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"source": [
"# Práctica 12: Diferenciación e integración numéricas con MATLAB®\n",
"\n",
"En ingeniería, es muy común usar el término derivada en diversos cursos como cálculo diferencial e integral, modelado de sistemas dinámicos, análisis de señales y control clásico entre otros. El concepto de derivada es de gran utilidad devido a que proporciona una medición de la razón de cambio de una variable respecto de los cambios que presenta una segunda variable de interés o bajo análisis. La derivada de una función $y=f(x)$ se denomina también como la razón de cambion entre la variable $y$ y la variable $x$. La derivada de una función se puede obtener usando la herramienta de cómputo simbólico disponible en MATLAB®, por ejemplo, la derivada de la función: $y=2x^3-4x^2+3$, definida como:\n",
"\n",
"$$\n",
"\\frac{dy}{dx}=y'=\\dot{y}=6x^2-8x\n",
"$$\n",
"\n",
"Se puede resolver la derivada de la función $y$ respecto de $x$ usando la herramienta de cómputo simbólico de MATLAB®, con las siguientes instrucciones:"
]
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"data": {
"text/latex": [
"$Derivada(x) =6\\,x^2 -8\\,x$"
]
},
"execution_count": 1,
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],
"source": [
"clear\n",
"close all\n",
"clc\n",
"\n",
"syms y(x) x; % Creación de variables simbólicas\n",
"\n",
"y(x) = 2*x^3-4*x^2+3; % Se especifica la función a diferenciar\n",
"Derivada = diff(y,x)\n"
]
},
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"source": [
"\n",
"## Diferenciación numérica\n",
"\n",
"Como se trató en la práctica pasada, existen muchos casos en la ingeniería donde no se cuenta con una función en específico o forma cerrada, sino que se cuenta con un conjunto de datos experimentales en forma de pares ordenados, de manera que la derivada se calcula de forma numérica ({cite:t}`Moore2013`):\n",
"\n",
"$$\n",
"\\frac{dy}{dx}=\\frac{\\Delta y}{\\Delta x}=\\frac{y_2-y_1}{x_2-x_1}\n",
"$$\n",
"\n",
"Considere los pares ordenados de la práctica anterior y mostrados en la siguiente tabla:\n",
"\n",
"\n",
" | $x$ | $y$ | \n",
" | :------ | ------: | \n",
" | 0.0 | 22.430 | \n",
" | 1.0 | 19.398 | \n",
" | 2.0 | 11.341 | \n",
" | 3.0 | 8.422 | \n",
" | 4.0 | 5.215 | \n",
" | 5.0 | 0.434 | \n",
"\n",
" Si se usa la función `diff()` para aplicarla a los datos reportados en las columnas de la tabla anterior, se encontrará la pendiente de la recta que une cada par de datos consecutivos:\n"
]
},
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"execution_count": 2,
"id": "7202ed67-26c7-4f59-8653-3c3834cf57d8",
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"text/html": [
"delta_x = 1×5 double\n",
" 1 1 1 1 1\n",
""
],
"text/plain": [
"delta_x = 1×5 double\n",
" 1 1 1 1 1\n"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear \n",
"close all\n",
"clc\n",
"\n",
"x=[0:5]; %vector x original\n",
"y=[22.430,19.398,11.342,8.422,5.215,0.434]; % vector y original\n",
"\n",
"delta_x=diff(x)"
]
},
{
"cell_type": "markdown",
"id": "51d5f310-0c6b-4452-9a3c-582205f47db8",
"metadata": {},
"source": [
"El resultado anterior refleja el hecho de que los datos en el vector $x$ están espaciados de manera uniforme. Ahora bien si se diferencian los datos contenidos en la columna $y$ se obtiene:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ee9f5419-eaba-4fc8-a59f-3436b1c3de66",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"delta_y = 1×5 double\n",
" -3.0320 -8.0560 -2.9200 -3.2070 -4.7810\n",
""
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"text/plain": [
"delta_y = 1×5 double\n",
" -3.0320 -8.0560 -2.9200 -3.2070 -4.7810\n"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
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"source": [
"delta_y=diff(y)"
]
},
{
"cell_type": "markdown",
"id": "e94fa7fc-ddf7-4b8e-a256-d408ffb4160d",
"metadata": {},
"source": [
"Para encontrar las pendientes de las rectas que unen a cada par de puntos se establece el cociente $\\frac{\\Delta y}{\\Delta x}$ de la siguiente manera:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "cecf6ecc-d735-4e99-822d-a5b0e420be04",
"metadata": {},
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{
"data": {
"text/html": [
"pendientes = 1×5 double\n",
" -3.0320 -8.0560 -2.9200 -3.2070 -4.7810\n",
""
],
"text/plain": [
"pendientes = 1×5 double\n",
" -3.0320 -8.0560 -2.9200 -3.2070 -4.7810\n"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pendientes=delta_y./delta_x"
]
},
{
"cell_type": "markdown",
"id": "052628ac-4964-4831-9b5d-e41193b073e3",
"metadata": {},
"source": [
"El arreglo o vector pendientes tiene un elemento menos que los datos originales de las columnas $x$ e $y$, debido a que se calculan diferencias entre los elementos de los arreglos originales. La siguiente figura ilustra gráficamente lo anteriormente expuesto: "
]
},
{
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"execution_count": 5,
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"
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"close all\n",
"figure\n",
"plot(x,y,\"o\",\"LineWidth\",3)\n",
"axis([-2,9,-5.5,25])\n",
"hold on\n",
"plot(x,y,\"k-\",\"LineWidth\",1)\n",
"title(\"Datos de muestra\")\n",
"\n",
"txt =\"Pendiente 1=(y_2-y_1)/(x_2-x_1)\";\n",
"text(0.6,22,txt,'FontSize',12)\n",
"\n",
"txt =\"Pendiente 2\";\n",
"text(1.6,15,txt,'FontSize',12)\n",
"\n",
"txt =\" ...\";\n",
"text(-1.55,9,txt,'FontSize',12)\n",
"\n",
"txt =\" ...\";\n",
"text(-0.5,5.5,txt,'FontSize',12)\n",
"\n",
"txt =\"Pendiente n=(y_n-y_{n-1})/(x_n-x_{n-1})\";\n",
"text(3,2.8,txt,'FontSize',12)\n",
"\n",
"\n",
"grid\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"set(gca,'fontsize',16);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');"
]
},
{
"cell_type": "markdown",
"id": "a0288e68-e4de-4b73-b088-95eadc3e803b",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"En el caso de que se conozca en forma cerrada la expresión o fórmula que relaciona los pares de datos, se puede usar la función de MATLAB® `diff()` para hacer una aproximación numérica de la derivada. Por ejemplo, para la función:\n",
