{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {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 -1 -1 -1 0 0 0 0 0 0 -1 0 }{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 }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 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Linear first order systems . p. 214 1, 3, 4, 5, 27, 29, 32." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "d1:=diff(y(t),t,t)+t*diff(y(t),t)-3*y(t)=t^2;\nd1a:= diff(y(t),t)=v(t);\nd1b:=simplify(subs(diff(y(t),t)=v(t),d1));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#d1G/,(-%%diffG6$-%\"yG6#%\"tG-%\"$G 6$F-\"\"#\"\"\"*&F-F2-F(6$F*F-F2F2F*!\"$*$)F-F1\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d1aG/-%%diffG6$-%\"yG6#%\"tGF,-%\"vGF+" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d1bG/,(-%%diffG6$-%\"vG6#%\"tGF-\" \"\"*&F-F.F*F.F.-%\"yGF,!\"$*$)F-\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "d1b:=diff(v(t),t)=solve(d1b,diff(v(t),t));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d1bG/-%%diffG6$-%\"vG6#%\"tGF,,(*&F ,\"\"\"F)F/!\"\"-%\"yGF+\"\"$*$)F,\"\"#\"\"\"F/" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 29 "s1:=\{d1a,d1b,y(0)=3,v(0)=-6\};" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#s1G<&/-%%diffG6$-%\"yG6#%\"tGF--%\"vGF,/-F(6$ F.F-,(*&F-\"\"\"F.F5!\"\"F*\"\"$*$)F-\"\"#\"\"\"F5/-F+6#\"\"!F7/-F/F>! \"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "dsolve(s1,\{y(t),v(t )\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$/-%\"yG6#%\"tG,&#!\"#\"\"$ \"\"\"*&,**$)F(#\"\"&\"\"#\"\"\"!\"\"*(-%+WhittakerWG6%#!\"(\"\"%#F-F= ,$*$)F(F4F5#F-F4F--%$expG6#,$F@#F6F=F-)F4F>F5#\"#6F=*&)F(#F,F4F5,&*&-% %sqrtG6#F4F5-FQ6#%#PiGF5#FJ\"#7F+F-F-F,*&)F(#\"\"(F4F5FNF5F-F5*$-FQ6#F (F5!\"\"F-/-%\"vGF'*&,,F0F+F7#\"#LF=*(FCF5FHF5-F96%#!\"$F=F>F?F-#!#6F4 FKF,FXF,F5*$)F(#\"\"$F4F5Fin" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "O f course, solving the system is not part of the problem." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "dsolve(\{d1,y(0)=3,D(y)(0)=-6\},y(t ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,*#!\"#\"\"$\"\" \"*$)F'\"\"#\"\"\"!\"\"*&*()F/#F,\"\"%F0-%+WhittakerWG6%#!\"(F6F5,$F-# F,F/F,-%$expG6#,$F-#F1F6F,F0*$-%%sqrtG6#F'F0!\"\"#\"#6F6*&,&*&-FE6#F/F 0-FE6#%#PiGF0#FI\"#7F*F,F,,&F'F+*$)F'F+F0F,F,F," }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 107 "s3:=\{diff(y(t),t,t,t,t)-diff(y(t),t,t,t)+7*y (t)=cos(t), y(0)=1, D(y)(0)=1, (D@@2)(y)(0)=0, (D@@3)(y)(0)=2\};" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s3G<'/,(-%%diffG6$-%\"yG6#%\"tG-%\" $G6$F.\"\"%\"\"\"-F)6$F+-F06$F.\"\"$!\"\"F+\"\"(-%$cosGF-/---%#@@G6$% \"DGF86#F,6#\"\"!\"\"#/-F,FEF3/--FCFDFEF3/---FA6$FCFGFDFEFF" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "evalf(rhs(dsolve(s3,y(t),met hod=laplace)));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,6-%$cosG6#%\"tG$\" +J#p2B\"!#5-%$sinGF&$\"+Q:YQ:!#6*&-%$expG6#,$F'$!+3!GyR*F*\"\"\"-F%6#, $F'$\"+pp(*>6!\"*F7$\"+^jW^TF**&F1\"\"\"-F,F9F7$\"+N,%*pSF**&%\"IGF7,& F0$\"+o+(\\.#F*F@$!+wJsv?F*F7$F7\"\"!*&FFFA,&F0$!+o+(\\.