{VERSION 4 0 "IBM INTEL LINUX22" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 0 0 255 1 0 2 0 
0 1 0 0 0 0 1 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 
{CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 
4 3 0 3 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Cour
ier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }
{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 128 0 0 1 
2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 
258 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 
0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "restart: \n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "with(pldx): with(student):wi
th(inttrans);" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 "reporter dans p
ldx" }}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 530 "xclone:= proc(z) ``||
qz||(convert(z, string)); end;\nxplif:= proc(ex,li::list) local var, c
hvar, ex2, ex3, ravch, ravch2; \n[seq(li[k*2-1],k=1..nops(li)/2)]; var
:=convert(indets(%), list); \nchvar:= map(id=xclone, var); ravch:= map
(xclone=id, var); ex2:= subs(chvar, ex);\n# print(chvar, ravch); \n(as
sume@op@subs)(chvar, li); \nravch2:= map(xclone=id, var); # print(chva
r, ravch, ravch2, ex2);\nvalue(ex2); if nargs=3 then args[3](value(ex2
)) else value(ex2) fi;\nex3:= subs(ravch2, ravch, %); (unassign@op@map
)(lhs, ravch);   \nex3; end:" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 
301 "eval(intparts): subs('student'[''intparts'']=procname, %): st:= c
onvert(%, string): \nou1:= searchtext(\"error \"\"\",st): ou2:= search
text(\"bounds\", st):\n\"\" || (substring(st,1..ou1-1)) || \"print(\" \+
|| (substring(st, ou1+6..ou2+5)) || \" \"\")\" || (substring(st, ou2+7
..-1)):\nxintparts:= parse(%); # xprint(%):" }}}{EXCHG {PARA 0 "" 0 "
" {MPLTEXT 0 21 170 "(xlap):=proc(f, tt)local _t, _s; global t;\n _s :
= '_s'; if nargs = 1 then _t := t else _t := tt end if; \nunapply(Int(
f(_t)*exp(-_s*_t), _t = 0 .. infinity), _s)\nend proc;" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }{MPLTEXT 1 0 37 "v
lap:= Lap=xlap: def_l:= vlap(f)(p); " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "vlap(1)(p): xplif(%,[p,positive]);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 35 "vlap(id)(p): xplif(%,[p,positive]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "vlap(id^ 3)(p): xplif(%,[p,p
ositive]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "vlap(id^ 3/3!
)(p): xplif(%,[p,positive]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 67 "vlap(t->exp(a*t))(p): res3:= xplif(%,[p-a,RealRange(0, infinity)
]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "vlap(exp@(I*id))(p):
 xplif(%,[p,RealRange(0, infinity)]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 107 "vlap(sin)(p): res4:= xplif(%,[p,positive], simplify)
;\nvlap(cos)(p): res5:= xplif(%,[p,positive], simplify);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "factor(res5+I*res4);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 71 "vlap(t->f(t-a))(p); lhs(%)=(xcombipo@expand@changevar
)(t-a=x,rhs(%),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "gra:=
 qqq-> displayf(plot(qqq,x=-5..10,linestyle=16, color=black), tickmark
s=[3,3],axes=boxed):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "ff:
= unapply(piecewise(x>0,sin(x),0),x); gra('ff'(x));" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 39 "gg:= unapply(ff(t-2),t);  gra('gg'(x));" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "hh:= unapply(ff(t+2)*Heav
iside(t),t);   gra('hh'(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 37 "xlap(ff)(p); xplif(%, [p, positive]);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 37 "xlap(gg)(p); xplif(%, [p, positive]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "xlap(hh)(p); xplif(%, [p, positive]
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "xlap(t->ff(t+a))(p); \+
xplif(%, [p, positive, a, positive]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 103 "xlap(t->ff(t-a))(p); xplif(%, [p, positive, a, posit
ive]):\nxplif(%,[t-a,positive,p,positive],simplify);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 46 "xlap(t-> sin(t+a))(p); xplif(%,[p,positiv
e]);;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "vlap(t->f(a*t))(p
): subs(t=x, %); lhs(%)=(changevar)(a*x=t,rhs(%),t):\n(xjoli@xplif)(%,
[a,positive]); \n((rhs=lhs)@subs)(Int=int,p=p/a,def_l); subs(%,%%);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "vlap
(f)(p); diff(%,p); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 144 "vlap(D(f))(p): \ndef_ld:= lhs(%)=convert(rhs(%), d
iff);\n(yjoli@xjoli@xintparts)(%, exp(-p*t));\nfor_1:= (eval@subs)(lim
it=0, (rhs=lhs)(def_l), %);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
87 "vlap(t-> diff(f(t),t,t))(p):  vlap(D(D(f)))(p): def_ldd:= lhs(%)=c
onvert(rhs(%), diff);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "(xintpart
s)(%, exp(-p*t));\n(yjoli@xjoli@eval@subs)(limit=0, (rhs=lhs)(def_l), \+