"\n",
"$$\n",
"y=2x^3-4x^2+3\n",
"$$\n",
"\n",
"se obtiene gráficamente lo siguiente:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "2f538cae-66a7-425c-8e6f-cd130e443b5e",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": [
"remove-input"
]
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear \n",
"clc\n",
"close all \n",
"\n",
"x=[-2:1:2];\n",
"y=2*x.^3-4*x.^2+3;\n",
"\n",
"\n",
"figure\n",
"subplot(2,2,1)\n",
"plot(x,y)\n",
"title(\"y=2x^3-4x^2+3, con \\Deltax=1\")\n",
"axis([-2,2,-5,5])\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n",
"pendientes=diff(y)./diff(x);\n",
"\n",
"subplot(2,2,2)\n",
"bar(x(1:max(size(x))-1)+diff(x)./2,pendientes)\n",
"axis([-2,2,-5,35])\n",
"title(\"Pendiente de y(x)\")\n",
"hold on\n",
"plot(x,6*x.^2-8*x)\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n",
"x2=-2:0.1:2;\n",
"pendientes=diff(2*x2.^3-4*x2.^2+3)./diff(x2);\n",
"\n",
"\n",
"subplot(2,2,4)\n",
"bar(x2(1:max(size(x2))-1)+diff(x2)./2,pendientes)\n",
"title(\"Pendiente de y(x)\")\n",
"axis([-2,2,-5,35])\n",
"hold on\n",
"plot(x2,6*x2.^2-8*x2)\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n",
"subplot(2,2,3)\n",
"plot(x2,2*x2.^3-4*x2.^2+3)\n",
"axis([-2,2,-5,5])\n",
"title(\"y=2x^3-4x^2+3, con \\Deltax=0.1\")\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n"
]
},
{
"cell_type": "markdown",
"id": "0413e00b-cbfc-491a-87d8-cb773e837c15",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"Las gráficas anteriores muestran el cálculo de la derivada de la función $y=2x^3-4x^2+3$ en forma de gráficas de barras con diferente resolución en los datos. Las siguientes líneas de código ilustran el cálculo numérico de la derivada de la función antes mencionada con las dos resoluciones que se muestran en la figura anterior:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "6a26b58c-ac81-43b2-b91b-33ece827ec6b",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear \n",
"clc\n",
"close all \n",
"\n",
"x=[-2:1:2];\n",
"y=2*x.^3-4*x.^2+3;\n",
"\n",
"\n",
"figure\n",
"subplot(2,2,1)\n",
"plot(x,y)\n",
"title(\"y=2x^3-4x^2+3, con \\Deltax=1\")\n",
"axis([-2,2,-5,5])\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n",
"pendientes=diff(y)./diff(x);\n",
"\n",
"subplot(2,2,2)\n",
"plot(x(1:max(size(x))-1)+diff(x)./2,pendientes)\n",
"axis([-2,2,-5,35])\n",
"title(\"Derivada de y(x)\")\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n",
"x2=-2:0.1:2;\n",
"pendientes=diff(2*x2.^3-4*x2.^2+3)./diff(x2);\n",
"\n",
"\n",
"subplot(2,2,4)\n",
"plot(x2(1:max(size(x2))-1)+diff(x2)./2,pendientes)\n",
"title(\"Derivada de y(x)\")\n",
"axis([-2,2,-5,35])\n",
"hold on\n",
"plot(x2,6*x2.^2-8*x2)\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n",
"subplot(2,2,3)\n",
"plot(x2,2*x2.^3-4*x2.^2+3)\n",
"axis([-2,2,-5,5])\n",
"title(\"y=2x^3-4x^2+3, con \\Deltax=0.1\")\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n"
]
},
{
"cell_type": "markdown",
"id": "80f7a6c6-772d-4c1d-a724-93c63e163082",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Diferencias divididas finitas\n",
"\n",
"En el caso de necesitar evaluar la derivada de un punto en específico en vez de la derivada numérica de un conjunto de pares ordenados experimentales, en forma de una curva, como en el caso anterior, se utiliza la pendiente de la recta que une dos puntos de interés, de manera que la derivada se aproxima de forma numérica como ({cite:t}`Moore2013`):\n",
"\n",
"$$\n",
"\\left ( \\frac{dy}{dx} \\right ) _{i}=\\frac{y_{i+1}-y_i}{x_{i+1}-x_i}\n",
"$$\n",
"\n",
"En este caso, es tambien completamente compatible la instrucción `diff()`. de manera que se asigna el resultado como la derivada evaluada en el primer punto en el rango. Dado que se utiliza un dato hacia adelante del conjunto, esta técnica de diferenciación se conoce como el método de diferencias finitas hacia adelante. \n",
"\n",
"EL siguiente ejemplo permite ilustrar el método de las diferencias divididas finitas hacia adelante:\n",
"\n",
"Por ejemplo, para la función $y=2x^3$ se sabe que su derivada es:\n",
"\n",
"$$\n",
"\\frac{dy}{dx}=6x^2\n",
"$$\n",
"\n",
"de manera que un programa para calcular la derivada de 10 puntos de esta función es el siguiente:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a54f82ba-39aa-4e6b-a53e-1beb148004bf",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" x 2*x.^3 Diferencias hacia adelante error %\n",
" __ ______ __________________________ _______\n",
"\n",
" -2 24 14 41.667\n",
" -1 6 2 66.667\n",
" 0 0 2 -Inf\n",
" 1 6 14 -133.33\n",
" 2 24 NaN NaN\n",
"\n"
]
}
],
"source": [
"clear \n",
"close all\n",
"clc\n",
"\n",
"% Programa para el cálculo de la derivada de y=3x^2 en 10 puntos \n",
"x=-2:1:2;\n",
"y=2*x.^3;\n",
"derivada=6*x.^2; % derivada analítica\n",
"dif_finitas=diff(y)./diff(x); % Diferencias divididas finitas\n",
"dif_finitas(length(x))=NaN; % Se ajusta el tamaño del arreglo para \n",
"%establecer compatibilidad\n",
"%cálculo del porcentaje de error\n",
"error=((derivada-dif_finitas)./derivada)*100;\n",
"%construcción de una tabla \n",
"titulo=[\"x\",\"2*x.^3\",\"Diferencias hacia adelante\",\"error %\"];\n",
"disp(table(x',derivada',dif_finitas',error','VariableNames',titulo))"
]
},
{
"cell_type": "markdown",
"id": "78ce9f7e-7e56-484e-942c-9aa1bec62bae",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"Como puede observarse, el error en la aproximación es muy grande. Esto se debe a la resolución o número de puntos utilizados para generar la función y los cálculos, si se utiliza una resolución mayor, es decir si se reduce el tamaño del incremento del vector $x$ se obtiene una mejor aproximación:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "e0e01816-cfe3-46e4-b58e-0cdd1bea6b57",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" x 2*x.^3 Diferencias hacia adelante error %\n",
" ____ ______ __________________________ _______\n",
"\n",
" -2 24 22.82 4.9167 \n",