#F*F@$\"+wJsv? F*F7FL*&-F26#,$F'$\"+,GyR9F=F7-F%6#,$F'$\"+;XF'4\"F=F7$\"+=Wy " 0 "" {MPLTEXT 1 0 19 "solve(r^4-r^3+7,r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'Root OfG6#,(*$)%#_ZG\"\"%\"\"\"\"\"\"*$)F)\"\"$F+!\"\"\"\"(F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "I'll do this one on the board too." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "d31:=diff(y(t),t)=y1(t);\nd 32:=diff(y1(t),t)=y2(t);\nd33:=diff(y2(t),t)=y3(t);\nd34:=diff(y3(t),t )=y3(t)-7*y(t)+cos(t);\nin3:=y(0)=1, y1(0)=1, y2(0)=0, y3(0)=2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d31G/-%%diffG6$-%\"yG6#%\"tGF,-%#y1 GF+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d32G/-%%diffG6$-%#y1G6#%\"tG F,-%#y2GF+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d33G/-%%diffG6$-%#y2G 6#%\"tGF,-%#y3GF+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d34G/-%%diffG6 $-%#y3G6#%\"tGF,,(F)\"\"\"-%\"yGF+!\"(-%$cosGF+F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$in3G6&/-%\"yG6#\"\"!\"\"\"/-%#y1GF)F+/-%#y2GF)F*/-%# y3GF)\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "dsolve(\{d31, d32,d33,d34,in3\},\{y(t),y1(t),y2(t),y3(t)\}, method=laplace);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<&/-%#y3G6#%\"tG,(-%$cosGF'#!\"\"\"#l- %$sinGF'#\"\")F.-%$sumG6$*&,*#\"%`>\"%*e%\"\"\"%'_alphaG#!%`9\"&XH#*$) F<\"\"#\"\"\"#\"%_YF?*$)F<\"\"$FC#\"%%)RF?F;-%$expG6#*&F " 0 "" {MPLTEXT 1 0 55 "d4:=diff(y(t),t$6)=(diff(y(t ),t))^3-sin(y(t))+exp(2*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#d4G/ -%%diffG6$-%\"yG6#%\"tG-%\"$G6$F,\"\"',(*$)-F'6$F)F,\"\"$\"\"\"\"\"\"- %$sinG6#F)!\"\"-%$expG6#,$F,\"\"#F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "# init is all at 0 are 0" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 70 "d5a:=diff(x(t),t)+diff(y(t),t)=-2*y(t);\nd5b:=x(t)- 2*y(t)=diff(y(t),t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d5aG/,&-%%d iffG6$-%\"xG6#%\"tGF-\"\"\"-F(6$-%\"yGF,F-F.,$F1!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d5bG/,&-%\"xG6#%\"tG\"\"\"-%\"yGF)!\"#-%%diffG6$F ,F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "dsolve(\{d5a,d5b\}, \{x(t),y(t)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%\"xG6#%\"tG*&- %$expG6#,$F(!\"\"\"\"\"%$_C2GF//-%\"yGF',(*&-F+6#,$F(!\"#F/%$_C1GF/F/F )F/*&F0\"\"\"F6F " 0 "" {MPLTEXT 1 0 103 "s27 :=\{\n diff(x(t),t)=x(t)+2*y(t)-z(t),\n diff(y(t),t)=x(t)+z(t),\n d iff(z(t),t)=4*x(t)-4*y(t)+5*z(t)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$s27G<%/-%%diffG6$-%\"zG6#%\"tGF-,(-%\"xGF,\"\"%-%\"yGF,!\"%F*\"\"& /-F(6$F/F-,(F/\"\"\"F2\"\"#F*!\"\"/-F(6$F2F-,&F/F:F*F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "dsolve(s27,\{x(t),y(t),z(t)\});" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#<%/-%\"yG6#%\"tG,.*&%$_C1G\"\"\"-%$exp GF'F,\"\"#*&F+\"\"\"-F.6#,$F(F/F,!\"\"*&%$_C2GF,-F.6#,$F(\"\"$F,F,*&F7 F1F2F1F5*&%$_C3GF,F8F1#F,F/*&F>F1F-F1#F5F//-%\"xGF',.F0F/F*!