{VERSION 3 0 "IBM INTEL NT" "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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 } {CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "N ormal" -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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 } {PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 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 18 "" 0 "" {TEXT -1 22 "Plotting a Slope Field" } }{PARA 18 "" 0 "" {TEXT -1 23 "Math 374 Winter 1999" }}{PARA 19 "" 0 "" {TEXT -1 30 "Jay Treiman, January 11, 1999" }}{PARA 19 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "It is always a go od idea to " }{HYPERLNK 17 "restart" 2 "restart" "" }{TEXT -1 22 " Map le before starting" }}{PARA 0 "" 0 "" {TEXT -1 56 "a new worksheet. T his guarantees that no variables are " }}{PARA 0 "" 0 "" {TEXT -1 16 " assigned values." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "Inpu tting a differential equation" }}{PARA 0 "" 0 "" {TEXT -1 56 "In Maple one needs to explicitly specify which variables" }}{PARA 0 "" 0 "" {TEXT -1 59 "in a differential equation are functions of other variabl e." }}{PARA 0 "" 0 "" {TEXT -1 41 "For example, in the differential eq uation" }}{PARA 256 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "diff(y,x) = x-y;" "6#/-%%diffG6$%\"yG%\"xG,&F(\"\"\"F'!\"\"" }{TEXT -1 1 "," }} {PARA 0 "" 0 "" {TEXT -1 32 "it is necessary to specify that " } {XPPEDIT 18 0 "y;" "6#%\"yG" }{TEXT -1 18 " is a function of " } {XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "Here is the differential equati on." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "de1 := diff(y(x),x)= x -y(x);" }}}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 41 "Plotting slope fields and solution curves" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "Maple has a set of routines that help when working with" }}{PARA 0 "" 0 "" {TEXT -1 54 "differential equations. They are in a package called " } {HYPERLNK 17 "DEtools" 2 "DEtools" "" }{TEXT -1 1 "." }}{PARA 0 "" 0 " " {TEXT -1 23 "First load the package." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}} {PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 46 "The rout ine one uses to plot a slope field and" }}{PARA 0 "" 0 "" {TEXT -1 24 "particular solutions is " }{HYPERLNK 17 "DEplot" 2 "DEtools,DEplot" " " }{TEXT -1 20 ". One can use it to" }}{PARA 0 "" 0 "" {TEXT -1 21 "p lot the slope field." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "DEplot(\{de1\},\{y(x)\},x=-5..5,y=-5..5); " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "One \+ can also add particular solutions by adding a " }}{PARA 0 "" 0 "" {TEXT -1 51 "list of initial conditions. Check the options for " } {HYPERLNK 17 "DEplot" 2 "DEtools,DEplot" "" }{TEXT -1 3 " to" }}{PARA 0 "" 0 "" {TEXT -1 50 "learn about adding a title or changing the colo rs." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "DEplot(\{de1\},\{y(x)\},x=-5..5,\n [[y(0)=3],[y( 0)=-4],[y(-3)=0]],\n y=-5..5,linecolor=blue,title=`diff(y,x)=x-y`) ;" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Exercises" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Plot the slope field for the differential equat ion " }{XPPEDIT 18 0 "diff(y,x) = x+y;" "6#/-%%diffG6$%\"yG%\"xG,&F( \"\"\"F'F*" }{TEXT -1 13 ". Print your" }}{PARA 0 "" 0 "" {TEXT -1 62 "result and then do problem 2 on page 25 of Edwards and Penney." }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Plot the slope field for the diff erential equation " }{XPPEDIT 18 0 "diff(y,x) = y-sin(x);" "6#/-%%dif fG6$%\"yG%\"xG,&%\"yG\"\"\"-%$sinG6#%\"xG!\"\"" }{TEXT -1 13 ". Print your" }}{PARA 0 "" 0 "" {TEXT -1 62 "result and then do problem 3 on \+ page 25 of Edwards and Penney." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Plot the slope field for the differential equation " }{XPPEDIT 18 0 "diff(y,x) = sin(x)+sin(y);" "6#/-%%diffG6$%\"yG%\"xG,&-%$sinG6#%\"x G\"\"\"-F+6#%\"yGF." }{TEXT -1 13 ". Print your" }}{PARA 0 "" 0 "" {TEXT -1 62 "result and then do problem 7 on page 26 of Edwards and Pe nney." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Plot the slope field for the differential equation " }{XPPEDIT 18 0 "diff(y,x) = -x^2+sin(y) ;" "6#/-%%diffG6$%\"yG%\"xG,&*$)%\"xG\"\"#\"\"\"!\"\"-%$sinG6#%\"yGF. " }{TEXT -1 13 ". Print your" }}{PARA 0 "" 0 "" {TEXT -1 63 "result a nd then do problem 10 on page 26 of Edwards and Penney." }}}}}{MARK "4 " 0 }{VIEWOPTS 1 1 0 1 1 1803 }