Matemtica Superior en Matlab1. Funciones1.1 Tipos de funcionesFunciones linealesf(x)=mx+bm=3; b=2f= @(x) m*x+b fplot(f,[0 5]) f(5) fzero(f,0) %razde fFunciones potencialf(x) = xn n=2f= @(x) xnfplot(f,[!2 2])f(2)Funciones de razf(x)=nxn=2f= @(x) x("#n)fplot(f,[0 5])f(5)Funciones recprocasf(x)="#xnFuncin valor absolutof(x)= |x| f= @(x) ab$(x) fplot(f,[!" "])Funcin entero mximof(x)= xf= @(x) %e&l(x)fplot(f,[0 5])Funciones exponenciales $'m$ xf=2xfplot(%(ar(f),[!"0 "0]))*emplo 5+ Peso de un astronauta, ,& -n a$trona-ta pe$a "30 l&bra$ en la $-per.%&e de la /&erra, enton%e$ $- pe$o %-ando e$t0 ( m&lla$ arr&ba de la /&erra $e expre$a med&ante la f-n%&1n["]w( h)=(39603960+h)2a) 23-0l e$ $- pe$o %-ando e$t0 "00 m&lla$ $obre la /&erra4$'m$ (5="30*(3670#(3670+())2$-b$(5,(,"00)b) 3on$tr-'a -na tabla de 8alore$ para f-n%&1n 5 9-e d: el pe$o a alt-ra$ de 0 a 500 m&lla$+ 2;-: %on%l-'e de la tabla4Por serie de datosh=0:100:500;f=eval(w);format bank[h;f]'limitesclear hsyms hsubs(w,h,100)lot(h,f)t!tle('w(h)=1"0#("$%0&("$%0'h))()')*label('h (m!llas +e la ,!erra)')ylabel('w = f(h) (eso +el astronauta)')a*!s([0 500 100 1"0])-r!+ onsubs(w,h,.h)l!m!t(w,!nf)Por serie de datosexpresinw=/(h) 1"0#("$%0&("$%0'h))()flot(w,[0 500],'r')f=!nl!ne(subs(w,h,h))h=0:100:500;hol+ onlot(h,f(h))w='1"0#("$%0&("$%0'h))()'flot(w,[0 500],'r')f=!nl!ne(subs(w,'h','h'))h=0:100:500;hol+ onlot(h,f(h))Por expresin de caractersyms hw=1"0#("$%0&("$%0'h))()flot(char(w),[0 500])h=0:100:500;f=eval(w);hol+ onlot(h,f,'r')syms hw=1"0#("$%0&("$%0'h))()e0lot(w,[0 500])h=0:100:500;f=eval(w);hol+ onlot(h,f,'r')1.!. "esplazamiento de funcionesTabularsyms *f=*()*=.10:1:10;[*' eval(f)']set(e0lot(f,[.10 10]), '1olor','r') -=f." h=f'"hol+ one0lot(-,[.1010])set(e0lot(h,[.10 10]), '1olor','k')Con uso de caracteressyms *f=*()*=.10:1:10;[*' eval(f)']lot(*,eval(f))hol+ on-=char(f.")flot(-,[.10 10],'r')h=char(f'")flot(h,[.10 10],'k')Con uso de cadenassyms *f=/(*) *2()*=.10:1:10;[*' f(*)']lot(*,f(*),'r')-=f(*).";h=f(*)'";hol+ onlot(*,-,'b')lot(*,h,'k')Con uso de cadenassyms *f=!nl!ne(*())*=.10:1:10;[*' f(*)']-=f(*).";h=f(*)'"; lot(*,f(*),*,-,'r',*,h,'k') syms *f=(*.10)()syms *f=!nl!ne((*.10)())-=(*'10)()*=.)0:1:)0;[*' eval(f)']set(e0lot(f,[.)0 )0]), '1olor','r')hol+ one0lot(-,[.)0 )0])-=!nl!ne((*'10)())*=.)0:1:)0;[*' f(*)' -(*)']lot(*,f(*),*,-(*),'r')1.