\"#F6F5F " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "W arning, new definition for trace" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^ r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdecompG%)QRdecompG%*W ronskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG%(augmentG%(backsub G%%bandG%&basisG%'bezoutG%,blockmatrixG%(charmatG%)charpolyG%)cholesky G%$colG%'coldimG%)colspaceG%(colspanG%*companionG%'concatG%%condG%)cop yintoG%*crossprodG%%curlG%)definiteG%(delcolsG%(delrowsG%$detG%%diagG% (divergeG%(dotprodG%*eigenvalsG%,eigenvaluesG%-eigenvectorsG%+eigenvec tsG%,entermatrixG%&equalG%,exponentialG%'extendG%,ffgausselimG%*fibona cciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG%(geneqnsG%*genma trixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG%+htransposeG%)ih ermiteG%*indexfuncG%*innerprodG%)intbasisG%(inverseG%'ismithG%*issimil arG%'iszeroG%)jacobianG%'jordanG%'kernelG%*laplacianG%*leastsqrsG%)lin solveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG%'mulrowG%)multiply G%%normG%*normalizeG%*nullspaceG%'orthogG%*permanentG%&pivotG%*potenti alG%+randmatrixG%+randvectorG%%rankG%(ratformG%$rowG%'rowdimG%)rowspac eG%(rowspanG%%rrefG%*scalarmulG%-singularvalsG%&smithG%,stackmatrixG%* submatrixG%*subvectorG%)sumbasisG%(swapcolG%(swaprowG%*sylvesterG%)toe plitzG%&traceG%*transposeG%,vandermondeG%*vecpotentG%(vectdimG%'vector G%*wronskianG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A:=matrix( 3,3,[1,2,-1, 1,0,1, 4,-4,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"A G-%'matrixG6#7%7%\"\"\"\"\"#!\"\"7%F*\"\"!F*7%\"\"%!\"%\"\"&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eigenvals(A);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvects(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%7% \"\"$\"\"\"<#-%'vectorG6#7%!\"\"F%\"\"%7%\"\"#F%<#-F(6#7%!\"#F%F,7%F%F %<#-F(6#7%F+F%F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "charpol y(A,r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"rG\"\"$\"\"\"\"\"\" *$)F&\"\"#F(!\"'F&\"#6F-F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"rG\"\"\"!\"\" F&F&,&F%F&!\"#F&F&,&F%F&!\"$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "s27:=\{diff(x(t),t)=-7*x(t)/100+y(t)/100+12,\n \+ diff(y(t),t)=-3*y(t)/100+3*x(t)/100,\n x(0)=-100, y(0)=0\};" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$s27G<&/-%\"yG6#\"\"!F*/-%%diffG6$-F (6#%\"tGF1,&F/#!\"$\"$+\"-%\"xGF0#\"\"$F5/-F-6$F6F1,(F6#!\"(F5F/#\"\" \"F5\"#7FA/-F7F)!$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "so l27:=dsolve(s27,\{x(t),y(t)\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%& sol27G<$/-%\"yG6#%\"tG,&*&\"\"\"F-*&,&\"\"&\"\"\"*$-%%sqrtG6#\"\"(F-F1 \"\"\",&!\"&F1F2F1\"\"\"!\"\"!%+O*&,*-%$expG6#,$*&F8F1F*F1#F1\"$+\"!%+ 9*&F3F--F@6#,$*&F/F1F*F-#!\"\"FEF1\"%+8*&F3F-F?F1!%+8FHFFF-*&F/\"\"\"F 8\"\"\"F;#!\"*F6/-%\"xGF),&F,F<*&,*FG\"$+%FO!$+%F?\"%+@FHFhnF-*&F/\"\" \"F8\"\"\"F;#\"\"*F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "plo t(\{rhs(sol27[2]), rhs(sol27[1])\}, t=0..55);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7S7$\"\"!$!1+++++++5!#87$$\"1mm;zM%))>\"!#:$!1 H%4Krqq\"y!#97$$\"1L$3-y]>C#F/$!1PF(eH_P1'F27$$\"1mmTNS.:MF/$!1&)Q\"[A 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