Programa

Tuesday, June 21, 2022

8:11 PM

 

<<Cronograma_CNiNo.pdf>>

 

 

Clases

domingo, 9 de marzo de 2025

00:57

 

C1 - EDO 1er Orden

Wednesday, June 8, 2022

6:47 PM

 

 

 

 

<<CN01a EDO de 1er Orden - PVI Euler - 2021.pptx>>

 

 

C1 - Runge Kutta Gi

Wednesday, June 8, 2022

6:48 PM

 

<<Runge Kutta Gi.ppt.pptx>>

 

 

 

C2 - Sistemas EDO de 1er Orden

Wednesday, June 22, 2022

3:19 PM

 

<<CN02a EDO de 1er Orden - Sistemas  8_06.pptx>>

 

 

 

C2 - Stock y Flujo

Wednesday, June 22, 2022

3:20 PM

 

<<CN02b Stock y Flujo clase 08_6.pptx>>

 

 

 

C3 - EDO Superior

Tuesday, June 21, 2022

8:16 PM

 

<<CN03 EDO de Orden Superior 15_6.ppt>>

 

C4 - EDO No lineales

Tuesday, June 21, 2022

8:22 PM

 

<<CN04 Ecuaciones No Lineales Gi.ppt>>

 

 

TPs

domingo, 9 de marzo de 2025

00:57

 

TP1

Wednesday, June 8, 2022

6:48 PM

 

<<CN TP 1 2021.pdf>>

 

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práctia 1 
C"ulo 
b) Considerando k —1/2, —25% discretizar el problerna por el métodode en el intervalo 
Con paso h a elección. utilizando Octave, representar en un gráfico la solución exacta 
y la aproximada. 
En el intervalo I (O, II se define la ecuación diferencial de primer orden 
Calcular, mediante el método de un valor aproximado de sabiendo que VIO) 
2 V considerando Ink Drawings
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TP2

Tuesday, June 21, 2022

8:23 PM

 

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TP3

Tuesday, June 21, 2022

8:22 PM

 

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Entrega II

Wednesday, June 22, 2022

4:35 PM

 

<<Entrega II.pdf>>

 

C"ulo 
Considere el siguiente esquema de Stock flujo: 
K, 
en el cual todos los flujos son proporcionales a los correspondientes stocks. 
a) plantee el que representa la evolución de Sistema enel tiempo. 
b) Discretice el sistema usando Euler, 
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Entrega III

Wednesday, June 22, 2022

5:03 PM

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Exámen

domingo, 9 de marzo de 2025

00:58

 

Para el parcial

Wednesday, June 22, 2022

7:34 PM

 

 

Rk no entra

 

Una de Euler

Una de stock y flujo

Una No lineal cambio de variable

Una teorica de ultimo tema

 

Parcial Simulacro

Wednesday, June 22, 2022

7:40 PM

Indicar cuál de los siguientes problemas de valores iniciales está bien planteado 
—y + sen(2ty), y'(l) ¯ 
ty + In(y+l), y(0) 
=2t-5y,

 

La siguiente expresión se obtuvo luego de aplicar el método de Euler a cierta ecuación 
diferencial. ¿Cuál 
es dicha ecuación? 
Yk+l = 
' -tA3-4yt 
-tA3 + 4ty=o 
-tA3 + 4t=o 
Yk + tk? ¯ 4Yktk)

 

Si al aplicar el método de Euler se obtiene y_k ¿Es cierto que las iteraciones siguientes son 
odas iguales a cero? Justificar

 

Explicar cuáles son las condiciones que tiene que cumplir una función f para que el método de 
Bolzano 
encuentre, aproximadamente, un cero de f en un intervalo [a, b]

Para que se pueda utilizar el metodo de Bolzano en el intervalo [a,b], una funcion debe ser continua en (a,b) y debe tener al menos dos puntos de signo opuestos.

 

Como se muestra en la figura, la función f tiene tres puntos fijos (A, C y D). 
¿Cuáles de ellos son posibles aproximar mediante la iteración de punto fijo y por qué?

Se puede en A y D porque su derivada es menor a 1. El crecimiento es lento, entonces se estabiliza la aproximacion.

 

2t3 _ 
Dada la siguiente ecuación diferencial de segundo orden definida en 2]se pide: 
a) Plantearla como un sistema de EDO de orden uno. 
b) Discretizar mediante el método de Euler 
c)Calcular un valor aproximado de considerando h (Non-enonymous question@) *

 

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Dado el siguiente diagrama de stock y flujo con X(O) =xO, 
a)Plantear el sistema de ecuaciones diferenciales representado en el diagrama 
b) Discretizar mediante el método de Euler (Non-enonymous question@) 
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Resumen Parcial

Tuesday, June 28, 2022

4:58 PM

 

Euler

y(to) = Yo

 

Yk+l 
k-1.2, „„M ı 
y(to) Yo

 

Sistema de ecuaciones

con { 
x(to) 
y(to) 
en el intervalo 
[to,tF]

 

Yk+l = Yk + 
x(to) = Xo, y (to) = Yo

 

Diagramas de stock y flujo

.4' = k1A + - k2A = (k1 -К2)А + 
В' = ,k2A - (k4 
+ Кз)в 
,4k+1 = Ак + h. ((k1 - К2)Ак + КИК) 
(К4 Кз)Вк)

 

Orden Superior

Yn-l 
y' 
en el intervalo [to,tF] 
• • Yn—l ) 
Yn-l ) Yo 
Yl (to) Yo 
y(to) 
= Yo 
en to

 

No lineal

 

PROBLEMAS A RESOLVER 
Nos referiremos a tres tipos de problemas: 
Se trata de 'Hallar x tales que _ 
2. 
[puntos de intersección] 
[localización de raíces] 
[puntos fijos] 
_ 0 g(x)"

 

Cualquiera de los 3 problemas se puede convertir en uno de los otros

 

Teorema de Bolzano 
Sea f una función continua en un intervalo [a, b] 
tal que f(a)f(b)< O. Entonces existe c e (a, b) tal 
quef(c )

 

Teorema de Newton-Ra hson 
Supongamos que Sp [a, b] tal que f (p) 0 
y que además f y f'(p) 
Entonces existe una distancia > O tal que la sucesión 
f(Pk-l ) 
g(Pk-1) converge 
generada por Pk = Pk-l ¯ 
f' (Pk-l) 
ap cualquiera sea la semilla po e 
Observación: La función 
se llama 
función de iteración de ewton- ap son.

 

Puntos fiios 
Definición: Un 
punto fijo de una función g(x) es un 
número real P tal que P=g(P). 
Definición: La iteración 
para . 
llama iteración de punto fijo 
se 
Teorema: Sean la función continua gy una sucesión 
generada por iteración de punto fijo. Si 
limk.Ak=P, entonces P es un punto fijo de g(x).