#$peraciones en funciones"espe%ar una variablesyms * ysolve(y.(*.))((1&)),y)solve(y.(*.))((1&)),*)&ra'car asntotassyms *f=("#*().)#*.1)&(()#*.1)#(*')))flot(char(f),[.)0 )0])*=.)0:02":)0;lot(*,eval(f))Fi(uras compuestas en trozosf1= /(*) *f)= /(*) *()f!-ureflot(f1,[.3 0])hol+ on-r!+ onflot(f),[020001 3])t!tle('4unc!5n comuesta')a*!s([.5 5 .5 5])Funciones pares e imparessyms *f=*(5'*-=subs(f,*,.*)r=f&- 67! r=.1 es !mar, r=1 es ar, r81 no es ar n! !mare0lot(f,[.33])hol+ one0lot(-,[.33])4=char(f)9=char(-)flot(4,[.33])hol+ onflot(9,[.33])1.) *mitessyms tv=10000&(5'1)35#e*((.2$:#t)))t=0:021:10;lot(t,eval(v))clear tsyms tformat bankl!m!t(v,!nf)subs(v,t,10)!. +%uste lineal polinomialexponencial!.1 +%uste de curva linealpolinomial+=[)25 3 % ; $ $25 1)25 1525];t=[15 )3 ") 5% 3$ :% $0 ;$];lot(t,+)e=olyf!t(t,+,1)syms t+=oly)sym(e,t)hol+ onflot(char(+),[15 ;$],'r')subs(+,t,1;)t=[0 3 ; 1) 1%];h=[5 "21 12$ 02; 02)];lot(t,h)e= olyf!t(t,h,))syms *=oly)sym(e,*)hol+ onflot(char(),[0 1%],'r')!.! Funcin polinomialFuncin polinomial ,aces de un polinomio* = (0: 021: )25)'y = erf(*) = olyf!t(*,y,%)* = (0: 021: 5)'y = erf(*)f = olyval(,*)lot(*,y,'o',*,f,'.')a*!s([050)])syms *f=*(" .%#*() .:)#* .):=sym)oly(f)r = roots()flot(char(f),[.%1"])-r!+ onf0ero(char(f),0)syms *f=*(" .%#*() .:)#* .):4=char(f)[*]=eval(solve(f,'*'))real(*) flot(4,[.%1"]),=[55 5; %3 %; :0 :5 ;0 ;3];&norm(>)uv=v&norm(v)uu=u&norm(u)!=[1 0 0]L=[0 1 0]k=[0 0 1]4=[ +ot(uw,!) +ot(uw,L) +ot(uw,k);2222+ot(uv,!) +ot(uv,L) +ot(uv,k);2222+ot(uu,!) +ot(uu,L) +ot(uu,k)]acos+(4)Determinar la matri de transformaci!n entre los ejes u = i + j

k, v = i

j y w=(16)1/ 2(i+j+2k) y las direcciones i,j,k.u=[1 1 .1];v=[1 .1 0];w=((1&%)())#[1 1 )]!=[1 0 0]L=[0 1 0]k=[0 0 1]uu=u&norm(u);uv=v&norm(v);?=[+ot(uu,!),+ot(uu,L),+ot(uu,k)];@=[+ot(uv,!),+ot(uv,L),+ot(uv,k)];1=[+ot(w,!),+ot(w,L),+ot(w,k)];C=[?;@;1]norm(C(:,1))4. Tensoressyms h n1 n) n",!k=[1 0 0;0 ) ";0 " 3],k!=,!k'7!k=025#(,!k',k!),!k=025#(,!k.,k!)R=[1.h 0 0;0 ).h ";0 " 3.h]n=[n1 n) n"]4=R#conL(n)'4=subs(4,h,'k')f3=n1()'n)()'n"().1f=+et(R)[h]=eval(solve(f))L=len-th(h);for !