" -1.9 21.66 20.54 5.1708 \n",
" -1.8 19.44 18.38 5.4527 \n",
" -1.7 17.34 16.34 5.767 \n",
" -1.6 15.36 14.42 6.1198 \n",
"\n"
]
}
],
"source": [
"clear \n",
"close all\n",
"clc\n",
"\n",
"% Programa para el cálculo de la derivada de y=3x^2 en 10 puntos \n",
"x=-2:0.1:2;\n",
"y=2*x.^3;\n",
"derivada=6*x.^2; % derivada analítica\n",
"dif_finitas=diff(y)./diff(x); % Diferencias divididas finitas\n",
"dif_finitas(length(x))=NaN; % Se ajusta el tamaño del arreglo para \n",
"%establecer compatibilidad de manera que al establecer el último elemento\n",
"% se indica que serán diferencias hacia adelante\n",
"%cálculo del porcentaje de error\n",
"error=((derivada-dif_finitas)./derivada)*100;\n",
"%construcción de una tabla \n",
"titulo=[\"x\",\"2*x.^3\",\"Diferencias hacia adelante\",\"error %\"];\n",
"disp(table(x(1:5)',derivada(1:5)',dif_finitas(1:5)',error(1:5)','VariableNames',titulo))"
]
},
{
"cell_type": "markdown",
"id": "9098fbdc-22b7-4bae-b5ce-dd5d9f27b397",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"### Diferencias divididas finitas hacia atrás\n",
"\n",
"El cálculo de las diferencias finitas hacia atrás es similar al caso anterior con la diferencia de que el planteamiento es el siguiente:\n",
"\n",
"$$\n",
"\\left ( \\frac{dy}{dx} \\right ) _{i}=\\frac{y_i-y_{i-1}}{x_i-x_{i-1}}\n",
"$$\n",
"\n",
"En este caso se utiliza la misma función `diff()` pero en este caso se establece el valor `NaN` al primer valor del arreglo en vez de el último.\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "0d1bf11b-6d57-4b38-bc91-564c242c6511",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" x 2*x.^3 Diferencias hacia adelante error %\n",
" ____ ______ __________________________ _______\n",
"\n",
" -2 24 NaN NaN\n",
" -1.9 21.66 22.82 -5.3555\n",
" -1.8 19.44 20.54 -5.6584\n",
" -1.7 17.34 18.38 -5.9977\n",
" -1.6 15.36 16.34 -6.3802\n",
"\n"
]
}
],
"source": [
"clear \n",
"close all\n",
"clc\n",
"\n",
"% Programa para el cálculo de la derivada de y=3x^2 en 10 puntos \n",
"x=-2:0.1:2;\n",
"y=2*x.^3;\n",
"derivada=6*x.^2; % derivada analítica\n",
"diff_finitas=diff(y)./diff(x); % Diferencias divididas finitas\n",
"dif_finitas=[NaN,diff_finitas]; % Se ajusta el tamaño del arreglo para \n",
"%establecer compatibilidad de manera que al establecer el primer elemento\n",
"% se indica que serán diferencias hacia atrás\n",
"%cálculo del porcentaje de error\n",
"error=((derivada-dif_finitas)./derivada)*100;\n",
"%construcción de una tabla \n",
"titulo=[\"x\",\"2*x.^3\",\"Diferencias hacia adelante\",\"error %\"];\n",
"disp(table(x(1:5)',derivada(1:5)',dif_finitas(1:5)',error(1:5)','VariableNames',titulo))"
]
},
{
"cell_type": "markdown",
"id": "3f89f87e-95fe-43fe-9919-d3efae15e499",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"Se observa en este caso que el error es negativo, debido a la dirección en la que se toman las diferencias divididas finitas.\n",
"\n",
"### Diferencias divididas centrales\n",
"\n",
"El cálculo de la derivada en los puntos de interés usando diferencias divididas finitas centradas es similar a los métodos antes expuestos con la diferencia principal de tomar en cuenta a los puntos siguiente y anterior del punto de interés:\n",
"\n",
"$$\n",
"\\left ( \\frac{dy}{dx} \\right ) _{i}=\\frac{y_{i+1}-y_{i-1}}{x_{i+1}-x_{i-1}}\n",
"$$\n",
"\n",
"Una desventaja de este método es que no se toman en cuenta el primer y último dato del conjunto. La aplicación del método de diferencias divididas finitas en MATLAB® se realiza con la función `gradient()`. Es necesario especificar el incremento del arreglo cuando se usa esta función, de no indicarse, se tomará como incremento 1 por defecto."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "77e5a71b-105e-4d01-a49e-1e647fdea4e8",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" x 2*x.^3 Diferencias hacia adelante error % \n",
" ____ ______ __________________________ _________\n",
"\n",
" -2 24 22.82 4.9167\n",
" -1.9 21.66 21.68 -0.092336\n",
" -1.8 19.44 19.46 -0.10288\n",
" -1.7 17.34 17.36 -0.11534\n",
" -1.6 15.36 15.38 -0.13021\n",
"\n"
]
}
],
"source": [
"clear \n",
"close all\n",
"clc\n",
"\n",
"% Programa para el cálculo de la derivada de y=3x^2 en 10 puntos \n",
"incremento=0.1;\n",
"x=-2:incremento:2;\n",
"y=2*x.^3;\n",
"derivada=6*x.^2; % derivada analítica\n",
"diff_finitas=gradient(y,x,incremento); % Diferencias divididas finitas\n",
"\n",
"error=((derivada-diff_finitas)./derivada)*100;\n",
"%construcción de una tabla \n",
"titulo=[\"x\",\"2*x.^3\",\"Diferencias hacia adelante\",\"error %\"];\n",
"disp(table(x(1:5)',derivada(1:5)',diff_finitas(1:5)',error(1:5)','VariableNames',titulo))"
]
},
{
"cell_type": "markdown",
"id": "7f93f76b-67a0-4398-8b5d-a9caba23de7e",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"El error se reduce de forma considerable usando este método principalmente en los valores de los datos centrales, pero se puede notar un error considerablemente mayor para el primer cálculo. Una comparación del desempeño de las técnicas se muestra en la siguiente gráfica:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "8fcf0731-5c15-4fc7-97e7-2bfcaa2007b1",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"data": {
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"
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear \n",
"close all\n",
"clc\n",
"\n",
"% Programa para el cálculo de la derivada de y=2x^3 en 10 puntos \n",
"incremento=0.1;\n",
"x=-2:incremento:2;\n",
"y=2*x.^3;\n",
"derivada=6*x.^2; % derivada analítica\n",
"\n",
"dif_finitas=diff(y)./diff(x); % Diferencias divididas finitas\n",
"dif_adelante=dif_finitas;\n",
"dif_adelante(length(x))=NaN; % Se ajusta el tamaño del arreglo para \n",
"%establecer compatibilidad de manera que al establecer el último elemento\n",
"% se indica que serán diferencias hacia adelante\n",
"\n",
"dif_atras=[NaN,dif_finitas]; % Se ajusta el tamaño del arreglo para \n",
"%establecer compatibilidad de manera que al establecer el primer elemento\n",
"% se indica que serán diferencias hacia atrás\n",
"\n",
"dif_centrales=gradient(y,x,incremento); % Diferencias divididas finitas centrales\n",
"\n",
"figure\n",
"plot(x,derivada,\"LineWidth\",1)\n",
"hold on\n",
"plot(x,dif_adelante,\"o-\",\"LineWidth\",1)\n",
"plot(x,dif_atras,\"*-\",\"LineWidth\",1)\n",
"plot(x,dif_centrales,\"^-\",\"LineWidth\",1)\n",
"title(\"Técnicas de diferencias divididas\")\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"axis([-1,0,-1,5])\n",
"grid\n",
"legend(\"Analítica: 6x^2\",\"Diferencias adelante\",\"Diferencias atrás\",\"Diferencias centrales\")\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "0f9d6e39-934f-4e4d-8c4d-d31c5bb06a8f",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"## Integración numérica\n",
"\n",
"En ingeniería y en otras áreas de la ciencia, una integral se interptreta de manera frecuente como el área bajo una curva, esta área se puede calcular si se divide en rectángulos pequeños al espacio que cubre dicha curva, de manera que se puede aproximar el cálculo de un área irregular en términos de la suma del área independiente de los rectángulos pequeños antes mencionados, usando la fómula básica $área=base\\times altura$ ({cite:t}`Moore2013`, {cite:t}`chapra2006metodos`).\n",
"\n",
"$$\n",
"A=\\sum^2_1\\frac{(x_{i+1}-x_i)(y_{i+1}+y_i)}{2}\n",
"$$\n",
"\n",
"Gráficamente se tiene:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "fe3bc6f6-9be1-4a7a-bd05-ae36ad772a52",
"metadata": {
"editable": true,
"scrolled": true,
"slideshow": {
"slide_type": ""
},
"tags": [
"remove-input"
]
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear \n",
"clc\n",
"close all \n",
"\n",
"x=[0:0.5:4];\n",
"y=0.5*(x-2.5).^2;\n",
"\n",
"\n",
"figure\n",
"subplot(1,2,1)\n",
"plot(x,y,'o-','LineWidth',2)\n",
"title(\"Curva a integrar\")\n",
"axis([0,2,0,2.5])\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n",
"\n",
"subplot(1,2,2)\n",
"plot(x,y,'o-','LineWidth',2)\n",
"hold on \n",
"b=bar(x,y,'histc');\n",
"b.FaceColor='none';\n",
"axis([0,2,0,2.5])\n",
"title(\"Aproximación\")\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "c5d7cb45-2840-4904-9412-077af38121c5",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"Como puede observarse, el área aproximada se puede calcular usando los comandos anteriormete analizados para el cálculo de las diferencias divididas finitas, usando las siguientes instrucciones ({cite:t}`Moore2013`):\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "a20900cd-ad41-41ce-9617-dab7be8d22fe",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"Area = 3.2500
"
],
"text/plain": [
"Area = 3.2500"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear \n",
"clc\n",
"close all \n",
"\n",
"x=[0:0.5:4]; %creación del vector de la variable independiente\n",
"y=0.5*(x-2.5).^2; % función a integrar en el intervalo [0,4]\n",
"\n",
"promedio_y=y(1:8)+diff(y)./2; %Aproximación trapezoidal\n",
"Area=sum(diff(x).*promedio_y)%Cálculo del área bajo la curva"
]
},
{
"cell_type": "markdown",
"id": "3fde5b9d-bae3-49e3-98d8-4d86a119e87c",
"metadata": {},
"source": [
"La función nativa de MATLAB® que permite hacer el cálculo de dicha integral es `trapz()`, que se refiere al método trapezoidal para calcular el área bajo la curva: "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "c449bf28-fb37-42e2-8223-1a895899b779",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"ans = 3.2500
"
],
"text/plain": [
"ans = 3.2500"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear \n",
"clc\n",
"close all \n",
"\n",
"x=[0:0.5:4];\n",
"y=0.5*(x-2.5).^2;\n",
"trapz(x,y)"
]
},
{
"cell_type": "markdown",
"id": "5344bf1b-c4aa-47e3-bf46-1c2b652ed9f5",
"metadata": {},
"source": [
"Aproximaremos el área bajo la curva formada por una función de prueba, aun cuando esta no haya sido producto de mediciones experimentales, con fines de calibración y mejor entendimiento del método numérico. A continuación calcularemos la integral de la función:\n",
"\n",
"$$\n",
"f(x)=y=0.5x^2\n",
"$$\n",
"\n",
"En el intervalo $0\\leq x \\leq 1$. La integral se calcula con MATLAB® usando las instrucciones:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "a227a0ae-80ed-4d85-8b06-8abae971ba41",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = 0.1675
"
],
"text/plain": [
"ans = 0.1675"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear\n",
"close all\n",
"clc\n",
"\n",
"x=[0:0.1:1];\n",
"y=0.5*x.^2;\n",
"trapz(x,y)"
]
},
{
"cell_type": "markdown",
"id": "5371c4c2-6db1-4b57-8c6b-91ea4d5737b0",
"metadata": {},
"source": [
"Este ultimo resultado corresponde a una aproximación numérica del resultado del cálculo de la integral:\n",
"\n",
"$$\n",
"\\int^1_0 0.5x^2 dx\n",
"$$\n",
"\n",
"La solución exacta de esta integral es:\n",
"\n",
"$$\n",
"\\int^1_0 0.5x^2 dx=0.5\\int^1_0 5x^2 dx=0.5\\frac{x^3}{3}| ^{1}_{0}=0.5 \\left ( \\frac{1^3}{3}-\\frac{0^3}{3} \\right )=0.1667\n",
"$$\n"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "55c99ba5-b41f-4b3b-a7d8-29555da738af",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = 0.1667
"
],
"text/plain": [
"ans = 0.1667"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"0.5/3"
]
},
{
"cell_type": "markdown",
"id": "80f91e94-f9c7-4b59-ba4e-97abd475fd38",
"metadata": {},
"source": [
"Gráficamente, este resultado equivale al área bajo la curva de la función $y=0.5x^2$ como se muestra en la siguiente figura:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "fd285702-da10-4fe0-9e7c-2dc810998b06",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"Area = 0.1675
"
],
"text/plain": [
