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Cell["INTERPOLACI\[CapitalOAcute]N NUM\[CapitalEAcute]RICA.", "Title",
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Cell[" El comando InterpolatingPolinomial.", "Section"],

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 "Este comando permite obtener el polinomio de interpolaci\[OAcute]n tomando \
como argumento una lista con las coordenadas (abscisas y ordenadas) de los \
puntos por los que tiene que pasar exactamente el polinomio de interpolaci\
\[OAcute]n. El resultado que se obtiene es una funci\[OAcute]n que se puede \
evaluar en cualquier punto y representar gr\[AAcute]ficamente. Tiene la forma \
correspondiente al polinomio de interpolaci\[OAcute]n de Newton con \
diferencias divididas. La forma b\[AAcute]sica de este comando es la \
siguiente:\n\tInterpolatingPolynomial[datos, var]. ",
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 "\nSe pide: \n1\.ba.- Obtener en primer lugar el polinomio de interpolaci\
\[OAcute]n correspondiente, y representarlo junto con los datos.\n2\.ba.-  \
Obtener un valor aproximado de f(1.5) mediante un polinomio de interpolaci\
\[OAcute]n de 2\.ba grado.Representar este polinomio junto con los datos.\n3\
\.ba.- Idem. para obtener un valor aproximado de f(3.5) mediante un polinomio \
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 "\nse pide:\na) Obtener el polinomio de interpolaci\[OAcute]n \
correspondiente a dicho conjunto de datos.\nb) Representar \
gr\[AAcute]ficamente dichos puntos y el polinomio de interpolaci\[OAcute]n en \
un mismo gr\[AAcute]fico.\nc) A\[NTilde]adir a la tabla el dato : f(0.47) = \
0.94423 , y calcular el polinomio de grado 4\.ba correspondiente.\n"
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\[AAcute]fico para comprobar el denominado \"efecto Runge\""
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siguiente tabla:\n",
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comprobar que su m\[AAcute]ximo valor en dicho intervalo es inferior a la \
cota m\[AAcute]xima obtenida.\n\[DownQuestion]Qu\[EAcute] error se comete al \
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gr\[AAcute]fica?"
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gr\[AAcute]ficamente S(x) junto con f(x). \nRepetir el ejercicio calculando \
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Cell["\<\
Ejemplo 2\.ba.
Sean los puntos:  f(0)=1, f(2) = 9, f(4) = 41 y f(6) = 41, 
a) Calcular la spline c\[UAcute]bica S(x) que verifique : S'(0) = 0 y S'(6) = \
-12 (spline con condiciones de contorno) y representarlar en negro, llamando \
al gr\[AAcute]fico g1.
b) Representar la interpolaci\[OAcute]n polinomial a trozos con polinomios de \
primer grado utilizando los comandos Show, Graphics y Line en azul, llamando \
al gr\[AAcute]fico g2.
c) Calcular el polinomio de interpolaci\[OAcute]n correspondiente y \
representarlo en verde, llamando al gr\[AAcute]fico g3.
d) Representar gr\[AAcute]ficamente en rojo la spline natural utilizando el \
paquete <<Graphics`Spline`, llamando al gr\[AAcute]fico g4.
e) Mostrar los 4 gr\[AAcute]ficos juntos de forma que se puedan comparar.
f) Mostrar los gr\[AAcute]ficos correspondientes a las dos splines \
conjuntamenete\
\>", "Subsubsection"],

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Representamos en primer lugar la interpolaci\[OAcute]n lineal a trozos en \
color azul\
\>", "Text"],

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A continuaci\[OAcute]n se calcula el polinomio de interpolaci\[OAcute]n y se \
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Cell["\<\
Comparando los cuatro gr\[AAcute]ficos, se puede observar que el polinomio de \
interpolaci\[OAcute]n (verde) es el que m\[AAcute]s oscila en los puntos pr\
\[OAcute]ximos a los extremos. La spline natural (rojo) y la de cond. de \
contorno (negro) est\[AAcute]n muy pr\[OAcute]ximas. \
\>", "Text"],

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 "  \nCalcular B y b, y representar gr\[AAcute]ficamente la spline.\nHallar \
f'(0) y f'(2).\n\[DownQuestion]Se trata de una spline natural?"
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Cell["\<\
Como s0''(0) es nula, con las 3 ec. que se obtienen al imponer la continuidad \
de la spline, de su derivada primera y de su derivada segunda en x=1, m\
\[AAcute]s la ec. que se obtiene al igualar a cero la derivada segunda en \
x=2, se tienen 4 ec. con 4 inc\[OAcute]gnitas,a,b,c yd,  con lo que es \
posible determinar la spline natural\
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(* End of internal cache information *)