=1:L k=h(!,1); f(1:",:)=eval(4); [n1 n) n"]=solve(f(1,:),f(",:),f3); syms 0 +!s( ' n1n)n"') n=eval([n1 n) n"]) syms n1 n) n"en+syms n1 n) n"f1=(1.h(),1))#n1'0#n)'0#n";f)=0#n1'().h(1,1))#n)'"#n";f"=0#n1'"#n)'(3.h(",1))#n";[n1 n) n"]=solve(f1,f",f3); +!s( ' n1n)n"') n=eval([n1 n) n"])).1 5nvariantes?=[1 " 5;) % $;." .) .;];7=025#(?'?')[S,C]=e!-(?)+et(?) +et(C)?+=+!a-(?)sum(?+)(?(),))#?(",").?(),")#?(",)))222 '(?(1,1)#?(),)).?(),1)#?(1,)))222 '(?(1,1)#?(",").?(1,")#?(",1))S=+!a-(C)S(1,1)#S(),1)'S(1,1)#S(",1)'S(),1)#S(",1)/=[5 !" 3;" !7 !7;!3 !"? "][M,N]=*ordan(/),=0+5*(/+/O)[M,E]=e&A(,)Determinar para el tensor sim"trico #ik = (7 3 03 7 40 4 7)los valores principales y las direcciones de los ejes principales.,!k=[: " 0;" : 3;0 3 :],k!=,!k'7!k=025#(,!k',k!)[S,C]=e!-(7!k)1=+!a-(C)format bank6Er!mer !nvar!ante suma +e las +!a-onalesT7=sum(+!a-(7!k)) 6!nvar!ante +el tensor s!mUtr!coTC=sum(1) 6!nvar!ante +el tensor valores ro!os67e-un+o !nvar!ante: +eterm!nante +e los mVn!mos valoresTT7=+et(7!k():",):"))'+et(7!k(1:),1:)))2222'+et([7!k(1,1) 7!k(1,");7!k(",1) 7!k(",")]) 6!nvar!ante +el tensor s!mUtr!coTTC=1(1,1)#1(),1)'1(1,1)#1(",1)'1(),1)#1(",1) 6!nvar!ante +el tensor valores ro!os6,ercer !nvar!ante:TTT7=+et(7!k) 6!nvar!ante +el tensor s!mUtr!coTTTC=1(1,1)#1(),1)#1(",1) 6!nvar!ante +el tensor valores ro!os[S,C]=e!-(,!k)$allar la ra% cuadrada del tensor Dik = (3 2 02 3 00 0 9)C=[") 0;) " 0;0 0 $];sKrt(C)!. "iste#as de ecuaciones?=[1 .1 " ." ";.5 ) .5 3 .5;222." .3 : .) :;) " 1 .1 1][=,W]=lu(?)a=[1 .1 " .";.5 ) .5 3;222." .3 : .);) " 1 .1]b=[" .5 : 1]c=!nv(a)c#b'syms w * y 0[w,*,y,0]=solve(w.*'"#y."#0.",222.5#w')#*.5#y'3#0'5,222."#w.3#*':#y.)#0.:,222"#w'"#*'y.0.1)&esolver el siguiente sistema de ecuaciones lineales'+(y++)u+v+*=(-'+y-+u-v+*=+(y+(u+(*=-,'-+u++v+-*=.('-)y+u+/v-)*=0)'+,y+(+u+(v+.*=)6Natr!0 !nversa?=[1 ) 1 " 1 1 ;.1 1 .1 1 .1 1;0 ) 0 ) 0 );1 0 .1 1 3 $;222) ." 0 1 5 .";" : ) 1 ) ; ];@=[) 3 .: ; 1 "];64orma 1*!=!nv(?)#@'64orma )*=?X@'6Sar!ablesY=ml+!v!+e(?,@)syms * y 0 u v w[*,y,0,u,v,w]=solve(*')#y'0'"#u'v'w.),222.*'y.0'u.v'w.3,)#y')#u')#w':,222*.0'u'3#v'$#w.;,)#*."#y'u'5#v."#w.1,222"#*':#y')#0'u')#v';#w.");+!s( '*y0uvw')[*,y,0,u,v,w]l!nsolve(?,@)6Oe+ucc!5n +e 9auss1=[?,@'];[=,W]=lu(1)soluc!=rref(1)soluc!