{VERSION 4 0 "SUN SPARC SOLARIS" "4.0" } {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 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 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 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 0 }3 3 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 0 }3 0 0 -1 -1 -1 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 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 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 {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 256 11 "Math 2280-2" }} {PARA 257 "" 0 "" {TEXT -1 13 "Tuesday Jan 9" }}{PARA 0 "" 0 "" {TEXT -1 133 "The geometric interpretation of a first order differential equ ation is connected to slope fields. Consider the differential equatio n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%#dyG\"\"\"%#dxG!\"\"-%\"fG6$% \"xG%\"yG" }}{PARA 0 "" 0 "" {TEXT -1 373 "The associated slope field \+ in the x-y plane is a field of slopes, where the slope at point (x,y) \+ is given by the formula f(x,y). A solution y(x) to the differential e quation above will have a graph y=y(x), the tangent line slope dy/dx w ill exactly ewqual f(x,y). This means that we can use the slope field to draw the graph of y(x), even if we don't have a formula for y." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Example 1 :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "with(DEtools): \n #Ma ple tools for differential equations\ndeqtn:=diff(y(x),x)=x-3;\n #Ex ample 1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&deqtnG/-%%diffG6$-%\"yG6 #%\"xGF,,&F,\"\"\"\"\"$!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "dfieldplot(deqtn, y(x),x=0..4,y=-1..3, arrows=line,\ncolor=black , dirgrid=[30,30]);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6acn7$7$$!+X6)3=#!#6$!+cctX$*!#57$$\"+X6)3=#F *$!+MkUl5!\"*7$7$$\"+,>$=:\"F-$!+15%*[$*F-7$$\"+*y)y1;F-$!+**e5l5F37$7 $$\"+6H'4_#F-$!+Hue_$*F-7$$\"+p%yi*HF-$!+d7uk5F37$7$$\"+7-@*)QF-$!+$\\ cnN*F-7$$\"+e=l'Q%F-$!+^VKk5F37$7$$\"+gaYc_F-$!+5'[:O*F-7$$\"++t,ydF-$ !+R^%Q1\"F37$7$$\"+C[gAmF-$!+&>)3n$*F-7$$\"+E')\\qrF-$!+!=\"Hj5F37$7$$ 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