MATLAB informe

CALCULO II

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II

UNIVERSIDAD ANDINA DEL CUSCO FACULTAD DE INGENIERIA Y ARQUITECTURA INGENIERÍA CIVIL

INTEGRANTES: YULIANA KAREN PUMA FLOREZ FLOREZ EDSON RODRIGO SOLO HUALLPA HOLLY HOLLY FARFAN AIMA AIM A GARDENIA BOCANGEL QUISPE MARTIN ROJAS BEJAR KEYLA DANITZA MOZO BARRANTES DIEGO MORALES MORALES DE LA CUBA VICTOR HIRAM PALIZA GAMARRA

PROFESOR: LISARDO LISARD O CALVO CALVO NEGRON

2


1. INDICE

2.

INTRODUCCIÓN

3. MATLAB 3.1 MARCO TEORICO 3.2 COMANDOS BÁSICOS DE ENTORNO. 4. Entorno Gráf!o "# M$tL$% &R2'14A(. ). *ORMATOS DE SALIDA DE LOS RESULTADOS &for+$t( ,. O-ERADORES  *UNCIONES EN MATLAB ,.1 O/#r$"or#0 $rt+t!o0 ,.2 *n!on#0 +$t#+át!$0 ,.3 O/#r$"or#0 r#$!on$#0  56!o0 ,.4 -r$!t7# !on o/#r$"or#0 r#$!on$#0  56!o0 ,.) S8+%oo0 n+r!o0 #0/#!$#0 ,., *n!on#0 $"!on$#0 /$r$ n9+#ro0 !o+/#:o0 ;. V$r$%#0 ;.1 A6no0 !o+$n"o0 "# S0t#+$ O/#r$tO SIMBÓLICO =.1 *n!on#0 $"!on$#0 !on #?/r#0on#0 0+%5!$0 =.2 *n!on#0 #0/#!$#0 /$r$ +#"r #f!#n!$ "# $6ort+o0 @. GRA*ICACIÓN @.1 Gráf!o "# fn!on#0 "# n$ <$r$%# @.2 Gráf!o "# fn!on#0 +/8!t$0  #!$!on#0 !on "o0 <$r$%#0 @.3 Gráf!o "# fn!on#0 "#fn"$0 #n for+$ /$r$+tr!$ 1'. EDITOR DE GRÁ*ICOS 1'.1 Gráf!o "# fn!on#0 "# "o0 <$r$%#0 1'.2 In0#rt$r # 6ráf!o #n n "o!+#nto 11. -ROGRAMACIÓN CON MATLAB 11.1 Ar!
UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II 11.2 E0tr!tr$0 "# !ontro "# f:o #n MATLAB 11.3 D#!0on#0 &n0tr!!5n f( 12. EN GENERAL LAS *UNCIONES EN MATLAB 13. INTERACCIÓN CON OTROS ENTORNOS 13.1 Int#r$!!5n !on ECEL 14. CONCLUSIONES 1). BIBLIOGRA*ÍA

2. INTRODUCCIÓN

E 0o "# $ +$t#+át!$ no #0 "# o <#n# 0#n"o 0$"o "#0"# o0 n$!+#nto0 "# $ !<$!5n !o+o 0# /#"# <#r #n $0 !#n!$0  $rt#0 "# !tr$0 $nt6$0 !o+o $ #6/!$ ro+$n$ o $ !tr$ In!$. En n#0tro0 "8$0 $ +$t#+át!$ !o%r$ +á0 r##<$n!$ "#%"o $ 0 t"$" /$r$ #nt#n"#r f#n5+#no0 n$tr$#0 /r#<#nr 00 !on0#!#n!$0 o r#0o<#r !o+/!$"o0 /ro%#+$0 "# n6#n#r8$  fn$n$0 7# 0on 0oo $6no0 #:#+/o0 r#/r#0#nt$t
4


3. MATLAB

3.1 MARCO TEORICO E0 $ $%r#<$tr$ "# &MATr? LABor$tor F $%or$toro "# +$tr!#0H(. E0 n$ #rr$+#nt$ "# 0oft$r# +$t#+át!o 7# ofr#!# n #ntorno "# "#0$rroo nt#6r$"o &IDE( !on n #n6$:# "# /ro6r$+$!5n /ro/o &#n6$:# M(. C$r$!t#r80t!$0 "# M$t$%. Cá!o n+r!o +á0 rá/"o  !on $t$ /r#!05n J C$/$!"$" /$r$ +$n#:o +$t#+át!o 0+%5!o J fn!on#0 /$r$ 6r$f!$r. E0 n$ "# $0 +!$0 0of0t!$"$0 #rr$+#nt$0 "# !o+/t$!5n "0/on%#0 #n # !o+#r!o /$r$ r#0o<#r /ro%#+$0 "# +$t#+át!$0 t$#0 !o+o M$/#M$t#+$t!$  M$tC$". A /#0$r "# o 7# $fr+$n 00 "#f#n0or#0 nn6n$ "# #$0 #0 $ +#:orH. To"$0 t#n#n fort$#$0  "#%"$"#0. C$"$ n$ /#r+trá #f#!t$r !á!o0 +$t#+át!o0 %á0!o0 /#ro "f#r#n #n # +o"o !o+o +$n#:$n o0 !á!o0 0+%5!o0  /ro!#0o0 +$t#+át!o0 +á0 !o+/!$"o0 !o+o $ +$n/$!5n "# +$tr!#0. -or #:#+/o MATLAB #0 0/#ror #n o0 !á!o0 7# n
)

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II /ro6r$+$ 0+$r #n n #n6$:# "# $to n<#. MATLAB #0tá "0/on%# #n <#r0on#0 t$nto /rof#0on$ !o+o #0t"$nt.

3.2 COMANDOS BÁSICOS DE ENTORNO. En $ <#nt$n$ "# !o+$n"o0 0# /#"# r#$$r o 06#nt# !! /" !#$r 0+0 No+%r#V$r$%# #/ No+%r#Co+$n"o

L+/$ $ <#nt$n$ "# !o+$n"o0 M#0tr$ # "r#!toro $!t$ #n "on"# no0 #n!ontr$+o0 E+n$ to"$0 $ <$r$%#0 D#!$r$ n$ <$r$%# 0+%5!$ -r#0#nt$ n$ $"$ 0o%r# # !o+$n"o

4. Entorno Gráf!o "# M$tL$% &R2'14A(. -#"# <$r$r !on $ <#r05n

*o"#r "# tr$%$:o &!rr#nt fo"#r( V#nt$n$ "on"# 0# <0$$ $0 fn!on#0 !r#$"$0. V#nt$n$ "# #"!5n V#nt$n$ "on"# 0# #"t$n $0 fn!on#0. E0t$!o "# tr$%$:o &PorQ0/$!#( <#nt$n$ /$r$ <0$$r $0 <$r$%#0 "#fn"$0. V#nt$n$ "# !o+$n"o0 &Co++$n" Pn"o( V#nt$n$ "on"# 0# n6r#0$n o0 !o+$n"o0.

,


). *ORMATOS DE SALIDA DE LOS RESULTADOS &for+$t( E r#0t$"o "# n$ o/#r$!5n /#"# !$+%$r 0#69n # for+$to "# 0$"$ 7# 0# #0tá 0$n"o. R#!r"#0# 7# 0#+/r# !$!$  $+$!#n$ !on "o%# /r#!05n #0 "#!r !on n$0 1, !fr$0 "#!+$#0 #7<$#nt#0 $0 /o0%"$"#0 "# <0$$!5n 0on >> format long

+#0tr$ 14 "#!+$#0

>> format bank

2 "#!+$#0

>> format rat

not$!5n r$!on$ &fr$!!on#0(

>> format short e

not$!5n !#nt8f!$

>> format long e

not$!5n !#nt8f!$ !on 14 "#!+$#0

>> format +

+#0tr$ 06no0 K  

>> format short

4 "#!+$#0 &MATLAB o 0$ /or o+05n(

>> format compact

0/r+# 8n#$0 $"!on$#0 #n $ 0$"$

>> format loose

n0#rt$ 8n#$0 #n %$n!o #n $ 0$"$&r#!o+#n"$"o(

>> format hex

for+$to #?$"#!+$

>> vpa(sqrt(2), 100)

<$r$%# /r#!0on $rt+#t!

>> format short

r#6r#0# $ for+$to nor+$ "# MATLAB

,. O-ERADORES  *UNCIONES EN MATLAB 6.1 Operadores aritméticos + - * /  ! ()

! 0# 0$ /$r$ /ot#n!$!5n / #0 "<05n $ $ "#r#!$  #0 "<05n $ $ 7#r"$

0t# o0 o/#r$"or#0  !$r$!t#r#0 #0/#!$#0

>> help ops

6.2 Funciones matemáticas #?/ o6 07rt 0n !o0 t$n ..... >> help elf"n

0t# $0 fn!on#0 +$t#+át!$0 ##+#nt$#0

6.3 Operadores relacionales y lógicos # #$ > >$ $$ %$ & ' % o0 tr#0 9t+o0 !orr#0/on"#n $ $$ r#/r#0#nt$ $ 08+%oo $ %$ r#/r#0#nt$ $ 08+%oo 6.4 Practique con operadores relacionales y lógicos >> t$sn(2) # 0 & log(2) > 0 # r#0t$"o #0 n <$or 56!o &' o 1(

;

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II 6.5 !m"olos numéricos especiales  2' nf #0 # 08+%oo  '' .a. 06nf!$ Not A N+%#rH &<$or n"#t#r+n$"o(  p !ont#n# $ !on0t$nt# π  eps #0 $ /r#!05n "# t/o r#$ #n MATLAB  realmn # +#nor n9+#ro r#$ #n MATLAB  realmax # +$or n9+#ro r#$ #n MATLAB   r#/r#0#nt$ $ 08+%oo !o+/#:o -1 6.6 Funciones adicionales para n#meros comple$os !on: r#$ +$6 $%0 $n6# !o+/#?

;. V$r$%#0 • • • • • •

No r#7#r#n 0#r "#!$r$"$0 S t/o "#/#n"# "# <$or $06n$"o -#"#n 0#r r#"#fn"$0 S#n0%# $ t/o "# #tr$ &+$90!$0 o +n90!$0( ans #0 $ <$r$%# /or o+05n /ro<0t$ /or MATLAB M$t$% r#$$ $ $06n$!5n "# +#+or$ $ <$r$%#0 "r$nt# $ #:#!!5n.

 ?F3  ?F+#n0$:#  sms ?  ?F2 ; 4  ?F2K3  ?  hos ?  sp&?(  ?Fnp"t&"$toW(  #?/&?(3  ans  F2Xans

? #0 "# t/o r#$ ? #0 "# t/o t#r$ &0# !o+$0 0+/#0( ? #0 n 08+%oo ? #0 n <#!tor ? #0 "# t/o !o+/#:o +#0tr# # !ont#n"o $!t$ "# $ <$r$%# +#0tr# # t/o $!t$ "# $ <$r$%# +#0tr# 0o$+#nt# # !ont#n"o n6r#0# n <$or /$r$ n$ <$r$%# "#0"# # t#!$"o $ <$r$%# ans !ont#n# # 9t+o r#0t$"o $ /#"# 0$r

%.1 &lgunos comandos del istema Operati'o 0t$ "# !o+$n"o0 >> help general >> ho 0t$ $0 <$r$%#0 #n 0o >> hos 0t$ $0 <$r$%#0 #n 0o  0 "#0!r/!5n %orr$ <$r$%#0 >> clear a b c "#0/#:$ $ <#nt$n$ "# !o+$n"o0 >> clc +#0tr$ !$ #0 # "r#!toro $!t$ >> p >> c cmatlabork c !$+%$ $ rt$ "# "r#!toro $!t$ >> r 0t$ # !ont#n"o "# "r#!toro $!t$ >> save pr"eba save $+$!#n$ $0 <$r$%#0 #n n $r!> loa pr"eba loa !$r6$ <$r$%#0  0 !ont#n"o >> elete pr"ebamat elete #+n$ $r!> q"t %.2 (omandos especiales >> ate >> clock

f#!$ f#!$ or$ <#$ 0 0o !on #/.

=

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II  for+$t r$t  !o!Q  for+$t 0ort

/$r$ <0$$r $ f#!$ !on +$0 !$r"$" <#<$ $ for+$to nor+$

%.3 (adenas de caracteres  ?FYM$t#+$t!$Y $06n$!5n "# n$ !$"#n$ &0# !o+$0 0+/#0(  ?&4( +$n#:o "# n !$rá!t#r "# $ !$"#n$ 0# n n"!#  tF?&2)(  nFlength &?(  !Fstrcat &?, t(  #/ strf"n

%.4 )ectores y *atrices  ?F3 1 4 ; 2  ?F3 1 4 ; 2  ?&2(F)  F?&2 4(  tF3; -1; 4; )  tF?  F3 ? , ;  F211'

3n 456758 los 9nces se escrben entre par:ntess  son n"meraos ese 1 +$n#:o "# n$ 0%!$"#n$ 0# (nco fnal)

on6t" "# $ !$"#n$ !on!$t#n$!5n "# !$"#n$0 0t# $0 fn!on#0 /$r$ !$"#n$0 $06n$!5n "r#!t$ "# n <#!tor f$ /#"# 0#/$r$r !on comas o !on espacos +$n#:o "# n !o+/on#nt# "# <#!tor. 3n 456758 los 9nces se escrben entre par:ntess  son n"meraos ese 1 /$r$ $06n$r /$rt# "# n <#!tor 0# (nco fnal) /$r$ $06n$r n <#!tor !o+n$ 0# ; /$r$ o%t#n#r $ tr$n0/#0t$ "# n <#!tor 0#  x #0 $ tr$n0/#0t$ "# <#!tor x

/#"# $06n$r n <#!tor 0$n"o otro <#!tor /#"# $06n$r n <#!tor +#"$nt# n$ 0#!#n!$ 3n 456758 las sec"encas se escrben valor ncal  ncremento  valor fnal s el ncremento es 1 p"ee omtrlo

 F2, ), 4,  ;, 3  ?F3 ) 2 '  F2X?  F#?/&?(  $F, 3 ; ) 1

-$r$ !ontn$r #n $ 06#nt# 8n#$ 0#  #0!r%$ $ !ontn$!5n "# $ 8n#$ $nt#ror /#"# r#$$r o/#r$!on#0 #0!$$r#0 o !r#$r <#!tor#0 !on fn!on#0 $06n$!5n "r#!t$ "# n$ +$tr 2?2 separe elementos con espacos o comas separe flas con p"nto  coma

 $&2,1(

+$n#:o "# o0 !o+/on#nt#0 "# n$ +$tr !on 8n"!#0 n+#r$"o0 "#0"# 1 (fla, col"mna)

 $F2, 3; ), 1; ', ; n$ +$tr 3?2  ?F; 3  $F?; ? n$ +$tr 2?2  %F), ,  !F$; % c #0 n$ +$tr $+#nt$"$ 3?2  "F$, % c #0 n$ +$tr $+#nt$"$ 2?3  ?F!&1, ( $06n# $ x $ /r+#r$ f$ "# c  ?F!& ,1( $06n# $ x $ /r+#r$ !o+n$ "# c  !&,2(F  #+n# $ 0#6n"$ !o+n$ "# c *atrices especiales  $Fones&)(  $Fones&3)(

+$tr )?) n!$"$ !on no0 +$tr 3?) n!$"$ !on no0

@

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II  $F
+$tr 4?) n!$"$ !on !#ro0 +$tr "#nt"$" )?) !$"r$"o +á6!o 4?4 +$tr "# %#rt )?) +$tr "# V$n"#r+on"# 4?4 0$n"o n <#!tor +$tr n$

+eneración de n#meros aleatorios  ?Fran 6#n#r$ n n9+#ro $#$toro #ntr# '  1  $Fran&)( 6#n#r$ n$ +$tr )?) !on n9+#ro0 $#$toro0  %Fran&4)( 6#n#r$ n$ +$tr 4?) !on n9+#ro0 $#$toro0

 "Ff?&r$n"X1'(K1

tr$n0fo+$!5n /$r$ o%t#n#r n #nt#ro $#$toro #ntr# 1  1'

,na matri- puede componerse con otras matrices

 $Fr$n"&3(  %F) 3 @  #F"$6&%(  !F##&3(  "F#ro0&3(  tF$ #; ! "

+$tr 3?3 !on n9+#ro0 $#$toro0 <#!tor "# tr#0 !o+/on#nt#0 +$tr 3?3 !on % #n $ "$6on$ +$tr "#nt"$" 3?3 +$tr !on !#ro0 3?3 +$tr !o+/#0t$ @?@

%.5 ditor de matrices En $ <#nt$n$ orkspace /#"# $!t<$r # #"tor "# $rr#6o0 0+$r $ n$ o:$ ##!tr5n!$ !on # !$ /#"# +o"f!$r !on f$!"$" $0 "+#n0on#0  # !ont#n"o "# <#!tor#0  +$tr!#0. 3lementos e vectores  matrces p"een mane?arse con otro vector o matr<

 ?F = ; @ ) ,  /F2 4 1  tFx(p)  $F4 ; 3; ) ; =; , ' @  /F1 3  7F2 3  tFa(p, q) Operaciones con matrices  $F3, 2; 1, 4  %F=, ,; ), ;  !F$

 !F2X$  !F$K%  !F$X%  !F$X%

<#!tor /$r$ "r#!!on$r $ <#!tor x t !ont#n# o0 ##+#nto0 2 4 .1 "# <#!tor x <#!tor /$r$ "r#!!on$r $0 f$0 "# $ +$tr a <#!tor /$r$ "r#!!on$r $0 !o+n$0 "# $ +$tr a t !ont#n# $0 f$0 1  3 !o+n$0 2  3 "# a

tr$n0/#0t$ "# a /ro"!to "# n #0!$$r /or +$tr 0+$ "# +$tr!#0 /ro"!to "# +$tr!#0 /ro"!to ##+#nto /or ##+#nto "# +$tr!#0 para operar elemento a elemento "se "n p"nto antes el operaor

 !F$Z2  !F$Z2  !F$$$%  !F$%$%  !F$>3

+$tr $ !$"r$"o #7<$# $ a*a caa elemento "# $ +$tr a ##<$r $ !$"r$"o !o+/$r# 6$"$" #ntr# +$tr!#0 &"# 6$ t$+$o( # r#0t$"o #0 n$ matr< bnara &!#ro0  no0( !o+/$r# 0 "o0 +$tr!#0 no 0on 6$#0 # r#0t$"o #0 n$ matr< bnara &!#ro0  no0( !o+/$r# 0 !$"$ ##+#nto "# a #0 +$or $ 3 # r#0t$"o #0 n$ matr< bnara &!#ro0  no0(

Funciones para matrices

 ?F2 ' , )

n <#!tor /$r$ o0 #:#+/o0

1'

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II  $F1 2 3; 4 ) ,;; = @ n$ +$tr /$r$ o0 #:#+/o0  nFlength &?( on6t" "# <#!tor x  n+Fs
/ro"!to /nto #ntr# "o0 <#!tor#0 r$n6o "# a tr$$ "# a "#t#r+n$nt# "# a n<#r0$ "# a nor+$ "# !o+n$ "# $ +$tr a nor+$ "# f$ "# $ +$tr a nor+$ "# f$ o !o+n$ "# <#!tor x n9+#ro "# !on"!5n "# $ +$tr a <#!tor !on $ "$6on$ "# $ +$tr a +$tr !on x #n $ "$6on$ rot# a @' 6r$"o0 &0#nt"o o/#0to $ r#o:(
%. 6 /ngreso de puntos desde la pantalla con el mouse  #/ot&Y0n&?(Y( #:#+/o /$r$ to+$r /nto0 "#0"# n 6ráf!o  6r" on  ?Fgnp"t&)( n6r#0# ) /nto0 "#0"# $ /$nt$$ . Aresone el botBn el mo"se para ngresar caa p"nto

 ?    /ot&?  YoY(

o%0#r<# $0 $%0!0$0  $0 or"#n$"$0 n6r#0$"$0 6r$f7# o0 /nto0 n6r#0$"o0

%.% Funciones adicionales para mane$o de datos con 'ectores y matrices  ?F2, ), 4; n <#!tor  $F),-1; 3, 4; 2, ;; n$ +$tr  tFmax&?( # +$or <$or "# <#!tor x 
11

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II 
0+$ "# !o+/on#nt#0 /or !o+n$0 /ro"!to #0!$$r /ro"!to #0!$$r /or !o+n$0

 tFc"ms"m&?( 
0+$ $!+$"$ 0+$ $!+$"$ /or !o+n$0 /ro"!to $!+$"o +#"$ $rt+t!$ +#"$n$ "#0<$!5n #0tán"$r or"#n$+#nto $0!#n"#nt# or"#n$+#nto "#0!#n"#nt# "$6r$+$ "# %$rr$0 0to6r$+$ "%:$ ? +#"$nt# #0!$on#0 6ráf!o t/o /$0t# /$0t# #n r##<# <#!tor /$r$ #?tr$#r 0#!tor#0 "# /$0t# 6ráf!o t/o /$0t# !on n 0#!tor 0#/$r$"o

%.0 Polinomios  $F2, -3, ', )[, "#fn# # /ono+o 2?3 J 3?2 K )  Fpolval &$4( #<$$!5n "# /ono+o !on n <$or  ?Froots &$( o%t#n6$ n <#!tor !on r$8!#0 &r#$#0  !o+/#:$0(  tFpolval&$ ?&1(( <#rf7# n$ r$8  /Fpol&?( /ro"!to "# to"$0 $0 r$8!#0  %F3, 4, -2; "#fn# # /ono+o 3?2K 4?  2  !Fconv&$%( /ro"!to "# /ono+o0  !, rFeconv &$%( "<05n "# /ono+o0  ! !o!#nt#  r r#0"o  ?F2 3 ) ; = $%0!0$0 "# /nto0 &?(  F32 41 )= ,4 ,3 or"#n$"$0 "# o0 /nto0  F32 <$or /$r$ nt#r/o$r < /#"# 0#r n <#!tor  Fnterp1&?\n#$r\( r#0t$"o "# $ nterpolacBn lneal  Fsplne&?( nt#r/o$!5n !on n tra
=. MANE>O SIMBÓLICO  sms ? "#fn!5n "# <$r$%# t/o 0+%5!o  2X?K3X? 0+$ $6#%r$!$  $F? ); 3X? 4 +$tr !on ##+#nto0 08+%oo0  tFnv&$( 0 n<#r0$ t$+%n !ont#n# 08+%oo0  tFsolve&2X?Z2K3X?2( 0o!5n "# n$ #!$!5n  fF3X?Z2K)X? "#fn!5n 0+%5!$ "# n$ fn!5n  tFfactor &f( f$!tor$r $ #?/r#05n  0Fexpan &t( #?/$n"r$  #Ftalor &#?/&?(( #?/$n05n !on $ 0#r# "# T$or  lmt&0n&?(?( o%t#n!8on "# 8+t#0 "# fn!on#0  sms 

12

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II  fF2X?Z3K3XZ2  6Fff &f?(  Fnt&f?(

n$ fn!5n "# "o0 <$r$%#0 "#r<$"$ /$r!$ nt#6r$r #n ?

0.1 Funciones adicionales con epresiones sim"ólicas  fF2XtK1 "#fn!5n "# n$ fn!5n #n for+$ t#r$  tF3  Feval&f( #<$$!5n "# $ fn!5n  $% F solve&$Z2 K $X%  % F 3,$Z2  4X%  ) F '( r#0#<# n 00t#+$ "# "o0 #!$!on#0 no n#$#0  $F"o%#&$( /$r$ #?/r#0$r$0 #n for+$ r#$  %F"o%#&%(  fFY#?/&?(/X?Y  ?F0o<#&f(  ?F"o%#&?( !$+%$ $ 0o!5n 0+%5!$ $ r#$ ?F '.))3= r#0t$"o0 "# MATLAB 1.,3=)  ?Ff
0o!5n "# n$ #!$!5n !on n <$or n!$ r#0t$"o "# MATLAB 0o!5n 0$n"o n r$n6o /$r$ $ r$ r#0t$"o "# MATLAB "f#r#n!$!5n nt#6r$!5n $n$8t!$ nt#6r$!5n #ntr# 8+t#0 nt#6r$ +/ro/$ 0o!5n $n$8t!$  6ráf!o "# n$ EDO "# /r+#r or"#n !on n$ !on"!5n #n # n!o

 Fsolve &YDF&?(?YY&'(F'YY?Y(  #/ot&'2(  6r" on EDO "# 0#6n"o or"#n !on !on"!on#0 #n # n!o  6ráf!o "# $ 0o!5n  Fsolve &YD2KDK2X?3F'YY&'(F'D&'(F1YY?Y(  #/ot&'2(  6r" on EDO "# 0#6n"o or"#n !on !on"!on#0 #n o0 %or"#0  Fsolve &YD2DK2X)X?3F'YY&'(F'&1(F2YY?Y(  #/ot&'2(  6r" on  fF\2X0n&?(X#?/&?(\  ?Ffmnbn &f22(  #/ot&f22(

#n!#ntr$ n +8n+o o!$ "# f #n 1

x

E

0.2 Funciones especiales para medir eiciencia de algoritmos  tc In!$ !ron5+#tro  toc +#0tr$ # t#+/o tr$n0!rr"o

13

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II  tc; $Fnv&ran&)'' )''((; toc t#+/o t$"o #n n<#rtr n$ +$tr )''?)''

@. GRA*ICACIÓN .1 +ráico de unciones de una 'aria"le  fF#?/&?(3X? fn!5n /$r$ # #:#+/o &0# !o+$0 0+/#0(  e
fn!5n %á0!$ /$r$ 6r$f!$r f #n 2π 2π

 e
fn!5n %á0!$ /$r$ 6r$f!$r f #n n "o+no "$"o

 gr on

!oo!$r !$"r8!$0 #n # "%:o

 ?F' '1 2X/

/nto0 /$r$ #<$$r $6n$ fn!5n

 F0n&?(

/nto0 "# $ fn!5n 0#no

 plot&?(

fn!5n /$r$ 6r$f!$r $ fn!5n !on 8n#$ !ont8n$

 /ot&?YoY(

6ráf!o !on /nto0. -#"# ##6r o  * + x --

 /ot&?YrY(

!$+%$r $ !oor ro:o. -#"# ##6r r,b,,m,g,,k

 /ot&?Yo6Y(

6r$f7# !on !8r!o0 <#r"#0.

 gr on

!oo!$r !$"r8!$0 #n # "%:o

 ttle&Y0#no "# ?Y(

n!$ n t8to #n # 6ráf!o

 gtext&Y0#no "# ?Y(

/o0!on# # t#?to #n # 6ráf!o !on # +o0#

 xlabel &YY(

rot# # #:# oront$

 label &YY(

rot# # #:# <#rt!$

 !F', 2X/, 2, 2

"#fn$ $ r#65n /$r$ # 6ráf!o

 axs&!(  hol on

0/#r/on#r 06#nt#0 6ráf!o0

 hol off

"#0$%t$r o/!5n $nt#ror

 clf

%orr$r # 6ráf!o

 fg"re&1( /#"# t#n#r <$r$0 f6r$0 $%#rt$0 !$"$ n$ #n n$ <#nt$n$ rot$"$ !on 1 2 ...  s"bplot &231( /#"# "<"r n$ f6r$ #n 0%6ráf!o0. E:. #n 2 f$0  3 !o+n$0. A!t<$n"o # 6ráf!o 1  clf(1)