=rref([? @'])$. %ntegrales5nte(rales simplesPnteAral n-m:r&%a %on -$o de f-n%&1n en%adenadaQQ f = @(x)x+*$&n(@*loA(x))QQ 9-ad(f,0+2,3)PnteAraln-m:r&%a tran$formando a f-n%&1n en%adenadaQQ $'m$ xQQ f=x*$&n(@*loA(x))QQ L=&nl&ne(f)QQ 9-ad(L,0+2,3)PnteAral $&mb1l&%aQQ $'m$ xQQ f=x*$&n(@*x)QQ L=&nt(f,x)QQ '=%(ar(f)QQ R=%(ar(L)QQ fplot(',[0 "0])QQ (old onQQ fplot(R,[0 "0])5nte(rales doblesPnteAral n-m:r&%a doble%on -$o de f-n%&1n en%adenadaQQ f = @(x,') "+#("+x+2+'2)QQ dbl9-ad(f,!",",0,")PnteAraln-m:r&%a tran$formando a f-n%&1n en%adenadaQQ $'m$ x 'QQ f = "#("+x2+'2)QQ L=&nl&ne(f)QQ dbl9-ad(L,!",",0,")PnteAral doble $&mb1l&%aQQ $'m$ x 'QQ f = ("+x2+'2)QQ L=&nt(&nt(f,'),x)QQ t=%(ar(f)QQ /=%(ar(L)QQ ez$-rf(t)QQ (old onQQ ez$-rf(/)5nte(rales triplesPnteAral n-m:r&%a tr&ple%on -$o de f-n%&1n en%adenadaQQ f=@(x,',z) x+*$&n(x)+z*%o$(')*%o$(x)QQ tr&ple9-ad(f,0,",0,",0,")PnteAraln-m:r&%a tran$formando a f-n%&1n en%adenadaQQ $'m$ x ' zQQf=x*$&n(x)+z*%o$(')*%o$(x)QQ L=&nl&ne(f)QQ tr&ple9-ad(L,0,",0,",0,")PnteAral tr&ple $&mb1l&%aQQ $'m$ x ' zQQ f = ("+x2+'2+z2)QQ L=&nt(&nt(&nt(f,z),'),x)QQ t=$ol8e(f,z)QQ /=$ol8e(L,z)QQ -=%(ar(t)QQ B=%(ar(/)QQ ez$-rf(-(","))QQ (old onQQ ez$-rf(B(",2))syms a b c * y 0?=[a#* b#y c#0];S=*#y#0;+!v=+!ff(?(1,1),*)'+!ff(?(1,)))'+!ff(?(1,"));4=!nt(!nt(!nt(+!v,*),y),0)subs(4,*#y#0,S)syms u?=["#s!n(u) )#cos(u) 0]n=len-th(?)for !=1:n!f ?(1,!)B=0f=!nl!ne(?(1,!))O(1,!)=Kua+(f,0,!&))elseO(1,!)=0en+en+syms t?=[t .t() (t.1)];@=[)#t() 0 %#t];n=len-th(?)1=cross(?,@)for !=1:n!f 1(1,!)B=0f=!nl!ne(1(1,!))O(1,!)=Kua+(f,0,))elseO(1,!)=0en+en+7=!nt(1,0,))7=eval(7)syms u?=["#s!n(u) )#cos(u) 0]n=len-th(?)for !=1:n!f ?(1,!)B=0f=!nl!ne(?(1,!))O(1,!)=Kua+(f,0,!&))elseO(1,!)=0en+en+syms t?=[t .t() (t.1)];@=[)#t() 0 %#t];n=len-th(?)1=cross(?,@)for !=1:n!f 1(1,!)B=0f=!nl!ne(1(1,!))O(1,!)=Kua+(f,0,))elseO(1,!)=0en+en+7=!nt(1,0,))7=eval(7)syms t * y 0 +* +y +0?=[()#y'") *#0 (y#0.*)]*=)#t();y=t;0=t(";+*=+!ff(*,t);+y=+!ff(y,t);+0=+!ff(0,t);+r=[+* +y +0]fh!=e*an+(+ot(conL(?),+r))format bank4r=!nt(fh!,t)O=!nt(fh!,0,1)O=subs(4r,t,1).subs(4r,t,0)3al%-le a)S( xF) ndsb) Snds,& L = (x+2') & ! 3z * + x I, S = @x + 3' ! 2z ' S e$ la $-per.%&e de 2x + ' + 2z = 7 l&m&tada por x=0, x=", '=0, '=2+syms * y 04=[(*')#y),."#0,*];f=)#*'y')#0.%;4r=[+!ff(4(1,"),y).+!ff(4(1,)),0),222+!ff(4(1,1),0).+!ff(4(1,"),*),222+!ff(4(1,)),*).+!ff(4(1,1),y)]-ra+=eval([+!ff(f,*),+!ff(f,y),+!ff(f,0)])n=-ra+&norm(-ra+)f=(+ot(4r,n));k=[0 0 1];fkn=+ot(k,n);7olu1=!nt(!nt(f&fkn,*,0,1),y,0,))0=(%.y.)#*)&);f!=3#*'"#y.)#0;f!=eval(f!)fn=s!mle(f!#n)7olu)=!nt(!nt(fn&fkn,*,0,1),y,0,))1i 2=(yi-3'+)y-()j+3'(+)k. Calcular S( xA) nds sobre la superficie de intersecci!n de los cilindros '( + y( = a(y'( + ( = a( en el primer octante.syms * y 0 a?=[)#y#0 .(*'"#y.)) (*()'0)]f=y.0;?r=[+!ff(?(1,"),y).+!ff(?(1,)),0),222+!ff(?(1,1),0).+!ff(?(1,"),*),222+!ff(?(1,)),*).+!ff(?(1,1),y)]-ra+=eval([+!ff(f,*),+!ff(f,y),+!ff(f,0)])0=y;un=-ra+&sKrt(sum((-ra+2())))6vector un!tar!o +e la normalf=eval(+ot(conL(?r),un))7olu=!nt(!nt(f&cos+(35),*,0,sKrt(a().y())),y,0,a)n=[0 1 .1];k=[0 0 1];nk=+ot(n,k)&(norm(n)#norm(k)) 6nk=cos(alfa)7olu=!nt(!nt(f&nk,*,0,sKrt(a().y())),y,0,a)&cuaciones diferenciales de 'ri#er orden f=C)y'3#Cy'5#y;f=C)y'y.(*.))#e*()#*); y#C)y.(Cy)(); f=)#*#(Cy)().C)ya) s!mle(+solve('Cy=*#(1'y())&(y#(1'*()))','*'))+solve('*#(1'y()).y#(1'*())#Cy','*')b) +solve('Cy=y&*','*')c) s!mle(+solve('*#(1'y()).y#(1'*())#Cy','*'))+) f=+solve('C*=3#t#sKrt(*)','*(1)=1','t')flot(char(f(1,1)),[.10 10])hol+ onflot(char(f(),1)),[.10 10])e) f=+solve('Cy=)#*'y','y(0)=3','*')f=/(*,y) *#y("'*();[*,y]=o+e35(f,[0:021:1],[0])lot(*,y,'r')r=olyf!t(*,y(:,1),))syms th=oly)sym(r,t)hol+ onflot(char(h),[0 1])=+solve('Cy=*'y()','y(0)=0','*')flot(char(),[0 1])hol+ onf=/(*,y) *'y()[*,y]=o+e35(f,[0:021:1],[0])lot(*,y,'r')f=/(*,y) *#y("'*();=+solve('Cy=*#y("'*()','y(0)=0','*')[*,y]=o+e35(f,[0:021:1],[0])lot(*,y)r=olyf!t(*,y(:,1),))syms th=oly)sym(r,t)hol+ onflot(char(h),[0 1])4cuacion 5y=(6'6y7-3y78))clear;clc;clfsyms * y Cy A y1 y)6Cef!n!c!5n +e var!ablesf=)#*#Cy.Cy(".y 6Dcuac!5n C!ferenc!al6667oluc!5n ?nalVt!ca or matlab +solvef1=+solve(f,*);1=symvar(f1);11=1;*o=12;;*ma*=";f)=subs(f1,1(1,1),11)yo=subs(f),'*',*o)hol+ on 6Nantener act!vo la ventana -raf!caset(e0lot(f)(),1)),'1olor','k') 69raf!car la e*res!5n f1(",1)a*!s([*o *ma* 0 10]) 64!Lar ran-os +e -raf!cos en Y y A6667oluc!5n ?nalVt!ca manualf=11&()'("#()&3).*;y=()#*#).(";=solve(f,'')y=subs(y,P''Q,P(",1)Q);flot(char(y),[*o *ma*],'..-')retty(y)66+y=solve(f,'Cy') 6CeseLar CyCy1=!nl!ne(+y(1,1))h=02);*=*o:h:*ma*;6NUto+o +e Oun-e Zutta[*,y]=o+e35(Cy1,*,[yo(),1)])lot(*,y,'or')66n=len-th(*);y=A#ones(1,n);*(1)=*o;y(1)=yo(),1);Cy=(y).y1)&hf"=subs(f,'Cy',Cy)f3=solve(f",'y)')6C!ferenc!as 4!n!tasfor !=1:n.1f5=subs(f3(1,1),Py1,y),'*','y'Q,Py(!),y(!'1),*(!),y(!)Q);y(!'1)=eval(f5);en+lot(*,eval(y),':')Tanque de almacenamientoF=500;6m("&s?=1)00;6m()a="00;6Eor Oun-e Zutta4=/(t,y) "#F#((s!n(t))())&?.a#((1'y)((125))&? [t,y]=o+e35(4,[0:021:10],[0])lot(t,y,'r')syms A+t=021t=0:+t:10;n=len-th(t)y=A#ones(1,n)y(1)=06Eor +!ferenc!as f!n!tasfor !=1:n.1f(!'1)=eval(("#F#((s!n(t(!)))())&?.a#((1'y(!))((125))&?)#+t'y(!))y(!'1)=f(!'1)en+y=eval(y)hol+ onlot(t,y)&cuaciones diferenciales de segundo ordensyms *=+solve('C)y.%#Cy'5#y=0','y(0)=1','y())=1','*')flot(char(),[0 )])4=/(*,y) [y());y(1)];f=+solve('C)y.y=0','y(0)=0','y(1)=.3','*')flot(char(f),[0 1])hol+ on[*,y]=o+e35(4,[0:021:1],[0 .3])lot(*,y(:,1),'r')4cuacion 5y='6y7-y776y=*#y[.y[[6Eor Oun-e Zutta4=/(*,0) [(.*'sKrt(*2()'3#0(1)))&);(.*.sKrt(*2()'3#0(1)))&)][Y A]=o+e35(4,[):021:"],[.1 .1]);fr!ntf(' * y1y)');[Y A]lot(Y,A(:,1),'..k',Y,A(:,)),'..k')6Eor +!ferenc!as f!n!tassyms A 0h=02);*=):02):";n=len-th(*);y=A#ones(),n);for k=1:n.1for !=1:)y(!,1)=.1;f(!,k)=*(k)#(y(!,k'1).y(!,k))&h'((y(!,k'1).y(!,k))&h)().y(!,k);resul=eval(solve(f(!,k)));y(!,k'1)=resul(!,1);en+en+fr!ntf(' * y1y)');soluc!on=[*' eval(y)']hol+ onlot(*,y(1,:),''',*,y(),:),'.o')41=.0'14)=.0()&3hol+ onflot(char(41),[) "],''-')hol+ onflot(char(4)),[) "],''-')1=eval(olyf!t(*,y(1,:),1)))=eval(olyf!t(*,y(),:),)))syms *f1=oly)sym(1,*)f)=oly)sym(),*)4cuacion 5y= '6y7-'6y77clear;clc;f!-ure(close)syms * y Cy C)y A y1 y) y" 6Cef!n!c!5n +e var!ablesf=*#C)y.*#Cy'y 6Dcuac!5n C!ferenc!al6667oluc!5n ?nalVt!ca or matlab +solvef1=+solve(f,'y(1)=)','y())=%',*);f)=subs(f1,P'D!(1)','D!())','D!(1, .*)'Q,P0,0,0Q);+!-!ts(");f"=va(f));hol+ on 6Nantener act!vo la ventana -raf!caflot(char(f"),[1 )],'..b')666NUto+o +e Oun-e Zutta61amb!o +e var!ables re+uc!en+o a r!mer or+en6[y(1)]=[y] [Cy(1)]=[y())]6[y())]=[Cy][Cy())]=[C)y]=[(*#Cy.y)&*]f3=solve(f,C)y)f5=subs(f3,P'y','Cy'Q,P'y(1)','y())'Q)f%(*,y)=['y())';f5]Cy=matlab4unct!on(f%)h=021;*=1:h:);[*,y]=o+e35(Cy,*,[) %])lot(*,y(:,1),'or');666C!ferenc!as 4!n!tasn=len-th(*);y = sym('A', [1 n]);C)y=(y".)#y)'y1)&h();Cy=(y).y1)&h;f)=subs(f,P'Cy','C)y'Q,PCy,C)yQ);*(1)=1;*(n)=);y(1)=);y(n)=%;for !=1:n.)f3(!,1)=subs(f),Py1,y),y",'*','y'Q,Py(!),y(!'1),y(!')),*(!),y(!)Q);en+Os=symvar(f3);[ A), A", A3, A5, A%, A:, A;, A$, A10]=solve(f3);+!-!ts(")y=va(eval(y));lot(*,y,'..r')4cuacion 5y= '7+y7+'-), '= '7-y7-y+)clear;clc;clfsyms C* Cy * y *1 *) y1 y) realf1=C*'Cy'*.y.";f)=C*.Cy.*.y'";[*,y]=+solve(f1,f))1=symvar(*);*=subs(*,1,[1,1]);y=subs(y,1,[1,1]);to=0;tf=10;hol+ onflot(char(*),[to tf])flot(char(y),[to tf],'r')h=02);t=to:h:tf;n=len-th(t);*(1,[1,n])=subs(*,'t',[to tf]);y(1,[1,n])=subs(y,'t',[to tf]);*=va(*);y=va(y);Y=sym('Y',[1 n]);A=sym('A',[1 n]);v*=f!n+(*==0);vy=f!n+(y==0);*(:,v*)=Y(:,v*);y(:,vy)=A(:,vy);Cy=(sym('y(!'1)').sym('y(!)'))&h;C*=(sym('*(!'1)').sym('*(!)'))&h;f"=subs(f1,P'C*','Cy'Q,PC*,CyQ);f3=subs(f),P'C*','Cy'Q,PC*,CyQ);m=len-th(symvar(*));for !=1:m f5(!,1)=subs(f",P'*','*(!)','*(!'1)','y','y(!)','y(!'1)'Q2222,P*(!),*(!),*(!'1),y(!),y(!),y(!'1)Q);f%(!,1)=subs(f3,P'*','*(!)','*(!'1)','y','y(!)','y(!'1)'Q2222,P*(!),*(!),*(!'1),y(!),y(!),y(!'1)Q);en+O=symvar([f5,f%]);7oluc!on=solve(f5,f%);Os=cell)num(struct)cell(7oluc!on));*=subs(*,O,Os')y=subs(y,O,Os')lot(t,eval(*),'..')lot(t,eval(y),'..r')4ncontrar la distribuci!n de temperaturasde una placa rectangular de acero, si los e'tremos est9n a las temperaturas#:, #0 , #(, #)#o : ;C#0 : ;C#( : ;C#) ):: ;Cclear;clc;syms ,o n w = k * yw==*="#=&3;y="#=&3;,o=100;,=(3#,o&!)#s!n(()#k'1)#!#*&=)#s!nh(()#k'1)#!#y&=)&(()#k'1)#s!nh(()#k'1)#!#w&(=)))+!-!ts(5),em=va(symsum(,,k,0,Tnf))clear;clc;syms C)W* C)Wyf=C)W*'C)Wy;n=3; 6C!v!s!ones en la laca+*=1&n;+y=+*;C)W*=(sym('W(!'1,L)').)#sym('W(!,L)')'sym('W(!.1,L)'))&+*();C)Wy=(sym('W(!,L'1)').)#sym('W(!,L)')'sym('W(!,L.1)'))&+y();f=subs(f,P'C)W*','C)Wy'Q,PC)W*,C)WyQ);W = sym(',', [n'1 n'1]); 6n'1 n\mero +e no+osW(:,[1 n'1])=0;W(1,:)=100;W(n'1,:)=0;for !=):nfor L=):n4(!,L)=subs(f,P'W(!,L)','W(!'1,L)','W(!,L'1)','W(!.1,L)','W(!,L.1)'Q,PW(!,L),W(!'1,L),W(!,L'1),W(!.1,L),W(!,L.1)Q);en+en+4(1,:)=[];4(:,1)=[];7=f!n+sym(4),=symvar(4);O=va(cell)num(struct)cell(solve(4))),5);W=subs(W,,,O)4ncontrar la distribuci!n de temperaturas de una placa rectangular de acero si en uno de sus e'tremos tenemos un flujo qo de entrada y si los e'tremos est9n a las temperaturas#:, #0 , #(.#o -0:: ;C#0 : ;C