{"id":3769,"date":"2017-12-08T06:30:41","date_gmt":"2017-12-08T11:30:41","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1013\/?p=3769"},"modified":"2026-04-05T20:08:35","modified_gmt":"2026-04-06T01:08:35","slug":"s2eva2008ti_t1_mn-produccion-petroleo","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-s2eva10\/s2eva2008ti_t1_mn-produccion-petroleo\/","title":{"rendered":"s2Eva2008TI_T1_MN Producci\u00f3n petroleo"},"content":{"rendered":"\n<p><em><strong>Ejercicio<\/strong><\/em>: <a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-2eva10\/2eva2008ti_t1_mn-produccion-petroleo\/\" data-type=\"post\" data-id=\"665\">2Eva2008TI_T1_MN Producci\u00f3n petroleo<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Literal a<\/h2>\n\n\n\n<p>Para el c\u00e1lculo de las derivadas se hace uso de las f\u00f3rmulas de diferenciaci\u00f3n presentadas en la unidad 6, y basadas en el polinomio de Taylor:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> f'(x_i) = \\frac{f(x_{i+1})-f(x_i)}{h} + O(h) <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> f''(x_i) = \\frac{f(x_{i+2})-2f(x_{i+1})+f(x_i)}{h^2} + O(h) <\/span>\n\n\n\n<pre class=\"wp-block-code\"><code>&#091; dia, prod, dprod, d2prod]\n&#091;&#091; 1.000e+00  3.345e+03 -1.000e+02  6.600e+01]\n &#091; 2.000e+00  3.245e+03 -3.400e+01  1.320e+02]\n &#091; 3.000e+00  3.211e+03  9.800e+01 -5.600e+01]\n &#091; 4.000e+00  3.309e+03  4.200e+01  1.900e+01]\n &#091; 5.000e+00  3.351e+03  6.100e+01 -2.430e+02]\n &#091; 6.000e+00  3.412e+03 -1.820e+02  8.700e+01]\n &#091; 7.000e+00  3.230e+03 -9.500e+01  9.200e+01]\n &#091; 8.000e+00  3.135e+03 -3.000e+00  0.000e+00]\n &#091; 9.000e+00  3.132e+03 -3.000e+00  0.000e+00]\n &#091; 1.000e+01  3.129e+03  0.000e+00  0.000e+00]]<\/code><\/pre>\n\n\n\n<p>representados en las siguientes gr\u00e1fica:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2017\/12\/2Eva2008TI_T1ProduccionPetroleo.png\" alt=\"2eva2008ti_t1 producci\u00f3n petroleo\" class=\"wp-image-18545\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">literal b<\/h2>\n\n\n\n<p>Dado que las f\u00f3rmulas de error usadas tienen error del orden h: O(h), el error de las f\u00f3rmulas es del orden de:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>h= dia&#091;1]-dia&#091;0] = 2-1 = 1<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">literal c<\/h2>\n\n\n\n<p>Para el d\u00eda dos se observa un decrecimiento en la producci\u00f3n, tal como lo refleja el valor negativo de la primera derivada.<br>Sin embargo para el d\u00eda siguiente, la producci\u00f3n no mantiene la tasa de decrecimiento, se observa la segunda derivada positiva, Empieza a \"acelerar\".<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p>Las instrucciones en Python para la tabla presentada son:<\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code alignwide\"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\n# 2Eva_IT2008_T1_MN Producci\u00f3n petroleo\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# INGRESO\ndia = np.array( &#x5B;1., 2, 3, 4, 5, 6, 7, 8, 9, 10])\nproduccion = &#x5B;3345., 3245, 3211, 3309, 3351, 3412, 3230, 3135, 3132, 3129]\nproduccion = np.array(produccion, dtype = float)\n\n# PROCEDIMIENTO\nn = len(dia)\n\n# primera derivada\ndp = np.zeros(n,dtype=float)\nfor i in range(0,n-1,1):\n    dp&#x5B;i] = (produccion&#x5B;i+1]-produccion&#x5B;i])\/(dia&#x5B;i+1]-dia&#x5B;i])\n\n# segunda derivada\nd2p = np.zeros(n,dtype=float)\nh = dia&#x5B;1]-dia&#x5B;0]\nfor i in range(0,n-2,1):\n    d2p&#x5B;i] = (produccion&#x5B;i]-2*produccion&#x5B;i+1]+ produccion&#x5B;i+2])\/(h**2)\n\ntabla = np.concatenate((&#x5B;dia],&#x5B;produccion],&#x5B;dp],&#x5B;d2p]),axis=0)\ntabla = np.transpose(tabla)\n\n# SALIDA\nprint(&quot; &#x5B; dia, prod, dprod, d2prod]&quot;)\nprint(tabla)\n\n# gr\u00e1fica\nplt.subplot(121)\nplt.plot(dia,produccion)\nplt.xlabel('dia')\nplt.ylabel('producci\u00f3n')\nplt.grid()\nplt.subplot(122)\nplt.plot(dia,dp,color='green',label='dp')\nplt.xlabel('dia')\nplt.plot(dia,d2p,color='orange',label='d2p')\nplt.axhline(0)\nplt.legend()\nplt.grid()\nplt.show()\n<\/pre><\/div>","protected":false},"excerpt":{"rendered":"<p>Ejercicio: 2Eva2008TI_T1_MN Producci\u00f3n petroleo Literal a Para el c\u00e1lculo de las derivadas se hace uso de las f\u00f3rmulas de diferenciaci\u00f3n presentadas en la unidad 6, y basadas en el polinomio de Taylor: representados en las siguientes gr\u00e1fica: literal b Dado que las f\u00f3rmulas de error usadas tienen error del orden h: O(h), el error de [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-mn-ejemplo","format":"standard","meta":{"footnotes":""},"categories":[47],"tags":[58,54],"class_list":["post-3769","post","type-post","status-publish","format-standard","hentry","category-mn-s2eva10","tag-ejemplos-python","tag-mnumericos"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/3769","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=3769"}],"version-history":[{"count":5,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/3769\/revisions"}],"predecessor-version":[{"id":23849,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/3769\/revisions\/23849"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=3769"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=3769"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=3769"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}