%);\nfor_2:= collect(subs((rhs=lhs)(def_ld), for_1, %), [Lap]); " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "vlap(t->f(t)/t)(p); (xjoli@
diff)(%,p); (yjoli@subs)((rhs=lhs)(def_l), %);\nmap(Int,%,p=s..infinit
y); (combine@value)(-%); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
93 "Int(f(x)*g(t-x)*Heaviside(x)*Heaviside(t-x),x=0..t);\nh:= unapply(
subs(0..t=0..infinity,%),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 129 "xlap(h)(p); tmp:= xfubini(%); op(1,%): %=changevar(t=x+y,%,y):
\nsubs(-x..infinity=0..infinity,%); (xcombipo@expand@subs)(%, tmp);\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 71 "eqd:= diff(f(t),t,t)+4*diff(f(t),t)+3*f(t)=Hea
viside(t)-Heaviside(t-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
39 "map(xlap@unapply,convert(eqd,D),t)(p); " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "(xjoli@expand)(%): tmp1:= (yjoli@combine)(%,power);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "map(xlap=Lap, \{f,D(f),D
(D(f))\})(p); subs(%, tmp1);\n(for_1, for_2,%); subs(%); tmp2:=collect
((xcombipo@xplif)(%,[p,positive]), Lap);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "cond_ini:= f(0)=0, D(f)(0)=1;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 123 "subs(cond_ini, tmp2);\n(op@solve)(\{%\}, \{La
p(f)(p)\}):\ntmp3:= collect(%,exp,factor);\ncollect(%,exp,zz->convert(
zz,parfrac,p));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "fu2:= t-
>-1/3-1/6*exp(-3*t)+1/2*exp(-t): vlap(%)(p);\nxplif(%,[p,positive]);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "aa:= 1; fu3:= unapply(fu2
(t-aa)*Heaviside(t-aa),t);\nxlap(fu3)(p); xplif(%,[p,positive]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "fu1:= t->(1/3-exp(-3*t)/3)*H
eaviside(t); vlap(%)(p);\n(factor@xplif)(%,[p,positive]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "fu:= fu1+fu3; vlap(fu)(p); (xcombip
o@expand@xplif)(%,[p, positive]);\ncollect(%, exp); %-tmp3;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "fu(t);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 151 "grb := proc (qqq) options operator, arrow; di
splayf(plot(qqq,t = -1 .. 5,linestyle = 16,color = black),tickmarks = \+
[[0,1,5], 3],axes = boxed) end proc;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "grb(rhs
(eqd));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "grb(fu(t));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grb(D(fu)(t) );" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "grb((D@@2)(fu)(t) );" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "collect(D(fu)(t), Dirac); xplif(%,
 [t,real], simplify):\nval_dfu:= collect(%, Heaviside, factor@xcombipo
@expand);;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "collect(diff
(val_dfu,t), Dirac); xplif(%, [t,real], simplify):\nval_dfu2:= collect
(%, Heaviside, factor@xcombipo@expand);;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "collect(val_dfu2+4*val_dfu+3*fu(t), Heaviside);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "eqd; dsol:= (rhs@collect)(ds
olve(\{eqd,f(0)=0, D(f)(0)=1\},f(t)), Heaviside); fu(t);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "eqd_k:= subs(f=k, lhs(eqd)); dso:=
 dsolve(%, k(t));\ndef_al:= alpha(t)= subs(dso,_C1=1, _C2=0, k(t)), be
ta(t)= subs(dso,_C1=0, _C2=1, k(t));   " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 98 "def_a:= y(t)=a(t)*alpha(t)+b(t)*beta(t), diff( y(t),t
)=a(t)*diff(alpha(t),t)+b(t)*diff(beta(t),t);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 46 "eq1:= subs(def_al, diff(def_a[1],t)-def_a[2]);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "(expand@subs)(f=y,def_a[2
],def_a[1],eqd);\neq2:= collect((expand@subs)(def_al,%),[a,b],xcombipo
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "sol:= (xcombipo@solve
)(\{eq1,eq2\},diff(\{a(t),b(t)\},t));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 163 "a(t)=A+Int(subs(sol,diff(a(t),t)),t); va:= collect(v
alue(%), Heaviside,xcombipo);\nb(t)=B+Int(subs(sol,diff(b(t),t)),t); v
b:= collect(value(%), Heaviside,xcombipo);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 68 "collect(subs(def_al, va,vb, def_a[1]), Heaviside, x
combipo@expand);;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 92 "eqdd:= subs(lhs(eqd))-g(t);\n(xlap)(unapply(%,t))(p
); tmp:= (yjoli@xcombipo@xjoli@expand)(%);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 178 "\{de
f_l, def_ld, def_ldd\}: map(rhs=lhs,%);\nsubs(%, ((rhs=lhs)@vlap)(g)(p
), for_1, for_2, tmp); collect(subs(cond_ini, %), Lap);\n(op@solve)(\{
%\}, Lap(f)(p)): tmp1:= collect(%, Lap);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "coeff(rhs(tmp1),Lap(g)(p)); fv:= unapply(invlaplace(%
,p,t),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "gv:= unapply(r
hs(eqd),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "Int(fv(t-x)*
gv(x),x=0..t); (xcombipo@expand@value)(%): collect(%+fv(t), Heaviside)
;;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "dsol;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "79" 0 }{VIEWOPTS 1 1 0 
1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }