{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 "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 "" {MPLTEXT 1 0 21 "plot(sin(x),x=0..13) ;" }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$7fr7$\"\"!F(7$$\"1LL$3-: oT\"!#;$\"1foWo'z?T\"F,7$$\"1nmmT+jLGF,$\"1sg`J6'ez#F,7$$\"1**\\i:KRmS F,$\"1@vNY$\\_&RF,7$$\"1LLe*Qc\"*H&F,$\"16#G5_0Y0&F,7$$\"1+]P4v_&o'F,$ \"1xrC>&4&)>'F,7$$\"1mm;H')*=2)F,$\"1X%e+KnMA(F,7$$\"1omm;&fuY*F,$\"1` O'ow$=:\")F,7$$\"1nmTS?I'3\"!#:$\"1'z-*Qg5\\))F,7$$\"1+vVV[>D7FP$\"1[q 8F'=(3%*F,7$$\"1L$ekk(3k8FP$\"1a@eUs6(y*F,7$$\"1mmT]LZG9FP$\"1()*\\Vp \"*))*)*F,7$$\"1+]Pa!fG\\\"FP$\"1yO6yUkp**F,7$$\"1mTN1>0D:FP$\"1oXNk!R &*)**F,7$$\"1LLLeZCd:FP$\"1fL,*y\"3****F,7$$\"1+DJ5wV*e\"FP$\"1ly0jDE) ***F,7$$\"1m;Hi/j@;FP$\"1GRWNA3()**F,7$$\"1+]PH\")H)o\"FP$\"1IAE?FP$\"1Hs:n*\\3)*)F,7$$ \"1m;HQ!QZuYuF,7$$\"1+]7Q !***QCFP$\"1s#\\wC#*>Y'F,7$$\"1m\"zWr'Q!e#FP$\"1/<*\\\\v?K&F,7$$\"1LL$ 3Ru^'[0$!#<7$$\"1++]AaB^KF P$!10-?=AB%4\"F,7$$\"1+++bs+#R$FP$!1SvN/l0yCF,7$$\"1++](3zF`$FP$!1Syc2 \\&G\"QF,7$$\"1++]K)Q%oOFP$!1ms;Cp4G]F,7$$\"1++]x&)4/QFP$!1[DV_e%4:'F, 7$$\"1LeRA1HFRFP$!1QGUQu=tqF,7$$\"1m;HnE[]SFP$!1Pl&4/?#))yF,7$$\"1LL$3 =dMM%FP$!1??#Q\"48F$*F,7$$\"1LL3-6bnWFP$!1!zl'ejw,(*F,7$$\"1LLLB]k\"f% FP$!14Tv.I>F**F,7$$\"1#z>hqKxi%FP$!14tfrz=k**F,7$$\"1]i!*)Q?Qm%FP$!1@k %zx2#))**F,7$$\"13Fpr!3**p%FP$!1\"e,Z9@#****F,7$$\"1m\"zWv&*ft%FP$!1t@ [IP@(***F,7$$\"1DcEPM3sZFP$!1x=I\\\")=#)**F,7$$\"1$3_+7r\"3[FP$!1gZ;nR ;a**F,7$$\"1S&QG!)eU%[FP$!1=oeww<8**F,7$$\"1**\\i&[Y.)[FP$!1zh2\\EGf)* F,7$$\"1m\"z>M@\"3]FP$!1QvZ!f*)ec*F,7$$\"1LLL)>'*e8&FP$!1;X4FA`;\"*F,7 $$\"1n\"zpY&3w_FP$!1ALzV!eGX)F,7$$\"1+]iNZF;aFP$!1&H_7ZJLi(F,7$$\"1++D r!o(\\bFP$!1,W2J<7%p'F,7$$\"1+](oShKo&FP$!1(=7(RmzXcF,7$$\"1n\"H#)pZD# eFP$!1')zwxM>XWF,7$$\"1LLe*)R$='fFP$!1&G1a\"**[eJF,7$$\"1L3_&GU(*3'FP$ !1VwV2$)QA>F,7$$\"1L$e9e]w@'FP$!13ZR.Ey[lFft7$$\"1+vVephbjFP$\"1nM#3VL oB(Fft7$$\"1mmTNLe$\\'FP$\"1U$QCn\"\\)3#F,7$$\"1mTNE;*oj'FP$\"1**>D%fq PY$F,7$$\"1m;H<**>!y'FP$\"17qQ*zM!oZF,7$$\"1LL$e?]\\!pFP$\"1ChgymqCeF, 7$$\"1+]P%\\+(HqFP$\"1:nlv#[3z'F,7$$\"1KekBUVkrFP$\"1zN^h-M:xF,7$$\"1m m\"H&z;*H(FP$\"1z]N]g)**\\)F,7$$\"1L$e*y5OQuFP$\"1^`wF%f'[\"*F,7$$\"1* ****\\?avd(FP$\"1w)yH.m.i*F,7$$\"1+D1k3kXwFP$\"1PTA7Xv$y*F,7$$\"1+]7Bv s8xFP$\"1KMB[]!=!**F,7$$\"1]il_3xZxFP$\"1Wye_$\\O%**F,7$$\"1+v=#=9=y(F P$\"1XL_%fqR(**F,7$$\"1\\(=<^de\"yFP$\"10BoOOt#***F,7$$\"1***\\7%3!*\\ yFP$\"1\\#pdt;*****F,7$$\"1uo/8&RG)yFP$\"1h\\..k$e***F,7$$\"1\\P%[=yd \"zFP$\"1S272?\"4)**F,7$$\"1C1kcor[zFP$\"1Aq()Q(f^&**F,7$$\"1*\\P%Gbl \")zFP$\"1o#ee`2'=**F,7$$\"1\\7.sG`Z!)FP$\"1lKn9OF8)*F,7$$\"1**\\i:-T8 \")FP$\"1\"f))*3sOl'*F,7$$\"1*\\(=K8qf#)FP$\"1t&3c%e=)=*F,7$$\"1)**\\( [C*fS)FP$\"1.%o-s#F,7$$\"1Me*[N&)HM*FP$\"1\\:`?P9q\")Fft7$$\"1++]-W-#[*FP$!1mk cFz^@dFft7$$\"1m\"H2J\\Gh*FP$!1H%[R-Y'p=F,7$$\"1J$e*=UnV(*FP$!1Zn*Re'= NJF,7$$\"1l;aVRU!))*FP$!1;GAK[U+WF,7$$\"1+D\"oO<<+\"!#9$!1:(3:5Fehl$!1&*H]Sd`RmF,7$$\"1LL3PpXG5Fehl$!1&H(>XX1xvF,7$$\"1 ;H2jQXU5Fehl$!1oGP,lT8%)F,7$$\"1+D1*y]k0\"Fehl$!1fPsJo?&3*F,7$$\"1%ekB \\J*p5Fehl$!1y5)RO_Vc*F,7$$\"1nmm&>7M3\"Fehl$!1z8T&f[*p)*F,7$$\"1UN@(o eo3\"Fehl$!1BB.u#z%>**F,7$$\"1(4\"Fehl$!1y3$*eq@(***F,7$$\"1U5 S`Yk+6Fehl$!1kz5x*3%****F,7$$\"1\"Fehl$!1!)pM9 H^?\"Fehl$!1C&)4.x.E\\F,7$$\"1nmm4u+=7Fehl$!1.mE8VgnPF,7$$\"1$e9\"H$Q< B\"Fehl$!1)=jWPEUY#F,7$$\"1+Dc[#paC\"Fehl$!1\"3'o<8Y96F,7$$\"1++]!\\6' e7Fehl$\"1'HGBy+V(>Fft7$$\"1+vVKPvr7Fehl$\"1=PB'R;f]\"F,7$$\"1](=i'o(e G\"Fehl$\"1ZHW`J\\#)GF,7$$\"#8F($\"14kEo.n,UF,-%'COLOURG6&%$RGBG$\"#5! \"\"F(F(-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F(F`am%(DEFAULTG" 2 336 336 336 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(inttrans);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7/%)addtableG%(fourierG%+fouriercosG%+fouriersinG%'hankelG%(hilbert G%+invfourierG%+invhilbertG%+invlaplaceG%*invmellinG%(laplaceG%'mellin G%*savetableG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "laplace(si n(2*t),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"\"F%,&*$)%\"sG \"\"#F%\"\"\"\"\"%F+!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "laplace(cos(2*t),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"sG \"\"\",&*$)F$\"\"#F%\"\"\"\"\"%F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "laplace(exp(2*t),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$,&%\"sG\"\"\"!\"#F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "laplace(exp(a*t),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$,&%\"sG\"\"\"%\"aG!\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "restart:with(inttrans);assume(n>1);assume(s>2); \+ laplace(t^n,t,s);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7/%)addtableG%(fo urierG%+fouriercosG%+fouriersinG%'hankelG%(hilbertG%+invfourierG%+invh ilbertG%+invlaplaceG%*invmellinG%(laplaceG%'mellinG%*savetableG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%#s|irG,&%#n|irG!\"\"F(\"\"\"F)-%&G AMMAG6#,&F'F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "assu me(n,integer);GAMMA(n+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&GAMMAG 6#,&%#n|irG\"\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "la place(1,t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$%#s|irG!\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart:with(inttrans ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "laplace(t*f(t),t,s); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%%diffG6$-%(laplaceG6%-%\"fG6#% \"tGF-%\"sGF.!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "c:='c ';assume(c>0);laplace(Heaviside(t-c)*sin(b*t),t,s);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"cGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*&-%$ex pG6#,$*&%\"sG\"\"\"%#c|irGF+!\"\"F+,&*&F*\"\"\"-%$sinG6#*&%\"bGF+F,F0F +F+*&F5F0-%$cosGF3F+F+F+F0,&*$)F*\"\"#F0F+*$)F5F " 0 "" {MPLTEXT 1 0 21 "diff(Heaviside(t),t);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%&DiracG6#%\"tG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "laplace(Dirac(t),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "int(Dirac(t -a)*f(t),t=a-1..a+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"fG6#%\"aG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "de1:=\{m*diff(x(t),t,t) +b*diff(x(t),t)+k*x(t)=Dirac(t), x(0)=0, D(x)(0)=0\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$de1G<%/--%\"DG6#%\"xG6#\"\"!F-/,(*&%\"mG\"\"\"- %%diffG6$-F+6#%\"tG-%\"$G6$F8\"\"#F2F2*&%\"bGF2-F46$F6F8F2F2*&%\"kGF2F 6F2F2-%&DiracGF7/-F+F,F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "lsol:=dsolve(de1,x(t),method=laplace);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%lsolG/-%\"xG6#%\"tG,$*&**-%$expG6#,$*&*&%\"bG\"\"\"F)F4\"\"\" %\"mG!\"\"#!\"\"\"\"#F4F6F5-%%sqrtG6#,$*&,&*$)F3F:F5F4*&F6F4%\"kGF4!\" %F5*$)F6\"\"#F5F7F9F5-%$sinG6#,$*&F;F5F)F5#F4F:F4F5F@F7!\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "de:=\{m*diff(x(t),t,t)+b*dif f(x(t),t)+k*x(t)=0, x(0)=0, D(x)(0)=1/m\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#deG<%/-%\"xG6#\"\"!F*/--%\"DG6#F(F)*&\"\"\"F1%\"mG! \"\"/,(*&F2\"\"\"-%%diffG6$-F(6#%\"tG-%\"$G6$F=\"\"#F7F7*&%\"bGF7-F96$ F;F=F7F7*&%\"kGF7F;F7F7F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "dsolve(de,x(t),method=laplace);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/-%\"xG6#%\"tG,$*&**-%$expG6#,$*&*&%\"bG\"\"\"F'F2\"\"\"%\"mG!\"\"#! \"\"\"\"#F2F4F3-%%sqrtG6#,$*&,&*$)F1F8F3F2*&F4F2%\"kGF2!\"%F3*$)F4\"\" #F3F5F7F3-%$sinG6#,$*&F9F3F'F3#F2F8F2F3F>F5!\"#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "rhs(%)-rhs(lsol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "dea sy:=diff(y(x),x,x)+y(x)=Dirac(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %&deasyG/,&-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\"\"\"F*F2-%&DiracGF, " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "dsolve(\{deasy,y(0)=0,D (y)(0)=0\},y(x),method=laplace);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/- %\"yG6#%\"xG-%$sinGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "de ase:=diff(y(x),x,x)+y(x)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&deas eG/,&-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\"\"\"F*F2\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "dsolve(\{dease,y(0)=0,D(y)(0)=1\},y (x),method=laplace);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG -%$sinGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "laplace(int(f( u)*g(t-u),u=0..t),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%(laplac eG6%-%\"fG6#%\"tGF*%\"sG\"\"\"-F%6%-%\"gGF)F*F+F," }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 18 "invlaplace(%,s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*&-%\"fG6#%$_U1G\"\"\"-%\"gG6#,&%\"tGF+F*!\"\" F+/F*;\"\"!F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "26 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 }