{VERSION 4 0 "SGI MIPS UNIX" "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 8 0 0 0 0 2 2 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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 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 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading \+ 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 " " 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 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 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 }} {SECT 0 {SECT 0 {PARA 5 "" 0 "" {TEXT -1 13 "Slope fields " }{TEXT 256 15 "slope_field.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Here's one way to make a slope field for the first-order differential equation\n dy/dt = 2*sin(t) - y \+ ." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "First load the package that \+ includes \"fieldplot\":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plo ts):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords ha s been redefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 194 "Now we wan t to draw little line segments with the slope specified by the differe ntial equation.\nThis can be done as follows. Dividing by \"len\" is \+ to make all the line segments the same length.:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "slope:=2*sin(t)-y;\nlen:=sqrt(1+slope^2):\nfieldplot ( [1/len,slope/len],\n t=0..5, y=-6..6, arrows=line, color= blue );" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&slopeG,&- %$sinG6#%\"tG\"\"#%\"yG!\"\"" }}{PARA 13 "" 1 "" {GLPLOT2D 334 252 252 {PLOTDATA 2 "6$-%'CURVESG6]dl7$7$$!3A\"*=rD%>n)[!#>$!3'QrUb;.KH'!# <7$$\"3A\"*=rD%>n)[F*$!39'GdW$oz1dF-7$7$$\"3w0hYO12x@!#=$!3eN!**)G8N'H 'F-7$$\"30O2Fes3'3$F7$!3Tk45r'[Oq&F-7$7$$\"3qV9#F-$!37c))fqGW)p&F-7$7$$\"3Ra1SED\"yK#F-$!3`#G W,&QP+jF-7$$\"38.D')y&H!4CF-$!3Y*QH&pax)e#F-$!3- K,+fKh)H'F-7$$\"3R_u?DCQuEF-$!3(z')**4u'Q,dF-7$7$$\"3l$\\txb\"4\\GF-$! 3OdoRJ\"zhH'F-7$$\"3+KqVE@QSHF-$!3kUJgo3#Qq&F-7$7$$\"3w%Q-Pk(z3JF-$!3U M1%*f=)HH'F-7$$\"3(\\#=)*H=*p?$F-$!3el$f+9=qq&F-7$7$$\"3^4Dc[+,oLF-$!3 I!pkZK$**)G'F-7$$\"3G%Q&f9_4uMF-$!3p4`Bvm+6dF-7$7$$\"3mr\">#*fnpi$F-$! 35$)H/.%RVG'F-7$$\"3?1CT`MXTPF-$!3*o,dpfgcr&F-7$7$$\"3e6i2)=dg)QF-$!3I jTAg9TziF-7$$\"3N]!HSlz'3SF-$!3qOexR&)e?dF-7$7$$\"3(=o(*=P(yXTF-$!3==r %)[>#\\F'F-7$$\"3.l7of_EvUF-$!3#=)G:^!y]s&F-7$7$$\"3%y2+n6(o1WF-$!35L \"*=vxyriF-7$$\"3,aDN/8oSXF-$!3*o'3\"[A7#GdF-7$7$$\"3M^CTNF:pYF-$!3'\\ c/E&zzqiF-7$$\"3ZlQ6v9`/[F-$!3/NaRZ??HdF-7$7$$\"3S-F]_HJL\\F-$!3\"QC#o FmAsiF-7$$\"3O*H(\\Zqom]F-$!3=cxJsLxFdF-7$7$$!31A&f1qQ,P&F*$!3F+L>4Frc cF-7$$\"31A&f1qQ,P&F*$!3Cd)pgRH,3&F-7$7$$\"3#*[\"[-uu\\8#F7$!3GC+tKb&3 m&F-7$$\"3)Gp)[aJ=GJF7$!3BLJ`sl)f2&F-7$7$$\"3w;?P\\lW*z%F7$!3d'*4Y8+&R m&F-7$$\"3Un;5S#pos&F7$!3%4;-=4#*G2&F-7$7$$\"3xCH$4i\\hX(F7$!3oa%Q-,^h m&F-7$$\"3y,wFjSKL$)F7$!3$GqC]4\"pq]F-7$7$$\"3w=tkQw_55F-$!36Uk37mgncF -7$$\"3'zTZ#>bt%4\"F-$!3S:n<$\\N#p]F-7$7$$\"3$)y_s3Oru7F-$!3@^i`i'G%oc F-7$$\"3&>9V'Q`'oN\"F-$!3I1psUMTo]F-7$7$$\"3=,y(y*p>Q:F-$!3A(eEMB%oocF -7$$\"3p.V'*Qxp>;F-$!3Hql$=(y:o]F-7$7$$\"3.J`q0j)4!=F-$!3L8]YeYRocF-7$ $\"3!zX51ACK)=F-$!3=W\")zYuWo]F-7$7$$\"3*H;Vw$>2j?F-$!36n(p:yNvm&F-7$$ \"3Y5j9yVXZ@F-$!3S!R$pBjIp]F-7$7$$\"3;Mh(=,HWK#F-$!3b+(=[pPgm&F-7$$\"3 OBqQ$48CT#F-$!3&pXW/T/32&F-7$7$$\"3)R0!)zmE]e#F-$!3W]\"R-$fyjcF-7$$\"3 g(ycnAJ\"yEF-$!322S-vh0t]F-7$7$$\"3=-h?$HZ[%GF-$!3*Hq4#33jgcF-7$$\"3YB W+\"REY%HF-$!3_aM0(H6i2&F-7$7$$\"3PT\"[!*H?R5$F-$!3+2sHkEj8#4&F-7$7$$\"3s0#QVPO(yQF-$!3[Z**=O)[yj&F-7$$\"3 @cqwn/+;SF-$!3/5K2pK**)4&F-7$7$$\"3o/8yV,vPTF-$!3O!)=o)=5:j&F-7$$\"3AU wz([-LG%F-$!3;x7e;>L0^F-7$7$$\"35tV?'zx\")R%F-$!3#)>y,6//FcF-7$$\"3ve# [[i!>\\XF-$!3qP`C%p,)4^F-7$7$$\"3>1*)3[\"*\\gYF-$!3!z#**>C>iDcF-7$$\"3 i5uVi]=8[F-$!3iHK1\"=?76&F-7$7$$\"3p*30xLo[#\\F-$!3\"*=Sn+$owi&F-7$$\" 337\\Hi;8v]F-$!3hQ\"*e/Q<4^F-7$7$$!3LB^`t^!p%fF*$!3BUK[8w`=]F-7$$\"3LB ^`t^!p%fF*$!3!G2VqfY^X%F-7$7$$\"31&yGfJQ^3#F7$!3mCyVO;6C]F-7$$\"3tc!3) y&>!yJF7$!3Q!\\)3uDd\\WF-7$7$$\"3$*H,EI**pbZF7$!3UD^T\\8?G]F-7$$\"3p`N @fehqdF7$!3i*=66'G[XWF-7$7$$\"3pce8q0&oT(F7$!3E!4Tm[n5.&F-7$$\"3&)pY29 Jis$)F7$!3xC_)Qs;EW%F-7$7$$\"3p>B0bp*o+\"F-$!3l=B4U=%H.&F-7$$\"3/vz\"F-$!3$eb3_=\\R.&F-7$$\"3d%oxIF \"p')=F-$!3?fxJD]tRWF-7$7$$\"3q/cO-mUf?F-$!3M\"oj9/^G.&F-7$$\"3uoQU8(* 4^@F-$!3qLE1pJ$3W%F-7$7$$\"3(Q'Ra!)fZ?BF-$!3??Va[3#4.&F-7$$\"3l$>>Z7mj T#F-$!3%[*>)>OjFW%F-7$7$$\"3QHP*)H#>1e#F-$!3j[c)*3i)z-&F-7$$\"3?7J%[mQ Do#F-$!3Tm1a,!)pXWF-7$7$$\"3]q5q!>?)RGF-$!3S[B>r?\"Q-&F-7$$\"3:b%4N\\` '\\HF-$!3jmRLR@()\\WF-7$7$$\"3msU;A%)4)4$F-$!3d;9s$GQ\"=]F-7$$\"31P*>: 0\"p)) o^Q!fdv$F-$!3:40D%[?=Z%F-7$7$$\"30_;!=#p))pQF-$!3'\\K@lOu?*\\F-7$$\"3) )4OI?*\\[-%F-$!32!*\\+W)4;[%F-7$7$$\"3%o7N1u_!GTF-$!3w*z'>;#**G)\\F-7$ $\"31?Q%4*)**HH%F-$!3G:&HV*\\y!\\%F-7$7$$\"3KJ_s%**RzQ%F-$!3C(yOI.tj( \\F-7$$\"3`+uKE%G%fXF-$!3!y_*[x6J(\\%F-7$7$$\"3bv-ov(*4]YF-$!3'z\"oiIS Hu\\F-7$$\"3FTg%[V%eB[F-$!33(\\**)z,R*\\%F-7$7$$\"3^'f`(zNq9\\F-$!3jbA Gk@Hx\\F-7$$\"3E0kC?kH&3&F-$!3UfSCY?R'\\%F-7$7$$!3a'yY,dW2k'F*$!3>nG9) >$)yP%F-7$$\"3a'yY,dW2k'F*$!3#\\gYw6VE$QF-7$7$$\"3'o/J9<%eD?F7$!3JYP#) ovc&Q%F-7$$\"3'\\z0LstvB$F7$!3!eslpue\\#QF-7$7$$\"3J^3bMOz.ZF7$!3mpG?j j4\"R%F-7$$\"3KKG#\\:AD#eF7$!3X-me_*H%>QF-7$7$$\"3[Q^Sg[^qtF7$!3G\")pM (y2\\R%F-7$$\"32)Q0Q#)e*=%)F7$!3$3\\U%G&=c\"QF-7$7$$\"39C(*eAnj-5F-$!3 I\"o=ZAptR%F-7$$\"3f7]INki-6F-$!3E\"zq54dJ\"QF-7$7$$\"3j[kO?d?n7F-$!3y <[>7vt)R%F-7$$\"3;s>+FKPk8F-$!3xaYf.))y6QF-7$7$$\"3Y[UOK'33`\"F-$!3O'4 :8hf\"*R%F-7$$\"3ScyZ/h3F;F-$!3?wVZ/nO6QF-7$7$$\"3%z`>,`iMz\"F-$!3m8!f DB\"o)R%F-7$$\"3+^i>'*zu!*=F-$!3!*e/B$3X=\"QF-7$7$$\"39,u=B\"[^0#F-$!3 W_ZQ\"e]sR%F-7$$\"3Is?g#>y`:#F-$!37?ZSMdF8QF-7$7$$\"3HfNJ*\\8eJ#F-$!3u I$p*\\Tr%R%F-7$$\"3B)f\\fgG5U#F-$!3#=9?e;7e\"QF-7$7$$\"3%Q*)HjZ(QvDF-$ !3s#z>L233R%F-7$$\"3uZpS=/x(o#F-$!3Rz'pCC=(>QF-7$7$$\"3[(*=c%=5Q$GF-$! 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