"Area = 0.1675"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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hw94sFACA0KDf0CC++8xcmToQDBgwwOVe6h4I9ZM15KfbCSFaW1u9ViIAACFD16FhyJAhcsPlU7USExNd7mU2m5V8oB73oDxOV+lyAAAA2uk6NIwbN05utLS0OK2Ki4uLjIyU27W1tTk5OXPnzq2srJSX3HvvvXLj448/bnvYpKQkn5RrRPJAECg4IWqcDSecEDXOhiHpOjSkpKTIVyiuXr0qL1GuLGRkZCibLVmy5K233iotLZ0xY4Z8/WLatGlyd8KlS5cuX74sb/avf/1LCBEREfGzn/3Mjx8CAACD0HVoMJvNeXl5FoulvLy8ublZCFFVVSWEGDlypPr2hxMnTsiNhoYGuU+if//+8hzS4t9zNly9evWTTz4RQixbtqxHjx7+/RwAABiBrkODEGL48OFr1qzp2bNnZmZmTk7O+vXrJ02aVFRUpN4mOztbbqSmpnbv3l1uP/LIIy+++GLfvn1XrlxZWFg4Y8aMvn37FhYW/td//Ze/PwMAAIZgcjnGUG8kSTpw4EBLS0tCQoIylEHNarXW1dWNGDGi7Y6VlZWXL1+++eab77zzTi3vxb3FatXV1cqoUghOyHdxNpxwQtQ4G2qG+WUJjsmdzGZzcnKymw1iYmLa23HYsGG+KQoAgNCi98sTAABAJwgNAABAE0IDAADQhNAAAAA0ITQAAABNCA0AAEATQgMAANCE0AAAADQhNAAAAE0IDQAAQBNCAwAA0ITQAAAANCE0AAAATQgNAABAE0IDAADQhNAAAAA0ITQAAABNCA0AAEATQgMAANCE0AAAADQhNAAAAE0IDQAAQBNCAwAA0ITQAAAANCE0AAAATQgNAABAE0IDAADQhNAAAAA0ITQAAABNCA0AAEATQgMAANCE0AAAADQhNAAAAE0IDQAAQBNCAwAA0ITQAAAANCE0AAAATQgNAABAE0IDAADQhNAAAAA0ITQAAABNCA0AAEATQgMAANCE0AAAADQhNAAAAE0IDQAAQBNCAwAA0ITQAAAANCE0AAAATQgNAABAE0ugC+iY3W7fsGFDaWlpTU1NUlJSVlbW4MGDtexotVr/+te/tl3+05/+9Ec/+pG3ywQAwOD0HhoaGxtnzJhRVVW1ZcuWhISEadOmTZkyZfny5ePHj+9w323btm3atKnt8unTp/ugUgAADE7vlydyc3OPHDly++23JyYmms3m9PR0SZIWLVpktVo73Hf79u1tF959990DBgzwQaUAgG+ZFrw/aFW1acH7gS4EXqbrnobq6uri4mIhRFRUlLwkIiJCCCFJ0tq1a1944QU3+5aXl1sslqlTpzot19JFAQDwmDormBa871iRGsBi4F26Dg07duyQG2FhYXIjPDxcbuzatSsvL89sbrenpLi4+JFHHsnKyvJ1kQAAmcuuBXkh0cEYdB0ajh49KjeUrGCxfFuwzWYrKysbNWqUyx3tdvuuXbvi4+OPHz8eHR09bNgwRj4CgE+pE4NjRWp1dXV0dLSykC4HY9B1aDh06JCbtTU1Ne2tev/995uamg4fPnz48GF5Sd++fR977LHMzEwvlwgA+C51OHCsSGVkg5HodyCkJElNTU1uNjh+/Hh7q95++22nJTU1Nc8//3xmZubVq1e9Ux8A4N+UZNC2O0FZQnowAP32NNjtdvcbuIkUDofjnnvuOXbsWF1dnSRJyvKysrLFixevXLnS/ZHj4uKUdklJibZ6jens2bOBLkFfOCFqnA0nnBAhRHV19aBV1XL709ku1vq7oMAZO3ZsoEvwPv2Ghg4poyPbKiwslBt2u33Pnj2bN2/et2+fvKS0tPTYsWPup4c6efKkF+sMdtHR0YEuQV84IWqcDSchfEK+TQPR0dFKe9Cq6n93M6jXhgr1T4n6b9Ggpt/LE+Hh4W1vjlB3PwwcOLDDg4SFhd13333r1q1bv369fLumEKKiosKLdQIAXF6DkBe6uXKBoKPf0CBU0zMo1KGhU3M0JScnr1q1Sm5/8cUXXa8NAODGp7OjBYnBcHQdGoYMGSI3HA5H27WJiYmdOtqIESPuvvtu9WEBAN7iFAuYEdKQdB0axo0bJzdaWlqcVsXFxUVGRsrt2tranJycuXPnVlZWuj9gv379LBZLe7M7AAA85iYi0M1gGLoODSkpKfIVCuU+ydbWVrmRkZGhbLZkyZK33nqrtLR0xowZ8vWLhQsXDh069Jlnnqmvr1cf8Ny5c48//njv3r399AEAIDS0HcqgtEkMRqLr0GA2m/Py8iwWS3l5eXNzsxCiqqpKCDFy5Mi0tDRlsxMnTsiNhoaGlpYWu91eXFz89ddfv/baaz//+c937twpr33llVduvvnmOXPm+P1zAEBocaxI/XR2NHHBeHQdGoQQw4cPX7NmTc+ePTMzM3NyctavXz9p0qSioiL1NtnZ2XIjNTW1e/fuYWFhTz/99PXXXy+E+PLLL+fPn5+YmDh+/PgbbrihoKAgAJ8BAAytvW4GGE8QzNOQnJy8d+/eAwcOtLS0zJs3TxnKoMjMzBw1alRdXd2IESPkJWlpaVOnTi0rK2tqarJYLLGxsf379/d74QBgfCSGkBIEoUEIYTabk5OT3WwQExPTdhcGPAKAT3F/RKjR++UJAEBQoJshFBAaAACe4MJECCI0AAA6jcQQmggNAABAE0IDAKBz6GYIWYQGAEAnkBhCGaEBAABoQmgAAGhFN0OIIzQAADQhMYDQAAAANCE0AAA6RjcDBKEBANAhEgNkhAYAAKAJoQEA4A7dDFAQGgAA7SIxQI3QAAAANCE0AABco5sBTggNAAAXSAxoi9AAAHBGYoBLhAYAAKAJoQEA8B10M6A9hAYAwH+QGOCGJdAFAAC8yWQyee1Q+V3a3eFweKkQ6AWhAQCMxuNfay92M3gxu0A/uDwBABCCCxPQgNAAAAA0ITQAAOhmgCaEBgAIdSQGaERoAAAAmhAaACCk0c0A7QgNABC6SAzoFEIDAADQhNAAACGKbgZ0FqEBAEIRiQEeIDQAQMghMcAzhAYAAKAJoQEAQgvdDPAYoQEAQgiJAV1BaAAAAJoQGgAgVNDNgC4iNABASCAxoOsIDQAAQBNCAwAYH90M8ApCAwAYHIkB3kJoAAAAmhAaAMDI6GaAFxEaAMCwSAzwLkIDAADQhNAAAMZENwO8zhLoAgAAXiMHBXVcECQGeA+hAQCMwCkoAL4QBJcn7Hb7unXrHnzwwXvuuWfhwoXHjh3z4CCSJD3yyCPJycleLw8AAs5NYqCbAV6k99DQ2NiYkZGRn5+/dOnSPXv2XLx4ccqUKcXFxZ09zqpVqyoqKurr631RJADoRNuIQA8EvEjvoSE3N/fIkSO33357YmKi2WxOT0+XJGnRokVWq1X7QcrLy19++WXfFQkAAaTEAseKVCICfErXoaG6ulruVIiKipKXRERECCEkSVq7dq3Gg1y+fHn+/Pk+qhAAAkudGJxWKUtIEvAWXYeGHTt2yI2wsDC5ER4eLjd27dolSZKWgyxYsCAmJsYX5QGArnCPJXxN16Hh6NGjckPJChbLt7d72Gy2srKyDo9QVFTUq1evqVOn+qhCANAJEgP8QNeh4dChQ27W1tTUuN+9srLyjTfeePrpp71aFADoiJt84ObKBeAZ/c7TIElSU1OTmw2OHz8+ceLE9tY2NDTMnz8/Pz+/R48enX3ruLg4pV1SUtLZ3Y3k7NmzgS5BXzghapwNJ/o5IdXV1YNWVatfBqqMgLyvTowdOzbQJXiffkOD3W53v4H7SLF48eJHHnlk6NChHrz1yZMnPdjLqKKjowNdgr5wQtQ4G04CdEKcf5vViSGA3Qwh/s9D/VOi/ls0qOk3NHRIGR3Z1qZNm1pbW7OysvxZDwD4H9M6wZ/0O6YhPDzcbHYuT939MHDgQJc7Wq3WvLy8CRMmfPhvp0+fllc5HI4PP/zw0qVLPqoZAPzJzTMmSAzwBV33NERFRZ05c0a9RB0aBgwY4HKvU6dONTc3L1y4sO0qm802ffr055577sEHH/RuqQAQWHJKcKxINeWTGOAr+u1pEEIMGTJEbjgcjrZrExMT/VsOAOgI91jC/3Td0zBu3Dh5RsiWlhanVXFxcZGRkXK7trY2Pz+/qakpKytr6NChSUlJTvNFVlRUrFu3TghhsVgKCwuZ6wlAsCMxICB0HRpSUlKioqLOnj179epVeUlra6vcyMjIUDZbsmTJ3r17hRAHDx4sKyvr06fPvffeqz7OlStX5IbJZHJaBQBBh8SAQNH15Qmz2ZyXl2exWMrLy5ubm4UQVVVVQoiRI0empaUpm504cUJuNDQ0tO2TAAAj4UESCCBdhwYhxPDhw9esWdOzZ8/MzMycnJz169dPmjSpqKhIvU12drbcSE1N7d69eyDKBIAAoJsBfmZyOcZQbyRJOnDgQEtLS0JCgjKUQc1qtdbV1Y0YMaLr7xUXF8fkTorq6uoQn57FCSdEjbPhxA8nRMuFCZNJF1/sOilDJwzzy6LrMQ0Ks9mcnJzsZgPGNgIwPIYyIOD0fnkCACAYygB9IDQAQJChmwGBQmgAAL3jwgR0gtAAALpGYoB+EBoAQL8YygBdITQAQHCgmwEBR2gAAJ3iwgT0htAAAHpEYoAOERoAQHdIDNAnQgMA6AuDH6FbhAYA0C+6GaArhAYA0BEuTEDPCA0AoBckBugcoQEAdIGhDNC/4Hg0NgDo36BBg7x4NFO+Fw8GeAehAQC8xuFweLajFy9MmEymruwOuMHlCQAIMIYyIFgQGgAgkBjKgCBCaAAAvaCbATpHaACAgOHCBIILoQEAAoPEgKBDaACAACAxIBgRGgAAgCaEBgDwN7oZEKQIDQDgVyQGBC9CAwD4D4kBQY3QAAB+wjxOCHaEBgAIALoZEIwIDQDgD1yYgAEQGgDA50gMMAZCAwD4FkMZYBiEBgDwH7oZENQIDQDgQ1yYgJEQGgDAV0gMMBhCAwD4BIkBxkNoAAAAmhAaAMD76GaAIREaAMDLSAwwKkugCwAAI5CDgtOUDCQGGAyhAQC6hLmbEDq4PAEAnnOTGOhmgPEQGgDAC9pGBHogYDyEBgDwkBILHCtSiQgIBYQGAPCEm8Sg9DqQJGAwhAYA6BLumEDoIDQAgNeQGGBshAYA8ISbfKC+cuGvcgB/IDQAgBcwjgGhgNAAAJ5wCgdtZ4SkmwHGw4yQANBp7rsTiAswqiAIDXa7fcOGDaWlpTU1NUlJSVlZWYMHD9ayY319/caNG/ft23fx4sXExMS0tLT77rvP19UCMDyXt0swjgGhwPuXJxYuXOjFozU2NmZkZOTn5y9dunTPnj0XL16cMmVKcXFxhztWVlY+8MADRUVFx48fr6+v37t376xZs1555RUv1gYgBLV3g6XcIDHA2LwfGv7xj38UFhZ662i5ublHjhy5/fbbExMTzWZzenq6JEmLFi2yWq1u9qqtrf3Nb34zbNiwqVOnDhkyRFm+fPny+vp6b9UGIMQRERBqfDIQsqCgIC4ubtasWbW1tV05TnV1tdypEBUVJS+JiIgQQkiStHbtWjc7rlmz5qWXXnr55ZefffbZ119//aGHHpKX22y2jz76qCslAQhljHNEiPN+aAgPD//oo48qKysfe+yxtLS00aNHv/HGG3a73YND7dixQ26EhYUpB5cbu3btkiSpvR0feuihYcOGKS/nzZuntG+77TYPKgEAEgPg/dAwceLEa6+9tnv37sOGDXv//fdLSkouXLiQlJQ0efLkL774olOHOnr0qNxQsoLF8u3ITZvNVlZW1t6OcXFx6pfK7uPHj+/fv3+nagAAQWIAhBC+CA1z5sxRv+zRo8ecOXN27dr15Zdf3n///XfddVdBQUFjY6OWQx06dMjN2pqaGo0lbdmyRQgxefLkvLw8jbsAgILEAMi8HxqcrkSUl5enpKTcc889ly5dEkJcuXKlsLBw+PDh9913n/tMIElSU1OTmw2OHz/eYTGSJP31r3/985//LFfi/h0BoC1meAQU3p+nIS0tTR7EsHEN079kAAAgAElEQVTjxsLCQpc//Pfff/+yZctWrVo1e/bsadOmzZo1q+02HQ6DcB8phBDnzp1LT0+Xw4r8Misr69VXX1UPd3BJfXWjpKTE/cbGdvbs2UCXoC+cELVQOBuDVlWrX346O7q6urq9jYUQ7tf6DWXowdixYwNdgvd5PzTU1NSMHj36yy+/bLuqe/fuv/71r2fMmCEPMsjNzc3NzS0uLk5ISKioqOjevXun3kgZHdme/v3779u3b/v27Xl5eXI9Nptt+fLlmzdvdr/jyZMnO1WJsUVHRwe6BH3hhKgZ+2x48MxrnZwQytAD9U+J00i74OWTGSHbJobIyMjly5f/6Ec/arvx+PHjW1paHnjggQ8++EC9PDw83Gw2O90ioe5+GDhwoJZiJkyYMHLkyMmTJ8tjIKqqqjR+CgBQMJQBEH6YRvrOO+/Mz8/v16+fy7U5OTnbt2+32Wwu10ZFRZ05c0a9RB0aBgwYoLGGPn36PP/884899pgQQpIkSZLMZp7UBcAdBj8Cbfnwt/PRRx89cuTI5s2b20sMQoi33npLTgzXX39927XKZI4Oh6Pt2sTERO3FJCcn33rrrUKIm266icQAwD0SA+CST34+p06devLkyZycnOuuu879lvfee6/cWLp0adu148aNkxstLS1Oq+Li4iIjI+V2bW1tTk7O3LlzKysr3bxXTEyM+pgA4BKJAWiP9y9PJCQkPPvssxo3Xrt2bW1t7fXXX+8yXqSkpERFRZ09e/bq1avyktbWVrmRkZGhbLZkyZK9e/cKIQ4ePFhWVnb06NE5c+bEx8c///zzffr0UTa7ePFiRETEzJkzPftcAEIBiQFww/s9DZ19WlWfPn3a65Awm815eXkWi6W8vLy5uVn8exjjyJEj09LSlM1OnDghNxoaGlpaWrZv315TU7Nv376JEycqs0a+8847n3/++erVq5X+CQBwwpQMgHt6v7o/fPjwNWvW9OzZMzMzMycnZ/369ZMmTSoqKlJvk52dLTdSU1O7d+8+ffp0efjCl19+mZmZOX78+IcffrikpOTtt98ePnx4AD4DgGDgwQ2WQKgxuRxjqDeSJB04cKClpSUhIcFlV4HVaq2rqxsxYoSy5KOPPqqtrZUkqVu3bqNGjepwUgdFXFwc8zQoqqurQ/xOayecEDUjnQ2vJAaTSRffqJShQ4b5ZfH5LZdeYTabk5OT3WwgD3JU69S9FQCgoI8BaI/eL08AgK8x+BHQKDh6GgCgPSaTyZtHy/fiwQCjITQACHoeXzv3bh+Dd+MLoENcngAQorjBEugsQgOAUMQNloAHCA0AQg6JAfAMoQFAaCExAB4jNAAIXSQGoFMIDQBCCFMyAF1BaAAQKkgMQBcRGgCEBBID0HWEBgDGx5QMgFcQGgAYHLdLAN5CaABgZCQGwIsIDQBCBYkB6CJCAwDDYvAj4F2EBgDGRGIAvI7QAMCASAyALxAaABgNiQHwEUIDAENhSgbAdwgNAIyDGywBnyI0AAhickpQ/6+CxAB4HaEBQLBSpwQSA+AHlkAXAACd5n7gAokB8BF6GgAEGW6OAAKF0AAgWJEYAD8jNAAIJko3g5wYXF6n4K5LwEcIDQCCFYMfAT8jNAAISiQGwP8IDQCCictw4HSpggAB+AihAYARMI4B8ANCA4Bg0uHIR7oZAN9hcicAQYM5nYDAoqcBQHBoO/JRnRJIDIAfEBoABIH27pWQGyQGwD8IDQD0jrsrAZ0gNADQNRIDoB+EBgD6RWIAdIXQAECnSAyA3hAaAOgRiQHQIUIDAN0hMQD6RGgAoC8kBkC3CA0AdITEAOgZoQGAXpAYAJ0jNADQBRIDoH+EBgCBR2IAggKhAUCAkRiAYEFoABBIJAYgiBAaAAQMiQEILpZAFwAgWA0aNMi7BzTle/d4ALwsCEKD3W7fsGFDaWlpTU1NUlJSVlbW4MGDtexotVrXrVtXUVFhMpmSkpKys7NjYmJ8XS0QUhwOh2c7erGPwWQyebwvgE7R++WJxsbGjIyM/Pz8pUuX7tmz5+LFi1OmTCkuLu5wx+3bt0+YMGHbtm3nz58/d+7c1q1bJ06cuHv3bj/UDMA9rkoAQUrvoSE3N/fIkSO33357YmKi2WxOT0+XJGnRokVWq9XNXlarNScnR5Iki+U/XSk2m23x4sX19fW+rxpAu0gMQPDSdWiorq6WOxWioqLkJREREUIISZLWrl3rZseioqLs7OxDhw598sknGzduvOmmm+TlDQ0N+/fv93HVANpFYgCCmq5Dw44dO+RGWFiY3AgPD5cbu3btkiSpvR1jYmLmz5/fo0cPIcSoUaOWLVumrKqurvZRtQDcIzEAwU7XoeHo0aNyQ8kKyuUGm81WVlbW3o4zZ85Uv/zJT36itGNjY71cJQANSAyAAeg6NBw6dMjN2pqams4e0GKxjB49ugsVAfAEiQEwBv2GBkmSmpqa3Gxw/PhxjYf65z//KTd++ctfyqMiAPgNiQEwDP3O02C3291v4D5SqL377rtCiMjIyCeeeELL9nFxcUq7pKRE47sY0tmzZwNdgr5wQpx0OEho0KrvbPDp7GhfjCvSz1glnVRCGXowduzYQJfgffoNDR1SRke619ra+re//c1sNhcUFGjsZjh58mTXSjOU6OjoQJegL5wQNfdnw299DPr5P0UnlVCGHqh/StR/iwY1/V6eCA8PN5udy1N3PwwcOFDLcVavXn3+/Pm8vLw777zTm/UBcIurEoDx6Dc0CNX0DAp1aBgwYECHR6isrFy9evVTTz01YcIELxcHoH0kBsCQdB0ahgwZIjdczm+fmJjofveGhoYnn3xyzpw5WVlZysL9+/cr4yIB+AKJATAqXY9pGDdunDwjZEtLi9OquLi4yMhIuV1bW5ufn9/U1JSVlTV06FBlmwULFtx6661Dhw798MMP5SVfffXV8uXLeQIF4DskBsDAdB0aUlJSoqKizp49e/XqVXlJa2ur3MjIyFA2W7Jkyd69e4UQBw8eLCsrkwdIFhQU7Nu3TwjhNAfUbbfd1naoBACvIDEAxqbrn0+z2ZyXl2exWMrLy5ubm4UQVVVVQoiRI0empaUpm504cUJuNDQ0yH0S77zzTmFhoctjanysNoDOIjEAhqfr0CCEGD58+Jo1a3r27JmZmZmTk7N+/fpJkyYVFRWpt8nOzpYbqamp3bt3t1qtTz31VHsHVMZJAOgKOSIoQYHEAIQCk8sxhnojSdKBAwdaWloSEhKUoQxqVqu1rq5uxIgRXX+vuLg45mlQVFdXh/id1k44IbJvI0L+fWK+ixFCfk4MJpNevsd0Ugll6JBhfll0PaZBYTabk5OT3WwQExPjt2KAUObUo9AWfQyAgen98gQA/VAnBpfhgMQAGBuhAUCnEQ6A0ERoAKCJ0s0gJwaX1yk6vHgBIKgRGgB0GvdKAKGJ0ACgc0gMQMgiNADQxM3IR6crFwCMitAAQJP2OhgYxwCEDkIDgI61TQZOM0IKuhmAEBAckzsBCCAmdAIgIzQAaFfbuND2qgSJAQgdhAYArrm/S8KxItWUT2IAQgtjGgC4wH2VANoiNABwRmIA4BKhAcB3kBgAtIfQAOA/SAwA3GAgJAAhiAsANKCnAQCJAYAmhAYg1JEYAGhEaABCGokBgHaEBiB0kRgAdAoDIYFQ5GZ+aABoD6EBCDl0MADwDKEBCD4mk8mbR8v34sEAGBmhAQhKDofDg72828fg3ewCQP8YCAmECq5KAOgiehoA42PYIwCvIDQABkcHAwBv4fIEYGQkBgBeRGgADIvEAMC7CA2AMZEYAHgdoQEwIBIDAF9gICRgKNwoAcB3CA2AcdDBAMCnuDwBGASJAYCvERoAIyAxAPADQgMQZOR8oE4JJAYA/sGYBiCYuMkKMhIDAN8hNADBwWVEUCMuAPA1Lk8AQUCdGFyGAxIDAD8gNADBhHAAIIAIDYDeKd0McmJweZ2iw4sXANB1hAYgaJgWvM+NEgACiIGQQFAiLgDwP3oagCDmdOUCAHyK0ADompsHUJEYAPgZlycAnWpvbGPbGSEBwD/oaQD0yGUHAzM0AAgsehoAfXFzPUJuc1UCQKDQ0wDoiPvEoF5CYgDgf/Q0ALqgJS4AQGDR0wAEHokBQFAIgtBgt9vXrVv34IMP3nPPPQsXLjx27Fhnj7B79+6HH3746tWrvigP6KK2kzySGADok94vTzQ2Ns6YMaOqqmrLli0JCQnTpk2bMmXK8uXLx48f3+G+drt98+bNr776anV1tR9KBTqLDgYAwUXvoSE3N/fIkSN33HFHYmKiECI9Pb2iomLRokXx8fExMTHt7dXY2Pjqq6/+9a9/ramp8WOxQCeQGAAEHV1fnqiuri4uLhZCREVFyUsiIiKEEJIkrV271s2ONptt6tSp+/fvnzx5sh/qBDrF5XOnSAwA9E/XoWHHjh1yIywsTG6Eh4fLjV27dkmS1N6OvXr16tOnjxBixIgRPq4R6Bw6GAAEL11fnjh69KjcULKCxfJtwTabraysbNSoUYGpDKFq0KBBXj+mKd/rhwQAn9B1aDh06JCbtYxXQEA4HA4P9vJuB4PJZPJ4XwDwmH5DgyRJTU1NbjY4fvz4xIkTffHWcXFxSrukpMQXbxEszp49G+gSdKezN+MMWuW8/aezoz04ThfL8BHKcKKTSihDD8aOHRvoErxPv6HBbre738B9pOiKkydP+ujIwSg6OjrQJehLp06I70Yw6OT/F8pwopNKKEMP1D8l6r9Fg5p+Q0OHlNGRgD61vUUiUJUAgFfoNzSEh4ebzWanWyTU3Q8DBw70e1GAJtwiAcCQ9BsahBBRUVFnzpxRL1GHhgEDBvi9IqBjdDAAMCpdh4YhQ4bIocHleHV5jkhAP+hgAGBsup7cady4cXKjpaXFaVVcXFxkZKTcrq2tzcnJmTt3bmVlpV/rA1RIDAAMT9c9DSkpKVFRUWfPnlUeUNna2io3MjIylM2WLFmyd+9eIcTBgwfLysraGyDZ2Nh43XXX+bhkhCLiAoAQoeueBrPZnJeXZ7FYysvLm5ubhRBVVVVCiJEjR6alpSmbnThxQm40NDQ49UmcPn1aaXvwTG1ATQ4HThGBxAAgdOi6p0EIMXz48DVr1vzud7/LzMyMjo7euXPnpEmTcnNz1dtkZ2c///zzQojU1NTu3bsLIex2+9atWysrK99++21lsz/84Q9Hjx4dNWrU8OHD/fwpYADqcNA2KMiICwCMzeTZnLh+JknSgQMHWlpaEhISlKEMalarta6uziuPp4qLi2NyJ0V1dXWIT88inCJC/n1i/m6Xm/kzMZhMuvgvlzKc6KQSytAhw/yy6L2nQWY2m5OTk91sEBMT47diEFLUicGxItXlw6XoYAAQInQ9pgHQj/aSAYkBQOggNADtUroZHCtSTQvedzmUob3xDQBgPIQGoGPcIgEAgtAAeIDEACA0ERoA19zfV6m+cuG/mgAgoILj7gnAn9zEBfnuCcYxAAhNhAbgP9yngbYzQtLNACCkEBoAIdqJC+pMwAOvAYDQgFDXYVxQljCOAUCIIzQgdHX2ERLymAYSA4CQRWhAiNLYwQAAUBAaEHKICwDgGUIDQghxAQC6gtCAkEBcAICuIzQgCJhMJp8c1tVzrgEA7SE0IDg4HI7O7uKL3gUfxRcACAqEBhgQFyMAwBd4YBWMhsQAAD5CTwOMg7gAAD5FaIAREBcAwA8IDdA75dmSLkMAcQEA/IbQAF1TZwK5rQQC4gIA+BmhATrV3tOkOvuUKQCAt3D3BPRInQzkNOAmEzhWpJIYAMAPCA3QtQ7TAHEBAPyGyxPQHaWbQQ4EykBIp82ICwDgZ4QG6Fd7wxcAAAHB5QkEE3oXACCA6GmAjrjpWlBfqhCkBwAIBEIDAs/9ZQjHilT5GdZcrQCAwCI0IGA0hoC2AyHpZgCAgCA0IAA6vAzR3pbEBQAIIEID/KfDyxAuFzKOAQB0gtAAf9DeteByA1M+iQEAAo/QAB/qSlYAAOgNoQHuDBo0yEdHlm+IAAAEEUIDOuBwOLRv7KOuBZPJ5PG+AABvITTAC7gMAQChgNCAdikTJLj54ScuAEDoIDTANXUakNvqEEBWAIAQRGiAs/YCQYcTOBIXAMDYCA34DqfZmuUJEjyYlAkAYDyEBrimRIH2EgNZAQBCDaEB/9F2HINLxAUACE2EBvDIaQCAJoSGENWpoCB3LZAtACDEERpCiCdBId85MXBtAgBCFqHByLrSnaCe04k+BgCAIDToU1f+rPcgKDgtUecG0eYmzM7WAwAwDEKDvvznFzr/PuH7R0FqPz5xAQBg5NBgt9s3bNhQWlpaU1OTlJSUlZU1ePDgQBfljnMnwfzdStPpN7uL3QmdqCf/vq4cAQBgJKZOPfg4iDQ2Ns6YMaOqqmrLli0JCQnTpk07fPjw8uXLx48f737HuLi4kydP+qdIJ+qrEiaTyeFweDyYwFs/83IZXjmUAcoQuqmEMnRYhtBNJZShQwH8ZfEuw/Y05ObmHjly5I477khMTBRCpKenV1RULFq0KD4+PiYmpr29TAveFz9f7f65jj7S9dsT6A8AAPiUMUNDdXV1cXGxECIqKkpeEhERIYSQJGnt2rUvvPBC212c/qb3W25o25fgNA7RDVICAMCfjBkaduzYITfCwsLkRnh4uNzYtWtXXl6e2WxWb+/y57nt86A7xUe3KRIUAACBYszQcPToUbmhZAWL5dtParPZysrKRo0a5XJHx4pU+cqTy+kKlCU+Kbod6nsgSQwAgAAyZmg4dOiQm7U1NTXql04/yadOnTKZTN/ZwMf3PbaHqRgBALpiwNAgSVJTU5ObDY4fPz5x4kS5reefZJ1kF6cyAkUnZQjdVEIZajopQ+imEp2UERcXF+gS4GUGDA12u939Bu4jhXp2hA55N2rwNGoAgJ4ZMDR0SBkd6UZALg24fJgkcQEAoBPmjjcJNuHh4U43R4jvdj8MHDhQabd9JpNjRWpgBxOo347EAADQD2P2NERFRZ05c0a9RB0aBgwY4HIv/TzXkawAANAhY4aGIUOGyKHB5SSm8hyRirbPdXRa65saAQAIMga8PCGEGDdunNxoaWlxWhUXFxcZGem0ULkk0eFCAABCljFDQ0pKijyB9NWrV+Ulra2tciMjI6O9vRhMAACAG8a8PGE2m/Py8jIzM8vLy5ubm6+99tqqqiohxMiRI9PS0tzsSFYAAKA9Rn506f79+3/3u9/1798/Ojp6586dDzzwQG5u7rXXXhvougAACEpGDg1CCEmSDhw40NLSkpCQ0HYoAwAA0M7goQEAAHiLMQdCAgAAryM0AAAATQgNAABAE2PecukBu92+YcOG0tLSmpqapKSkrKyswYMHB7oo3/L4I1ut1nXr1lVUVJhMpqSkpOzs7JiYGF9X62te+QcgSdK0adM+//zz/fv3+6JIf/LKCTl37tx7771XWVnZrVu3ESNGKI+kDzpd+Y9ly5Yt586ds9vtYWFhP/jBD9LT0/v37+/rgnVi9+7d//3f/71+/frrrrsu0LX4Q2c/b1B+lzrgcDQ0NKSlpcXHx1dVVdnt9oyMjPj4+O3btwe6Lh/y+CNv27YtPj4+VmXw4MHvvfeeH2r2HW/9AygoKIiNjb3jjjt8UaQ/df2EnDlzZs6cObGxsY8//vgnn3ziu1L9wOOzsXbt2tjY2DFjxpw+fdrhcLz//vuxsbE//OEP9+3b5/uqA8lms7322ms/+9nP5K+IpqamQFfkW5593iD9LiU0OBwOx4IFC2JjYydNmiS/3LFjR2xsbHx8/KlTpwJbmO949pFPnTo1ePBg+R+3+t/68OHD6+rq/FK4T3jlH0BZWZl8NgwQGrp4QkpKSu68887Y2Ni//OUvvizTTzw7G3JEiI2NXbt2rbJwxowZ8n8vRv0dbWhoePnll8eMGaP+fjDqh3V04fMG73cpYxpEdXV1cXGxEEKeeVoIERERIYSQJGnt2rWBrMxnPP7IRUVF2dnZhw4d+uSTTzZu3HjTTTfJyxsaGoK3Q94r/wAuX748f/58H1XoZ108IcXFxXPnzm1qavrtb3+bnp7u01L9wOOz8frrr7ddeMsttwghGhoaDh486P1adcBms02dOnX//v2TJ08OdC3+4PHnDd7vUkKD2LFjh9wICwuTG+Hh4XJj165dkiQFpixf8vgjx8TEzJ8/v0ePHkKIUaNGLVu2TFlVXV3to2p9zSv/ABYsWBAEFyO16coJsVqtixcvFkLExsY+9thjvizTTzw+G1999ZXcePPNNw35NeJSr169+vTpI4QYMWJEoGvxB48/b/B+lxIaxNGjR+WG8l1gsXw7PtRms5WVlQWmLF/y+CPPnDlT/fInP/mJ0o6NjfVylf7S9X8ARUVFvXr1mjp1qo8q9LOunJCcnBybzSaEePTRR31Yoh95fDZuvvlmuVFdXb1kyRK5XV9fL4To1avXmDFjfFQwgkLwfpcSGsShQ4fcrK2pqfFbJX7j9Y9ssVhGjx7dhYoCqYtno7Ky8o033nj66ae9WlQgeXxCysvL5Z9Ys9kcExPzyiuvPP300zt37lQeNhuMPD4b6hD51ltvPfroo8eOHdu9e3dERMSqVat4CA5c0v93aaiHBkmSmpqa3Gxw/PhxvxXjH178yP/85z/lxi9/+Uv5Qm/Q6eLZaGhomD9//gsvvCB3MxpAV07I1q1blXZOTs7mzZs3bdo0f/78++67r7Ky0ptV+ktXzkZycvITTzyhvDx48OCkSZO+//3v79ixY/jw4d6sEsEviL5LQz002O129xu4/8oIRl78yO+++64QIjIyUv3lGFy6eDYWL178yCOPDB061KtFBVJXTkh5ebncSElJ2blz5zvvvDN27FghRF1d3Zw5c4Kxv6GL/zxmzZq1bNkys/k/X7OnT59+9dVXvVMcDCSIvktDPTR0SBn9FDo0fuTW1ta//e1vZrO5oKBA59G4K9ycjU2bNrW2tmZlZfmznoBr74RIknT+/Hm5ff3118uN2bNny42amhr5HgSDcf8fS319vdVq7d69e1xcnLJw3bp1+fn5vi8NQSO4vktDPTSEh4er/w6Qqf+8GDhwoH8r8jlvfeTVq1efP38+Ly/vzjvv9GZ9/uXx2bBarXl5eRMmTPjw306fPi2vcjgcH3744aVLl3xUs095fELU25hMJrkRExOjjB88fPiwNwv1i678x3Lu3LkpU6Zs2rRp5syZW7dunTBhgrKqqKhI6Y4Gguu7NNRDg1Ddfq1QfykMGDDAv+X4Q9c/cmVl5erVq5966in1V2GQ8uxsnDp1qrm5eeHChdP/rbCwUF5ls9mmT5+u85ut3fDshKj/5nY4HEo7OjpabrS2tnqtRD/y+D+WJUuWnDt3Tghx//33h4WFvfDCCz/72c+UtTt37vR2pQhKQfddSmgQQ4YMkRvqbzpFYmKif8vxhy5+5IaGhieffHLOnDnqnvn9+/cH6R9PIfgPwD3PTojZbFbygfpKvzydkVDdshhcPDsbra2tyvRNP/jBD+RGbm6ucrvm2bNnvVwoglAwfpfywCoxbtw4+WprS0uL06q4uLjIyMhAFOVbGj9ybW1tfn5+U1NTVlaWeqzfggULbr311qFDh3744Yfykq+++mr58uW7d+/2S/le5tnZSEpKcpoQsKKiYt26dUIIi8VSWFgYvHM9efzP495775Xnpfn444/bHjYpKcm3dfuGZ2dDnqxCqCZ1EEL06tXrxz/+8XvvvSeE+N73vueP6qEPRvouJTSIlJSUqKios2fPKqO7lX7UjIyMwNXlQxo/8pIlS/bu3SuEOHjwYFlZmdz/XFBQsG/fPiGE07Q2t912W9urv0HBs7PRp0+fe++9V32cK1euyA2TyeS0Krh4/M9j2rRp8uDQS5cuXb58uXfv3kKIf/3rX0KIiIgIded8EPHsbHTv3r1fv37nz5+32WzKqRCqizjjx4/332cItMbGxhB5yqWs7ec10nepfivzG7PZnJeXZ7FYysvLm5ubhRBVVVVCiJEjR6alpQW6Op/Q+JFPnDghNxoaGuQ/s9555x3lyr2T4H2SuMdnw6g8PiH9+/eX55AW/56z4erVq5988okQYtmyZUE6lYXHZ+N3v/udvESZvqKhoaGiokIIMWvWrODtiNJIGRcshDh27FgAK/EP95/XSN+lYeopr0NWv379EhMTDxw4sHv37sOHD2/ZsmXChAkrVqxQdy0ajJaPbDab5dF8qampEydOtFqtM2bMaO/O9Yceeih4L/97cDbaHsRqtZaWlgohwsLCZs2a5bfifcHjE5KYmPj973+/srJSfvrzyy+/LElSXl5ekHYzyDw7Gz/4wQ/i4+MPHz7897//vb6+/rPPPlu2bJnNZnvqqaeys7MD9mF8zG63v/XWW3/5y182b96sPHGjoqKisbExLCysX79+gS3P6zR+XiN9l5pcju4JTZIkHThwoKWlJSEhwZBDGdrq8CNbrda6uroQefYMZ8OJxydEkqTKysrLly/ffPPNQXEXmRYen41jx45duHBBCBEZGZmQkOCPWqE/hvn2IDQAAABNGNMAAAA0ITQAAABNCA0AAEATQgMAANCE0AAAADQhNAAAAE0IDQAAQBNCAwAA0ITQAAAANCE0AAAATQgNAABAE0IDAADQhNAAAAA0ITQAAABNCA0AAEATQgMAANCE0AAAADQhNAAAAE0sgS4AQHD47LPPVq1a1dDQoCwJCwt76KGHoqKiXnrppW+++UYI8cMf/nDOnDmBqxGAb5kcDkegawAQHOrr69PT06urq+WXU6dOffbZZ4UQr732WkFBwbp164YOHRrQAgH4FpcnAGjVq1evF198UXlZWlra2NgohHj77bdfeuklEgNgeGHLli0LdA0Agkbfvn3PnTt34sQJIURzc7PFYjl9+nS3bt0efvjhQJcGwOe4PMH2/bkAAAFDSURBVAGgc86fP/+Tn/zEZrMJIcLDwwcMGPDmm29ed911ga4LgM9xeQJA5/Tr1+/RRx+V262trdHR0SQGIETQ0wCg0+rr6++7776mpib55fbt2+Pi4gJbEgA/oKcBQKf16tVr+vTpykv16EgABkZoANBpkiTt3r375ptvll/u27fvyJEjgS0JgB9weQJApxUUFISHh/fu3Xvp0qXykiFDhrz++uuBrQqAr9HTAKBzysvLP/jgg1mzZqWlpUVHR8sLq6qqdu/eHdjCAPgaoQFAJ1it1nnz5s2YMUN+mZmZqaxatmyZepJpAMbDsycAaPLxxx//7//+b0lJSXNzc1FRUWtra1hY2LZt25QNampqMjIyZs2aNW7cuADWCcB3GNMAAAA04fIEAADQhNAAAAA0ITQAAABNCA0AAEATQgMAANDk/wM46cov7KMnGgAAAABJRU5ErkJggg=="
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear\n",
"close all\n",
"clc\n",
"\n",
"x=[0:0.1:1];\n",
"y=0.5*x.^2;\n",
"\n",
"promedio_y=y(1:10)+diff(y)./2; %Aproximación trapezoidal\n",
"Area=sum(diff(x).*promedio_y)%Cálculo del área bajo la curva\n",
"figure\n",
"plot(x,y,'o-','LineWidth',2)\n",
"hold on \n",
"b=bar(x(1:10),promedio_y,'histc');\n",
"b.FaceColor='none';\n",
"axis([0,1.2,0,0.6])\n",
"title(\"Aproximación\")\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');"
]
},
{
"cell_type": "markdown",
"id": "3be78b71-71a3-4e46-90fe-4cc5412effb7",
"metadata": {
"editable": true,
"slideshow": {
"slide_type": ""
},
"tags": []
},
"source": [
"Las funciones `quad('f(x)',x_0,x_1)` y `quadl('f(x)',x_0,x_1)` permiten calcular la integral de una fucnión sin la necesidad de especificar de forma manual los rectángulos o el incremento para los datos usados para el cálculo del área bajo la curva. Las siguientes instrucciones ejemplifican lo antes expuesto:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "aecc2b23-f78a-4efd-9950-b5565559f57f",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = 0.1667
"
],
"text/plain": [
"ans = 0.1667"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear\n",
"close all\n",
"clc\n",
"\n",
"quad('0.5*x.^2',0,1)"
]
},
{
"cell_type": "markdown",
"id": "af9074df-bbb8-45eb-aeef-aa51527afe82",
"metadata": {},
"source": [
"La función `quadl('f(x)',x_0,x_1)` usa una cuadratura adaptativa conocida como cuadratura de Lobatto ({cite:t}`Moore2013`)."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "281c4719-1dc7-47ca-8c17-06ad60459aa8",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = 0.1667
"
],
"text/plain": [
"ans = 0.1667"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear\n",
"close all\n",
"clc\n",
"\n",
"quadl('0.5*x.^2',0,1)"
]
},
{
"cell_type": "markdown",
"id": "65a5832e-0418-4ded-b7bb-254b8151efb7",
"metadata": {},
"source": [
"En las funciones anteriores, usadas para calcular una integral definida, se proporciona la estructura de la función en forma de una cadena de caracteres, dado que se proporciona entrecomillada la función a integrar. \n",
"\n",
"Una forma alternativa para generar gráficas de funciones es usar la sintaxis para la creación de las denominadas funciones anónimas y la función `fplot(función,[x_nin,x_max])` las siguientes líneas de código generan la gráfica de la función\n",
"\n",
"$$\n",
"y=f(x)=-3.5x^3+12x^2-50\n",
"$$\n",
"\n",
"En el intervalo $-15\\leq x \\leq 15$"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "7ac8b946-b18f-4f42-a206-4e643452abed",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear\n",
"close all\n",
"clc\n",
"\n",
"%Ejemplo de código para la creación de funciones anónimas en MATLAB\n",
"%x=-30:0.01:30;\n",
"\n",
"f_x= @ (x) -3.5*x.^3+12*x.^2-50; %Sintaxis de la función interna al código \n",
"%o tambien conocida como función anónima\n",
"\n",
"fplot(f_x,[-15,15],\"LineWidth\",2)%Comado para graficar funciones anónimas\n",
"\n",
"title(\"f(x)=-3.5x^3+12x^2-50\")\n",
"xlabel(\"x\")\n",
"ylabel(\"y\")\n",
"grid\n",
"set(gca,'fontsize',15);\n",
"set(gca,'fontname','Times New Roman','FontWeight','Bold');\n"
]
},
{
"cell_type": "markdown",
"id": "636b9760-dbed-4811-8f87-3c49921b802c",
"metadata": {},
"source": [
"Es posible calcular la integral definida en un intervalo, haciendo una combinación de los comandos `quadl('f(x)',x_0,x_1)` y `quad('f(x)',x_0,x_1)` con la sintaxis para la especificación de funciones anónimas:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "f3e479e0-3369-43a8-9166-ce8da5cfcb9f",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = -84
"
],
"text/plain": [
"ans = -84"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear\n",
"close all\n",
"clc\n",
"\n",
"%Cálculo de una integral definida usando una combinación \n",
"%de quad y función anónima\n",
"\n",
"\n",
"f_x= @ (x) -3.5*x.^3+12*x.^2-50; %Sintaxis de la función interna al código \n",
"%o tambien conocida como función anónima\n",
"\n",
"quad(f_x,-3,3)% Se invoca a la función anónima y se cacula la integral definida\n"
]
},
{
"cell_type": "markdown",
"id": "86a84ab0-454c-4279-bff2-5bbbd4b3f134",
"metadata": {},
"source": [
"El paquete de cálculo simbólico también permite la evaluación de integrales indefinidas o definidas especificando expresiones, cuando se usa la función `int(expresión,[x_0,x_1])`."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "2b23da77-50ca-4035-a8f9-769b02b0d9c7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"integral indefinida de la función f(x)=0.5x^2\n"
]
},
{
"data": {
"text/latex": [
"$I =\\frac{x^3 }{6}$"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"integral definida de la función f(x)=0.5x^2 en el intervalo [-1,1]\n"
]
},
{
"data": {
"text/latex": [
"$I_def =\\frac{1}{3}$"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"clear\n",
"close all\n",
"clc\n",
"\n",
"syms x\n",
"\n",
"fx = 0.5*x^2;%Creación de la función o expresión a integrar\n",
"disp(\"integral indefinida de la función f(x)=0.5x^2\")\n",
"I = int(fx) %sintaxis para calcular la integral indefinida\n",
"disp(\"integral definida de la función f(x)=0.5x^2 en el intervalo [-1,1]\")\n",
"I_def = int(fx,[-1 1]) %sintaxis para calcular la integral indefinida\n"
]
},
{
"cell_type": "markdown",
"id": "893f3587-81d8-407f-9e6b-99910c2f7447",
"metadata": {},
"source": [
"## Ejercicio de la práctica 12\n",
"\n",
"1. Considere la función:\n",
"\n",
"$$\n",
"y=2x^4-5x^3+2x^2-2.5x+40\n",
"$$\n",
"\n",
"Construya un vector $x$ con el intervalo $[-2.5,2.5]$ y uselo con la función $y$ para aproximar la derivada de $y$ respecto de $x$, use el método de diferencias divididas finitas hacia adelante y compare los resultados con los obtenidos de manera analítica:\n",
"\n",
"$$\n",
"\\frac{dy}{dx}=8x^3-15x^2+4x-2.5\n",
"$$\n",
"\n",
"Construya una tabla para reportar la comparación y el porcentaje de error.\n",
"\n",
"2. Repita el ejercicio anterior para las funciones $y=3cos(4x)$ y $y=3.5e^{2x}$, aplicando el método de las diferencias divididas centrales.\n",
"\n",
"\n",
"3. Considere el polinomio:\n",
"\n",
"$$\n",
"y=3x^3-15x^2+2.5x+10\n",
"$$\n",
"\n",
"a) Use la función `trapz()` para estimar la integral de y respecto de x en el intervalo $[-2,2]$. Use 11 valores de $x$ para calcular los valores correspondientes de $y$ como entrada a la función `trapz()`.\n",
"b) Use las funciones `quad()` y `quadl()` para encontrar la integral de y respecto de $x$ en el intervalo $[-2,2]$.\n",
"c) Use el paquete de cálculo simbólico para calcular la integral:\n",
"\n",
"$$\n",
"\\int^{b}_{a} 3x^3-15x^2+2.5x+10\n",
"$$\n",
"\n",
"4. Repita el ejercicio anterior para la función:\n",
"\n",
"$$\n",
"y=4.5cos(15x)e^{-3x}\n",
"$$\n",
"\n",
"En el intervalo $[0,3]$."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f86e4273-9e24-415e-ac60-ce1abcbf41c3",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "MATLAB Kernel",
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