.25]], COLOR(HUE,0.5)), \n TEXT([0,-0.37], '`Red`', COLOR(RGB,1,0,0)),\n AXESSTYLE(FRA ME), VIEW(-4..4,-1..1)\n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PAGEBK }{PARA 260 "" 0 "" {TEXT -1 20 "Programming Language " }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Procedures" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "half:=proc(x)\n evalf(x/2);\nend proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "half(3);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "half(a);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(half(x),x=-10..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "SUM:=proc(n)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " local i, to tal;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " total:=0;" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 22 " for i from 1 to n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " total:=total+i;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " total;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "time(SUM(10000));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "st := time():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "S UM(1000000);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "time() - st;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "st := time():" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "add(n,n=1..1000000);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "time() - st;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "st := time():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sum(n,n=1..1 000000);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "time() - st;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "L:=[]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "st := time():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f or i from 1 to 2000 do L:=[L[],i] end do:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "time() - st;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nop s(L);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "L:=[]:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 13 "st := time():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "L:=[seq(i,i=1..20000)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " time() - st;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nops(L);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ABS:=proc(x)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " if x<0 then -x else x end if;" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 9 "end proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ABS(-18);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ABS(a);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(ABS(x),x=-1..1);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ABS:=proc(x)" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 " if type(x,numeric) then" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 33 " if x<0 then -x else x end if;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " else" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " \+ 'procname'(x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " end if;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ABS(a);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "ABS(-2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(ABS(x), x=-1..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Fibonacci:=pro c(n::nonnegint)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " if n<2 then" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " n;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " else" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " Fibon acci(n-1)+Fibonacci(n-2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " end i f;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 13 "Fibonacci(3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Fibonacci(-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "st := time():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Fibonacci( 30);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "time() - st;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Fibonacci:=proc(n::nonnegint)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " option remember;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " if n<2 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " RETURN(n);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " else" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " Fibonacci(n-1)+Fibonacci(n-2); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " end if;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "st := time():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Fibonacci(30); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "time() - st;" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 5 "Addon" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "print(Fibonacci);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "print(solve);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "interface(verboseproc=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "print(solve);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "print(map);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "info level[all] := 5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(( x-4)^3+y^2=0,\{x,y\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f actor(x^4-5*x^2+6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "trac e(SUM);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "SUM(5);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "untrace(SUM);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "SUM(5);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }