proyecto final calculo ii electronica

8/16/2019 Proyecto Final Calculo II Electronica

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UNIVERSIDAD TÉCNICA DE AMBATOFACULTAD DE INGENIERÍA EN SISTEMAS, ELECTRÓNICA E INDUSTRIAL

PERÍODO ACADÉMICO: OCTUBRE 2015 – MARZO 2016

UNIVERSIDAD TÉCNICA DE AMBATO

Facultad de Ingeniería en Sistemas Electr!nica e Industrial

"r#$ect# de %r#&lemati'aci!n $Res#luci!n de %r#&lemas

Títul#: APLICACIONES DE LA INTEGRAL SIMPLE, MÚLTIPLE YECUACIONES DIFERENCIALES A LA INGENIERÍA EN ELECTRÓNICA YCOMUNICACIONES, INGENIERÍA INDUSTRIAL EN PROCESOS DE

AUTOMATIZACIÓN E INGENIERÍA EN SISTEMAS COMPUTACIONALES EINFORMATICOS MEDIANTE USO DE SOFTWARE.

Carrera: ELECTRÓNICA Y COMUNICACIONES(rea Acad)mica: CIENCIAS BÁSICAS*ínea de In+estigaci!n: CIENCIAS BÁSICAS

Cicl# Acad)mic# $ %aralel#: Octu!" #$%& ' M(!)* #$%+ Tercer# ,A-

Alumn#s %artici%antes:

• L"(-* S/0( E1*- P(u/• Su2" P(/(t" C3!t(- W/(14!

• B((-t" Ru) Lu15-6 R"-"

M!dul# $ D#cente: Calculo II Ing. Washington Medina

I. INFORME DE* "RO/ECTO

0.0Títul#: APLICACIONES DE LA INTEGRAL SIMPLE, MÚLTIPLE YECUACIONES DIFERENCIALES A LA INGENIERÍA EN ELECTRÓNICA Y

COMUNICACIONES, INGENIERÍA INDUSTRIAL EN PROCESOS DE AUTOMATIZACIÓN E INGENIERÍA EN SISTEMAS COMPUTACIONALESE INFORMATICOS MEDIANTE USO DE SOFTWARE

0.1O&2eti+#s

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sen( x)

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f ( t )=cos( t )

t <g (t )=

sen(t )t "- "/ -t"!0(/*.

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COMANDOS DE MA"*ECOMANDOS B(SICOS "ARA ARITMÉTICA / A*


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(-4(t"F8,t, 8(.., t c..1, =!(4" -

COMANDOS RE*ACIONADOS CON *IMITES DE SUCESIONES

"9(-, - (.. uc";- 1" -4"!* (- 2(!( - 1" ( 3(t( /4t(-, - -=-t


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!"4 !"t*!-( "/ !"t* 1"/ -u4"!(1*! 1011* 2*! "/ 1"-*4-(1*!

COMANDOS "ARA INTE!4-* 1" variable.

J @15 sin1G:

D"!0(-1* u-( 0"),J di@@@1GG:

D"!0(-1* X 0"c",J di@@@1GG:

CA*CU*ANDO INTE


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J IntlnGG: H C#n I maiscula

J intlnGG: H C#n i minscula

J Int0J sKrt0L1GG: H C#n i minscula

J F5sinL1Gc#sG:

@5di@@FG: int@G:e%andG:

Definidas:

Cu(-1* -t"!2!"t(4* /( -t"6!(/ c*4* "/ !"( (7* /( cu!0( 1" u-( =u-c;- "-u- -t"!0(/* @(, "-t*-c" -"c"t(4* c(/cu/(! /( -t"6!(- 1"=-1(.O!1"-........: -tS-t(8......: -t "82!";-, 0(!(/"(...P!*2;t*...: C(/cu/(! /( -t"6!(- 1"=-1( 1" /( expresión "- t>!4-* 1" /(variable, 9u" 0(!?( 1"1" a 3(t( b.

J restart:@5: [email protected]:

∫0

2

xdx

ECUACIONES DIFERENCIALES


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U-( "cu(c;- 1="!"-c(/ " 1" /( =*!4(...:Orden ........: 1*/0"

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L( "cu(c;-:dy

dx =a CITATION M"-%+ d/ X$e# @%

E u-( "cu(c;- 1="!"-c(/ 9u" 2*1"4* "c!! dyadx < */uc*-(!/( 2(!( <-t"6!(-1*, " 1"c!:

∫ ydx=∫ adx

O>!0"/* (3*!(, "c!t* ( 4(-"!( 1" /( */uc;- 1" u-( Ecu(c;- D="!"-c(/,2(!( u- 0(/*! -c(/ 1" y!"# v .J ecuaci#n5D$GtGa:ds#l+eecuaci#n$tGG:ds#l+eecuaci#n$G+P$tGG:

J ec5di@@$tGtQ1Gg: c#nd5$G3D$GG6:ds#l+eec$tGG: ds#l+eecc#ndP$tGG:

COMO INSERTAR FUNCIONES EN MA"*E

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• I-6!"(4* ( -u"t!* *=t5(!", "- "t" c(* 4(2/".


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• U-( 0") 9u" -* "t"4* tu(1* "- /( 0"-t(-( 2!-c2(/ 1" 4(2/""-c*-t!(!"4* 0(!( *2c*-" 2(!( t!((7(!, ( c*-t-u(c;-

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• E-c*-t!(4* t(4>- /( 2"t(( 1" ?4*/* c*4u-".


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• T(4>- "-c*-t!(4* /( 2"t(( 1" 4(t!c" 9u" 2"!4t! c(/cu/(! u-(4(t!) 1"/ "/ -4"!* 1" =/( < c*/u4-( 9u" 1"""4*.

• E- =- "-c*-t!(!"4* 4uc3( 4 *2c*-" 2(!( 1="!"-t" c/cu/*,2"!* "t( *- /( 4 42*!t(-t" "- /* 9u" c*!!"2*-1" ( c(/cu/*0"ct*!(/ " -t"6!(/, ( c*-t-u(c;- !"*/0"!"4* "7"!cc* 2(* ( 2(*2(!( ! -*t(-1* /( =*!4( 1" c(/cu/(! "- 4(2/".

DESARRO**O DE E9ERCICIOS MEDIANTE E* SOFTARE MA"*E

E9ERCICIOS SOBRE *=MITES "ASO A "ASO5

Calcular l#s siguientes límites5

0.

( C*4* 2!4"! 2(* -"!t(4* /( "cu(c;- "- /( 0"-t(-( 1" 4(2/".


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U-( 0") 9u" 3(


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• Lu"6* "- /( (!!( 1" 3"!!(4"-t( "/"cc*-(4* /( *2c;- (


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• Lu"6* "- /( 6u"-t" 0"-t(-( c*2(!"4* -u"t!( =u-c;- <

c*/*c(!"4* -u"t!* /?4t", c/c "- -c(!, < "- /( *2c;- 9u" 1c" 2(*( 2(* 1(!"4* c/c < -* !( 1"2/"6(-1* c(1( 2!*c"* 9u" 9u" "/*=t5(!" 4(2/" 6u" 2(!( //"6(! (/ !"u/t(1*, "t* t(4>- "!0! 2(!(-**t!* "-t"-1"! c*4* =u" !"u"/t* "/ "7"!cc*.

• D" "t( 4(-"!( " 1"2/"6(!( t*1* "/ 2!*c"*, "/ cu(/ 2*1!"4* c*2(!( 1*-1" 1"""4*.

• F-(/4"-t" c*2(!"4* "/ 2!*c"* !"(/)(1* 2*! "/ *=t5(!" M(2/" 2(!(

1"2/"6(! "/ !"u/t(1*.


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E9ERCICIO SOBRE DERIVADAS

Calcular la siguiente deri+ada

0.

• Para ver el proceso de resolución seguimos los mismos pasos anteriores con la

única diferencia que esta vez seleccionaremos la opción derivación.

• Finalmente copiamos el proceso para llegar al resultado.


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EJERCICIOS SOBRE INTEGRALES

Calcular la siguiente integral simple

0.

• Para ver el proceso de resolución seguimos los mismos pasos anteriores con la

única diferencia que esta vez seleccionaremos la opción integración.


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• Finalmente copiamos el proceso para llegar al resultado.

EJERCICIOS DE INTEGRALES MÚLTIPLES

Calcular la siguiente integral triple

!"

•

Para lo cual seguimos los mismos pasos anteriores de la integral simple.


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EJERCICIOS SOBRE SOLIDOS DE RE#OL$CI%N

Para realizar este tipo ejercicios en la opción herramientas escogemos tutoriales,

calculo en una variable y volumen de revolución en lo cual nos aparecerá una

ventana en donde nos dará un espacio para colocar la función.

EJERCICIOS DE #OLÚMENES DE SOLIDOS

alcular el volumen del solido de la siguiente función

!." y= x2

#$%$%'

• (ngresamos la función en la ventana anteriormente mostrada


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• )e lo cual podremos ver el proceso y su respectivo grafico.

EJERCICIOS DE EC$ACIONES DI&ERENCIALES

alcular la siguiente ecuación diferencial

!."


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• Para resolver este tipo de ecuaciones utilizaremos los comandos previamente

dados en la parte teórica, para generar la función será el siguiente código.

>

• * finalmente para obtener el resultado será el siguiente comando

>

'."


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