%orr$ # 6ráf!o 1

 clf

%orr# to"o0 o0 6ráf!o0

 ?F''11'[;  F#?/&?(  semlogx &?(

6r$f!$r #n #0!$$0 o6$r8t+!$0

 semlog&?(  loglog&?(

"o%# o6$r8t+!$

14

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II  6r" on  $F''.'12X/  rF0n&3X$(

Yro0$Y "# 3 /t$o0

 polar &$ r(

6r$f7# #n !oor"#n$"$0 /o$r#0

.2 +ráico de unciones impl!citas y ecuaciones con dos 'aria"les  fFY&?2(Z2K&3(Z2)Y  #/ot&f(

Gr$f!$r $ !r!nf#r#n!$ (x - 2)2 + ( - C)2 $  #n # "o+no 2π≤?≤2π 2π≤≤2π

 #/ot&f1)',(

Gr$f!$r f #n # "o+no 1≤?≤) '≤≤,

 6r" on

Coo!$r !$"r8!$0

 o" on

S/#r/on#r # 06#nt# 6ráf!o

 6F\2X&?3(Z23\

n$ /$rá%o$ $2(x-C) 2-C #n # +0+o "o+no

 #/ot&61)',(

.3 +ráico de unciones deinidas en orma paramétrica  #/ot&Y0n&t(YY!o0&t(Y//( Gr$f!$r x$x(t), $(t) #n  #/ot&Y0n&3Xt(X!o0&t(YY0n&3Xt(X0n&t(Y'/(

t

Un$ ro0$ "# 3 /t$o0

1'. EDITOR DE GRÁ*ICOS D#0/0 7# # 6ráf!o $ 0"o r#$$"o 0# /#"# t$r $0 f$!"$"#0 "# #"tor "# 6ráf!o0 /$r$ !$+%$r $0 /ro/#"$"#0 "# $0 f6r$0 !oor t/o #t!. T$+%n 0# /#"# r#$$r #0t$"80t!$0 %á0!$0  $:0t# "# !r<$0. A"!on$+#nt# 0# /#"# n0#rt$r "r#!t$+#nt# #n # 6ráf!o t#?to 8n#$0 f#!$0 r5to0 #t!. -$r$ $%t$r # #"tor "# 6ráf!o0 0# "#%# 0##!!on$r # %ot5n tools #n $ %$rr$ "# o/!on#0 "# 6ráf!o  #6o #:$ et plot. -$r$ r#$$r #0t$"80t!$0 %á0!$0  $:0t# "# !r<$0 ##6r r#0/#!t<$+#nt# Fata Gtatstcs  8asc Httng

1.1 +ráico de unciones de dos 'aria"les  $F1 3 2; ) 3 ;; 4 ) 2; n$ +$tr 3?3  mesh($( 6r$f!$r o0 ##+#nto0 !o+o /nto0 0o%r# # /$no. E 06#nt# #:#+/o #0 n$ r#f#r#n!$ /$r$ 6r$f!$r fn!on#0 "# "o0 <$r$%#0 Gr$f!$r < $ x2 I 2, -2 x 2, -C  C "o+no "# $ fn!5n /$r$ # #:#+/o

 ?F2'12;  F3'13;  <Fmeshgr &?(  < +$tr!#0 7Y !ont#n#n !$"$ /$r or"#n$"o ?  FZ2 J <Z2 /nto0 "# $ fn!5n  F ?2 J 2  mesh&?  ( 6ráf!o "# +$$  conto"r &?  ( 6ráf!o "# !ontorno  s"rfc&?  ( 6ráf!o "# 0/#rf!#  !ontorno  s"rf &?  ( 6ráf!o "# 0/#rf!#  xlabel &YY( rot$!5n "# #:# x t$+%n !on label,
1)

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II 5conalmente se p"ee "sar las opcones el etor e grLfcos para etar la fg"ra, rotar, cambar la perspectva, nsertar t9t"los, etc

1.2 /nsertar el gráico en un documento S "#0#$ n0#rt$r # 6ráf!o #$%or$"o !on 456758 #n n "o!+#nto 0$+#nt# #0!rto #n MNOF /#"# 0#6r # 06#nt# /ro!#"+#nto E:$ #n $ %$rr$ "# o/!on#0 "# 6ráf!o # %ot5n Hle  #6o $ o/!5n 3xport E:$ n$ !$r/#t$ /$r$ $+$!#n$r # 6ráf!o  n no+%r# /$r$ # 6ráf!o. G$r"# # 6ráf!o !on t/o . ?pg Co/# # 6ráf!o $+$!#n$"o  /6#o #n # "o!+#nto #n # 6$r ##6"o.

11. -ROGRAMACIÓN CON MATLAB 11.1 &rci'os de comandos -$r$ !r#$r n $r!
G$r"# # $r!> pr"eba

-$r$ #"t$r n $r!
11.2 structuras de control de lu$o en *&7&8 nstr"ccones e 3ntraa  Gala

In6r#0o "# n "$to "#0"# # t#!$"o E:.

<$r$%#Fn/t&]+#n0$:#\(

x $ np"t(ngrese "n ato );

S$"$ "# n r#0t$"o $ $ /$nt$$ E:.

"0/&<$or(

x$exp(2); sp(x);

S$"$ "# +$0 "# n r#0t$"o $ /$nt$$ E:.

"0/&<$or <$or ^(

x$2!Q; $sqrt(p); sk(=x, );

S$"$ "# r#0t$"o0 for+$t#$"o0 $ /$nt$$ E:.

f/rntf&]for+$to0\<$r$%#0(

1,

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II x$2!Q; $sqrt(p); fprntf(P PfR,x,);

-#"# #0/#!f!$r !$nt"$" "# !o+n$0  " #!+$#0 E:. x$2!Q; $sqrt(p); fprntf(P PCfR,x,);

Otr$0 #0/#!f!$!on#0 "# for+$to /#"# <#r$0 !on help fprntf

11.3 9ecisiones :instrucción i; i condición instrucciones en

i condición instrucciones else

n0tr!!on#0 en

E:. E0!r%$  $+$!#n# # 06#nt# /ro6r$+$ /$r$ +o0tr$r # +$or #ntr# "o0 "$to0 a$np"t(ngrese el prmer ato ); b$np"t(ngrese el seg"no ato ); f a>b m$a; else m$b; en sp(m); Gár"#o !on # no+%r# pr"eba  90#o "#0"# $ <#nt$n$ "# !o+$n"o0 >> pr"eba

n6r#0# # /r+#r "$to ) n6r#0# # 0#6n"o "$to = =

nt#r$!!5n !on MATLAB

9ecisiones m#ltiples :instrucción s
E:. E0!r%$ # 06#nt# /ro6r$+$ /$r$ n0tr+#nt$r $ "#fn!5n ? =1  3C  2? + 1C ? = 2C3C4  #?C otro ? 

F x$np"t(ato ); stch x case 1, $C; case S2,C,ET, $2*x+1; otherse $exp(x); en sp();

A+$!n#o !on $69n no+%r#. E:#+/o pr"eba2 -$r$ 0$ro #0!r%$ #n $ <#nt$n$ "# !o+$n"o0 >> pr"eba2 OepetcBn conconaa al nco (nstr"ccBn hle)

1;

UNIVERSIDAD ANDINA DEL CUSCO INGENIERÍA CIVIL CALCULO II hle !on"!5n


E:. S+# o0 n /r+#ro0 tr+no0 "# $ 0#r# $r+5n!$ n$np"t(canta e termnos ); s$0; hle n>0 s$s+1/n; n$n-1; en sp(s);

A+$!n#o !on $69n no+%r#. E:#+/o pr"ebaC -$r$ 0$ro #0!r%$ #n $ <#nt$n$ "# !o+$n"o0 >> pr"ebaC OepetcBn conconaa a "na sec"enca (nstr"ccBn for ) for <$r$%#Fn!o n!r#+#nto fn$


E:. S+# o0 n /r+#ro0 tr+no0 "# $ 0#r# $r+5n!$ n$np"t(canta e termnos ); s$0; for $1n s$s+1/; en sp(s);

A+$!n#o !on $69n no+%r#. E:#+/o pr"ebaE -$r$ 0$ro #0!r%$ #n $ <#nt$n$ "# !o+$n"o0 >> pr"ebaE A"ee nterr"mpr "na repetcBn (nstr"ccBn break)

E:. L#$ n "$to0. C$!#  +#0tr# $ r$8 !$"r$"$. -#ro 0 #ntr$ n <$or n#6$t
-$r$ <#r $ "#0!r/!5n "# $0 #0tr!tr$0 "# #n6$:# "# MATLAB #0!r%$ >> help lang

12. EN GENERAL LAS *UNCIONES EN MATLAB En 6#n#r$ n$ fn!5n #n o0 #n6$:#0 "# /ro6r$+$!5n #0 n !on:nto "# n0tr!!on#0 7# 0# #0!r%#n 0#/$r$"$+#nt# "# /ro6r$+$  7# r#$$n $6n$ t$r#$ #0/#!f!$"$. Lo0 0$ro0 /#"#n "#fnr fn!on#0  $6r#6$r$0 $ $0 fn!on#0 /ro/$0 "# MATLAB. E +#!$n0+o 0$ /$r$ tr$0+tr "$to0 $ $0 fn!on#0 #0 +#"$nt# n$ 0t$ "# <$r$%#0 7# 0# "#no+n$n /$rá+#tro0. Sn #+%$r6o $ "f#r#n!$ "# o0 /ro6r$+$0 $0 <$r$%#0 7# 0# 0$n "#ntro "# n$ fn!5n no #0tán "0/on%#0 f#r$ "# #$ $ +#no0 7# 0# 0# n$ "#!$r$!5n #?/8!t$  7# 0# <#rá +$0 $"#$nt#. FeclaracBn e "na f"ncBn en 456758 f"ncton varable $ nombre (parLmetros)

1=


nstr"ccones varable !ont#n"rá # r#0t$"o 7# #ntr#6$ $ fn!5n 0on <$r$%# 7# r#!%#n o0 "$to0 7# #ntr$n $ $ fn!5n parLmetros "#ntf!$ $ $ fn!5n nombre nstr"ccones 0# n!#n #n $ fn!5n 0#69n $ t$r#$ #0/#!f!$"$

L$0 fn!on#0 0# #0!r%#n #n $ <#nt$n$ "# #"!5n "# M$t$%  0# $0 $+$!#n$ #n $6n$ !$r/#t$. E0 !on<#n#nt# 7# # no+%r# $06n$"o 0#$ 6$ $ no+%r# 0$"o #n $ "#!$r$!5n "# $ fn!5n. E 0o "# n$ fn!5n #0 0+$r $ 0o "# $0 fn!on#0 !o+n#0 "# MATLAB. E no+%r# "#%# !on!"r !on # no+%r# $06n$"o $n7# o0 /$rá+#tro0 /#"#n t#n#r no+%r#0 "f#r#nt#0 /#ro 0 0o "#%# 0#r !o#r#nt#. E:. E0!r%$ n$ fn!5n /$r$ ##6r # +$or #ntr# "o0 n9+#ro0 A%r$ n "o!+#nto n#b m $ a; else m $ b; en

#0 $ <$r$%# 7# #ntr#6$ # r#0t$"o m maor #0 # no+%r# "# $ fn!5n a, b 0on o0 /$rá+#tro0 7# n6r#0$n o0 "$to0 $ $ fn!5n

13. INTERACCIÓN CON OTROS ENTORNOS 13.1 /nteracción con =(7 1) mportar "na tabla e atos ese 3xcel a "na matr< en 456758

$( En 3xcel !r## $ t$%$  $+$!n#$ !on for+$to t/o t#?to "#+t$"o !on t$%$!on#0. E:$ $69n no+%r#. E:#+/o 6txt %( En 456758 !$r6# $ t$%$ 6  90#$ !o+o n$ +$tr >> loa 6txt; >> 5$6 2) 3xportar "na matr< e atos ese 456758 a "na tabla en 3xcel

$( En 456758 !r## n$ +$tr  $+$!n#$ !on # !o+$n"o save !on # 06#nt# for+$to. E:$ o0 no+%r#0. E:#+/o 5 no+%r# "# $ +$tr #n MATLAB 6 no+%r# /$r$ $ t$%$ $+$!#n$"$ >> save 6 5 -asc

%( En 3xcel $%r$ # $r!
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14. CONCLUSIONES c

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c

En !on!05n <#+o0 7# MATLAB #0 n$ /ot#nt# #rr$+#nt$ 7# "0/on#+o0 /$r$ r#$$r !á!o0 #n # $+%#nt# "# n6#n#r8$  otr$0 #0/#!$"$"#0 !on!$/$!"$"#0 7# 6r$"$+#nt# /o"#+o0 r n!#n"o $ n#0tro0 !ono!+#nto0  $/!$!on#0 "# 7# $!#r $%or$ # nt##!t$. G#n#r$+#nt# # #0t"$nt# o In6#n#ro 7# tr$%$:$ #n /ro!#0o0 !o!$ !on $ "f!t$" "# o0 !o+/#:o0 !á!o0 +$t#+át!o0 7# $ 7# "#0$rro$r /$r$ r#0o<#ro0 /ro%#+$0 7# 0# 6#n#r$n #n 0 ár#$ "# tr$%$:o. En!ontr$r $ 0o!5n $ #0to0 /ro%#+$0 +!$0 <#!#0 0# torn$ #n6orro0o  0# !orr# # r#06o "# 7# # +á0 +8n+o #rror 7# 0# !o+#t$ #n o0 /ro!#"+#nto0 no /#r+t$n #n!ontr$r n$ r#0/#0t$ o #0t$ 0#$ #rr5n#$. Gr$!$0 $ $0 f$!"$"#0 "# MATLAB 0# /#"# #0t$r 0#6ro 0o%r# $$r $ r#0/#0t$ !orr#!t$ !on +#no0 #0f#ro0  $"#+á0 0# t#n# n $orro "# t#+/o !on0"#r$%#. o #n "8$ MATLAB #0 n /ro6r$+$ + /ot#nt# !on n #ntorno $6r$"$%# 7# n!# #rr$+#nt$0 "# !á!o !#nt8f!o  t!n!o  "# <0$$!5n 6ráf!$ $08 !o+o n #n6$:# "# /ro6r$+$!5n "# $to n<# 7# no0 /#r+t# r !o+o 0#+/r# 6r$"$+#nt# n!r#+#nt$n"o $0 !$/$!"$"#0 "# $0 /o0%#0 $/!$!on#0 7# 0# /#"$n r#$$r. MATLAB #0 n$ #rr$+#nt$ "# !5+/to or#nt$"$ /$r$ r#$$r !á!o0 0o%r# +$tr!#0. C#nt$ !on n$ 6r$n !$nt"$" "# too%o?#0 /$r$ $ná00  /ro!#0$+#nto "# "$to0. A"#+á0 !#nt$ !on n$ 6r$n !$nt"$" "# #rr$+#nt$0 /$r$ 6r$f!$r fn!on#0 "#"o0  tr#0 "+#n0on#0 $0 !$#0 #0tán nt#6r$"$0 "#ntro "# MATLAB. T$+%n /ro/or!on$ n $+%#nt# "# /ro6r$+$!5n # !$ /#"# 0#r $+/$"o /or # 0$ro "#0$rro$n"o 00 /ro/o0 $r!
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1). BIBLIOGRA*ÍA -r# L5/# C0$r. &2''2(. MATLAB  00 $/!$!on#0 #n $0 !#n!$0  $ n6#n#r8$.-r#nt!# $. 0 >o0 M$ro -!o _0/#. &2'14(. G8$ $!$"+!$ "# +to"o0 n+r!o0. Un<#r0"$" N$!on$ S$n Antono A%$" "# C0!o. 0 U0n6 M$t$% V#r0on , Co+/t$ton V0$$ton -ro6r$++n6 T# M$t PorQ0 In!. 0

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MATLAB informe

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