{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 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 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 56 " F\366ljande tre exempel g
ick jag igenom p\345 f\366rel\344sning 5. " }}{PARA 0 "" 0 "" {TEXT 
-1 67 "# De handlar om att l\366sa ekvationssystem, hitta station\344r
a punkter " }}{PARA 0 "" 0 "" {TEXT -1 30 "# och att hitta Taylorpolyn
om." }}{PARA 0 "" 0 "" {TEXT -1 11 "# Exempel 1" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "solve(\{3*x^2*y-2*y,x^3-2*x+2*y\});" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 52 "allvalues(\{x = RootOf(_Z^2-2,label = _L1
6), y = 0\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " evalf(%);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "allvalues(\{x = RootOf(
3*_Z^2-2,label = _L17), y =" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "2/3*
RootOf(3*_Z^2-2,label = _L17)\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Exemp
el 2" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "f:=(x,y)->1+x-2*y+4*x^2-x*y
/2+1/6*y^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " solve(\{dif
f(f(x,y),x)=0,diff(f(x,y),y)=0\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 " y1:=2;x1:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 " y2:= -31/16;x2:= -63/256;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "mtaylor(f(x,y),[x=x1,y=y1],3);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "mtaylor(f(x,y),[x=x2,y=y2],3);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "fx:=unapply(diff(f(x,y),x),(x,y));" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 35 " fy:=unapply(diff(f(x,y),y),(x,y));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "fx(x2,y2);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 11 " fy(x2,y2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "fxx:=unapply(diff(f(x,y),x,x),(x,y));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "fxy:=unapply(diff(f(x,y),x,y),(x,y)
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "fyy:=unapply(diff(f(x
,y),y,y),(x,y));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " with(plots):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "plot3d(f(x,y),x=-2..2,y=-4..4);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 34 "f(x1,y1);f(x2,y2);evalf(f(x2,y2));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "# Exempel 3" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 39 " f:=(x,y)->1+x-2*y+4*x^2-x*y/2+1/3*y^3;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "solve(\{diff(f(x,y),x)=0,dif
f(f(x,y),y)=0\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "allvalues(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " evalf(%);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 " y
1:= 1/64+1/64*sqrt(7937);x1:= -127/1024+1/1024*sqrt(7937);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 " y2:= 1/64-1/64*sqrt(7937);x2:= -12
7/1024-1/1024*sqrt(7937);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 " mtaylor(f(x,y),[x=x1,y=y1],3);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 " simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 54 "-3969/2048-1/2048*sqrt(7937)+(1/64+1/64*sqrt(7937))^2;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " evalf(%);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 30 "mtaylor(f(x,y),[x=x2,y=y2],3);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " simplify(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 " -3969/2048+1/2048*sqrt(7937)+(1/64
-1/64*sqrt(7937))^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " ev
alf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "fx:=unapply(diff
(f(x,y),x),(x,y));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "fy:=u
napply(diff(f(x,y),y),(x,y));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 10 "fx(x2,y2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "  " }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 11 " fy(x2,y2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 " simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 37 "fxx:=unapply(diff(f(x,y),x,x),(x,y));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 37 "fxy:=unapply(diff(f(x,y),x,y),(x,y));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "fyy:=unapply(diff(f(x,y),y,y
),(x,y));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " plot3d(f(x,y),x=-2..2,y=
-4..4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " f(x1,y1);simpli
fy(%);evalf(%);f(x2,y2);simplify(%);evalf(%);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 0 0" 10 }{VIEWOPTS 1 1 0 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }