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Cell["\<\
TEMA 3:
Introducci\[OAcute]n a las listas y tablas\
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Cell["  Definici\[OAcute]n de Listas", "Section 1",
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 "Una lista de n elementos es un objeto de ",
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 " de la forma:\n{elem.1, elem.2, .....,elem.n}\nLos elementos de la lista \
van siempre entre llaves y separados por comas. \nLas listas se pueden crear \
de muchas formas, por ejemplo introduciendo los elementos uno a uno, \
importandolos de otros programas, o bien cre\[AAcute]ndola con los comandos \
Table o Array. Sea f una funci\[OAcute]n dada y n un n\[UAcute]mero, el \
comando:\n\tTable[f[i],{i,n}]\ncrea la lista:\n\t{f[1], f[2],...f[n]}\nEl \
comando :\n\tArray[f, n]\ntambi\[EAcute]n crea la misma lista.\n\
Adem\[AAcute]s el comando :\n\tRange[n]\ngenera la lista:\n\t{1,2,...,n}."
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Cell["\<\
Ejemplo 1
Generar de varias formas distintas la lista:{1,2,3,4,5,6,7,8,9,10}.\
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mediante la ley : ",
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x=1/2.\nc) Evaluar cada polinomio para x=0,0.2,0.4,...,1. Presentar el \
resultado utilizando el comando TableForm.\nd) Representar \
gr\[AAcute]ficamente los polinomios  en el intervalo [-1,1]"
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Cell[CellGroupData[{

Cell["  Operaciones con Listas", "Section 1"],

Cell[TextData[{
 "Para seleccionar o extraer elementos de una lista se utiliza el doble \
corchete o el comando Part. As\[IAcute] ",
 StyleBox["lista[[2]]",
  FontWeight->"Bold"],
 " o ",
 StyleBox["Part[lista,2]",
  FontWeight->"Bold"],
 " dan como resultado el segundo elemento de la lista. ",
 StyleBox["First[lista]",
  FontWeight->"Bold"],
 " o ",
 StyleBox["Last[lista]",
  FontWeight->"Bold"],
 " dan el primero o \[UAcute]ltimo elemento de la lista. El comando ",
 StyleBox["Length",
  FontWeight->"Bold"],
 " da el n\[UAcute]mero de elementos de la lista. Hay muchos m\[AAcute]s \
comandos que operan sobre listas. Consultar la Ayuda relativa a los comandos ",
 StyleBox["Take, Drop, Extract, Append, Flatten, Join...\n\n",
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 "Cuando la lista tiene muchos elementos y no se quiere tener  la salida en \
pantalla se coloca al final un ;. Para obtener una salida abreviada se puede \
utilizar el comando Short. Por ejemplo podemos definir una lista, valsen, con \
los valores de sin(x) con x variando desde 1 a 1000, sin obtener su salida en \
pantalla. "
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Para obtener una salida de menos de una linea o una salida con un \
n\[UAcute]mero determinado de t\[EAcute]rminos,\
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 "\ntiene siete ra\[IAcute]ces reales en el intervalo -0.5, 1.5 que se \
calculan de la siguiente manera:\n",
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 "\nLa lista que se presenta a continuaci\[OAcute]n almacena las siete raices \
de dicho polinomio\n\nraices={-0.478944, -0.121534, -0.0203346, 0.5, 1.02033, \
1.12153, 1.47894}\na) Determinar el n\[UAcute]mero de elementos de la lista.\n\
b) Extraer el tercer y quinto elemento.\nc) Extraer una nueva lista formada \
por los tres primeros elementos de raices. Otra por los elementos de cuarto y \
sexto y otra por los dos \[UAcute]ltimos elementos de raices. (Utilizar el \
comando Take)\nd) Determinar la posici\[OAcute]n del elemento -0.0203346 , \
utilizando el comando Position. "
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Cell["\<\
Representaci\[OAcute]n gr\[AAcute]fica de listas de puntos y listas de \
funciones\
\>", "Section 1",
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Cell[TextData[{
 "El comando ListPlot permite representar los puntos de una lista. Por \
ejemplo, para representar gr\[AAcute]ficamente el conjunto de ptos: (x,senx), \
para x=1,2,..100 incrementando ",
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Cell["\<\
En el siguiente ejemplo se representa gr\[AAcute]ficamente una lista de \
funciones que pertenece a la familia de los polinomios de Hermite.\
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 "Ejemplo 4\nLos polinomios de Hermite , son una familia de polinomios \
ortogonales en el intervalo (-\[Infinity] , \[Infinity]) con la \
funci\[OAcute]n de peso ",
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 ", donde n es el grado del polinomio y x la variable independiente. \n\
Definir una lista que contenga los  polinomios de Hermite hasta grado cinco y \
representarlos gr\[AAcute]ficamente.\n"
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Cell["Listas como argumentos de funciones", "Section 1"],

Cell["\<\
Un comando que nos permite evaluar una funci\[OAcute]n en cada uno de los \
elementos de una lista es el comando Map[f,lista].\
\>", "Text",
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Cell["\<\
Ejemplo 5
Crear una tabla de 30 valores igualemnte espaciados en el intervalo \
(0,2\[Pi]) y otra con los Senos de los elementos de la tabla anterior.
A continuaci\[OAcute]n unir los valores de ambas tablas para conseguir una \
representaci\[OAcute]n del Sin(x) en el intervalo (0, 2\[Pi])\
\>", "Subsection",
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Cell["Esto tambi\[EAcute]n se puede hacer:", "Text"],

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Cell["Otras operaciones con listas", "Section 1"],

Cell["\<\
El comando Apply[operaci\[OAcute]n, lista] permite aplicar la \
operaci\[OAcute]n que se indique a los elementos de la lista.\
\>", "Text",
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Cell["\<\
Ejemplo 6
Definir una lista formada por los 100 primeros n\[UAcute]meros naturales y
 calcular su suma y su producto.\
\>", "Subsection",
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Cell[TextData[{
 "Esto tambi\[EAcute]n se puede hacer utilizando los s\[IAcute]mbolos de la \
paleta ",
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Cell["\<\
Interpolaci\[OAcute]n y ajuste polin\[OAcute]micos\
\>", "Section 1",
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Cell["\<\
En muchos casos pr\[AAcute]cticos de ingenier\[IAcute]a, f\[IAcute]sica y \
otras \[AAcute]reas se presenta el siguiente problema. Se tiene un conjunto \
de datos pertenecientes a una funci\[OAcute]n desconocida, procedentes por \
ejemplo de medidas experimentales, y se desea obtener una funci\[OAcute]n que \
pueda sustituir a esa funci\[OAcute]n desconocida en determinadas operaciones \
matem\[AAcute]ticas. Este es el problema que se resuelve dentro del An\
\[AAcute]lisis Num\[EAcute]rico mediante la Interpolaci\[OAcute]n y la \
Aproximaci\[OAcute]n Num\[EAcute]ricas.\
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Cell[TextData[StyleBox["1.- Interpolaci\[OAcute]n num\[EAcute]rica.",
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Cell[TextData[{
 "La Interpolaci\[OAcute]n Num\[EAcute]rica, explicada en t\[EAcute]rminos \
muy sencillos, consiste en, dado un conjunto de puntos (abscisas y \
ordenadas), obtener el polinomio que pasa por todos esos puntos. El polinomio \
de interpolaci\[OAcute]n se puede utilizar para estimar el valor de la funci\
\[OAcute]n en un punto en el que no est\[AAcute] tabulada. El polinomio de \
interpolaci\[OAcute]n tambi\[EAcute]n puede sustituir a la funci\[OAcute]n si \
se desea tener una estimaci\[OAcute]n del valor de la integral o la derivada \
de esa funci\[OAcute]n.\n\nSi se dispone de dos puntos, el polinomio de \
interpolaci\[OAcute]n es de primer grado ( una recta), si se dispone de tre \
es de segundo grado (una par\[AAcute]bola), etc. En general con N+1 puntos se \
podr\[AAcute] determinar un polinomio de grado N como m\[AAcute]ximo. Se \
puede demostrar que el polinomio de interpolaci\[OAcute]n de un conjunto de \
puntos existe y es \[UAcute]nico.\n\n",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " dispone del comando InterpolatingPolynomial que nos permite obtener el \
polinomio de interpolaci\[OAcute]n de forma muy sencilla. Su sintaxis es la \
siguiente:\n\n\tInterpolatingPolynomial[datos,x]\n\nOtras veces se conoce la \
funci\[OAcute]n pero tiene una expresi\[OAcute]n muy compleja e interesa \
sustituirla por el polinomio de interpolaci\[OAcute]n en un conjunto de \
puntos de la misma ya que los polinomios son funciones matem\[AAcute]ticas \
con las que resulta muy sencillo trabajar. A este caso pertenece el ejemplo \
que se muestra a continuaci\[OAcute]n."
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 "Ejemplo 7\nSea f(x) = ",
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 ". \n1\.ba.- Almacenar en una variable graff la representaci\[OAcute]n gr\
\[AAcute]fica de f en el intervalo [1 , 4].\n2\.ba.- Definir una funci\
\[OAcute]n que de el polinomio interpolador que pasa por n+1 puntos \
igualmente espaciados de la curva f en el intervalo (1,4).\n3\.ba.- Crear una \
lista, polinomios, que contenga las gr\[AAcute]ficas de los polinomios \
interpoladores de hasta grado 8.\n4\.ba.- Crear otra lista de \
gr\[AAcute]ficas en las que se represente la funci\[OAcute]n, y cada uno de \
los 8 polinomios interpoladores.\n5\.ba.- Finalmente utilizar el comando \
Animate para hacer una animaci\[OAcute]n de las gr\[AAcute]ficas obtenidas.\n"
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Cell["\<\
La  funci\[OAcute]n InterpolatingPolynomial obtiene los polinomios \
interpoladores que pasan por un conjunto de puntos. En este caso es necesario \
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no est\[AAcute]n todav\[IAcute]a definidos.\
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Cell["\<\
Creamos una tabla de polinomio interpoladores de hasta grado 8\
\>", "Text",
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visualizaci\[OAcute]n del comportamiento din\[AAcute]mico de una expresi\
\[OAcute]n que depende de un par\[AAcute]metro. Mediante estas funciones se \
pueden hacer animaciones y explorar el com portamiento de una \
expresi\[OAcute]n al variar los par\[AAcute]metros de los que depende. Una de \
estas funciones es ",
 StyleBox["Animate",
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 " y ",
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Cell["\<\
Este ejercicio se puede realizar de forma m\[AAcute]s sencilla utilizando el \
comando Module. Esto se ver\[AAcute] posteriormente. \
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Cell["2. - Ajuste de un conjunto de puntos a una curva", "Section"],

Cell[TextData[{
 "En otras ocasiones, dado un conjunto de puntos, no nos interesa una funci\
\[OAcute]n que pase exactamente por todos los puntos, sino una \
funci\[OAcute]n sencilla y que pase lo m\[AAcute]s cerca posible de los \
puntos. A esta funci\[OAcute]n se denomina \"funci\[OAcute]n de aproximaci\
\[OAcute]n\". La Aproximaci\[OAcute]n Lineal Minimocuadr\[AAcute]tica \
consiste en obtener la funci\[OAcute]n de aproximaci\[OAcute]n como combinaci\
\[OAcute]n lineal de funciones conocidas, \"funciones base\", es decir,\n\t",
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 ", ..se establece la condici\[OAcute]n de que el error cuadr\[AAcute]tico \
cometido sea m\[IAcute]nimo, es decir,\n\tE=",
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 " sea m\[IAcute]nima.\n",
 StyleBox["Mathematica",
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 " facilita todo este c\[AAcute]lculo y el comando Fit nos devuelve la funci\
\[OAcute]n de aproximci\[OAcute]n. Su sintaxis es la siguiente:\n\t",
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 "\nEl comando ",
 StyleBox["Fit",
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 " ajusta la lista \"datos\", donde est\[AAcute]n contenidas las coordenadas \
de los puntos, usando las funciones contenidas en \"conjunto de funciones\" \
mediante aproximaci\[OAcute]n m\[IAcute]nimo cuadr\[AAcute]tica. Las \
funciones ",
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Cell[TextData[{
 "Ejemplo 8\nDefinir la lista \"datos\" que contiene los valores:\n",
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 "\ny representarla gr\[AAcute]ficamente utilizando el comando ListPlot.\nA \
continuaci\[OAcute]n aproximarla mediante:\na) Aproximarla mediante un \
polinomio de segundo grado y representar este polinomio junto con los datos.\n\
b) Repetir el apdo. anterior para un polinomio de aproximaci\[OAcute]n de \
sexto grado.\nc) Idem. para el polinomio de interpolaci\[OAcute]n que pasa \
por todos los puntos.\nd) Calcular en cada uno de los casos anteriores el \
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