{VERSION 5 0 "IBM INTEL NT" "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 }{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 "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 "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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 135 "These Maple solutions are NOT an example of how your assignments (and EXAMS) should be presente d - I do require a HAND written 'report'" }}{PARA 0 "" 0 "" {TEXT -1 77 "(in addition to your Maple computation) - most of you ARE doing it OK though." }}{PARA 0 "" 0 "" {TEXT -1 8 "Sec 8.9)" }}{PARA 0 "" 0 " " {TEXT -1 4 "Q20:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "grad:=proc(f);[diff(f,x),diff(f,y),diff(f,z)]end:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "mag:=proc(r);sqrt(add(r[i]^ 2,i=1..3))end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "n:=grad(x ^2+y^2+2*z^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG7%,$*&\"\"#\" \"\"%\"xGF)F),$*&F(F)%\"yGF)F),$*&\"\"%F)%\"zGF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "n:=eval(n,\{x=2,y=2,z=3\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG7%\"\"%F&\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalm(n/mag(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#- %'vectorG6#7%,$*&\"#6!\"\"F)#\"\"\"\"\"#F,F',$*(\"\"$F,F)F*F)F+F," }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q30:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "dot:=proc(r,q);add(r[i]*q[i],i=1..3 )end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "n:=grad(x-y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG7%\"\"\"!\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "evalm(dot(n,[2,1,0])/mag([2,1,0])); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"&!\"\"F%#\"\"\"\"\"#F(" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q34:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "n:=grad(x^2+3*y^2+4*z^2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG7%,$*&\"\"#\"\"\"%\"xGF)F),$*& \"\"'F)%\"yGF)F),$*&\"\")F)%\"zGF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "n:=eval(n,\{x=1,y=0,z=1\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG7%\"\"#\"\"!\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "dot(n,[-1,-1,1])/mag([-1,-1,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"#\"\"\"\"\"$#F&F%F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Sec. 8.10" }}{PARA 0 "" 0 "" {TEXT -1 5 "Q13b:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "div:=proc(g) dif f(g[1],x)+diff(g[2],y)+diff(g[3],z) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "div(evalm(f(x,y,z)*[v1(x,y,z),v2(x,y,z),v3(x,y,z)])); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,.*&-%%diffG6$-%\"fG6%%\"xG%\"yG% \"zGF+\"\"\"-%#v1GF*F.F.*&F(F.-F&6$F/F+F.F.*&-F&6$F(F,F.-%#v2GF*F.F.*& F(F.-F&6$F7F,F.F.*&-F&6$F(F-F.-%#v3GF*F.F.*&F(F.-F&6$F?F-F.F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "evalm(f(x,y,z)*div([v1(x,y, z),v2(x,y,z),v3(x,y,z)]))\n+dot([v1(x,y,z),v2(x,y,z),v3(x,y,z)],grad(f (x,y,z)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&-%\"fG6%%\"xG%\"yG% \"zG\"\"\",(-%%diffG6$-%#v1GF'F(F+-F.6$-%#v2GF'F)F+-F.6$-%#v3GF'F*F+F+ F+*&-F.6$F%F(F+F0F+F+*&-F.6$F%F)F+F4F+F+*&-F.6$F%F*F+F8F+F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "simplify(%-%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q2 0:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "di v(grad(z-sqrt(x^2+y^2))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"\"F%*$,&*$ )%\"xG\"\"#F%F%*$)%\"yGF+F%F%#F%F+!\"\"F0" }}}}{MARK "22" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }