{"id":10629,"date":"2025-01-29T06:00:00","date_gmt":"2025-01-29T11:00:00","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/analisisnumerico\/?p=10629"},"modified":"2026-04-05T20:40:56","modified_gmt":"2026-04-06T01:40:56","slug":"s2eva2024paoii_t1-area-de-incendio-forestal-en-cerro-azul","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-s2eva30\/s2eva2024paoii_t1-area-de-incendio-forestal-en-cerro-azul\/","title":{"rendered":"s2Eva2024PAOII_T1 \u00c1rea de incendio forestal en Cerro Azul"},"content":{"rendered":"\n

Ejercicio<\/strong>: 2Eva2024PAOII_T1 \u00c1rea de incendio forestal en Cerro Azul<\/a><\/p>\n\n\n\n

\"\u00c1rea<\/figure>\n\n\n\n

literal a<\/h2>\n\n\n\n

Calcular los tama\u00f1os de paso dxi<\/code> en cada frontera y plantear la integraci\u00f3n con f\u00f3rmulas compuestas.<\/p>\n\n\n\n

Usando los datos de las coordenadas de obtiene cada<\/p>\n\n\n\n

dxi = xi[i+1]-xi[i]<\/code><\/p>\n\n\n\n

De forma semejante se encuentra cada dxj<\/code>, seleccionando los m\u00e9todos seg\u00fan se disponga de tama\u00f1o de paso iguales y consecutivos como se muestra en la tabla ampliada.<\/p>\n\n\n\n

Frontera superior<\/strong><\/p>\n\n\n\n

 <\/td> <\/td>Trapecio<\/td>Trapecio<\/td> <\/td>Trapecio<\/td>Trapecio<\/td> <\/td>Simpson 1\/3<\/td><\/tr>
 <\/td>Trapecio<\/td>Trapecio<\/td>Simpson 1\/3<\/td>Trapecio<\/td>Simpson 1\/3<\/td> <\/td> <\/td><\/tr>
dxi<\/strong><\/td>40<\/td>100<\/td>-30<\/td>66<\/td>20<\/strong><\/td>20<\/strong><\/td>79<\/td>125<\/td>54<\/td>50<\/strong><\/td>50<\/strong><\/td>20<\/em><\/strong><\/td>20<\/em><\/strong><\/td>--<\/td><\/tr>
xi<\/td>410<\/td>450<\/td>550<\/td>520<\/td>586<\/td>606<\/td>626<\/td>705<\/td>830<\/td>884<\/td>934<\/td>984<\/td>1004<\/td>1024<\/td><\/tr>
yi<\/td>131<\/td>194<\/td>266<\/td>337<\/td>402<\/td>483<\/td>531<\/td>535<\/td>504<\/td>466<\/td>408<\/td>368<\/td>324<\/td>288<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Frontera Inferior<\/strong><\/p>\n\n\n\n

 <\/td> <\/td> <\/td> <\/td>Trapecio<\/td><\/tr>
 <\/td>Simpson 3\/8<\/td> <\/td><\/tr>
dxj<\/strong><\/td>190<\/strong><\/td>190<\/strong><\/td>190<\/strong><\/td>44<\/td>--<\/td><\/tr>
xj<\/td>410<\/td>600<\/td>790<\/td>980<\/td>1024<\/td><\/tr>
yj<\/td>131<\/td>124<\/td>143<\/td>231<\/td>288<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Desarrollando con instrucciones sobre el arreglo en Python con la instrucci\u00f3n np.diff(xi)<\/code>.<\/p>\n\n\n\n

>>> xi = [410, 450, 550, 520, 586, 606, 626, 705, 830,\n          884, 934, 984, 1004, 1024]\n>>> xi = np.array(xi)\n>>> dxi = np.diff(xi)\n>>> dxi\narray([ 40, 100, -30, 66, 20, 20, 79, 125, 54,\n        50, 50, 20, 20<\/strong>])\n>>> xj = [410, 600, 790, 980, 1024]\n>>> dxj = np.array(xj)\n>>> dxj = np.diff(xj)\n>>> dxj\narray([190, 190, 190, 44<\/strong>])\n>>><\/code><\/pre>\n\n\n\n
literal b<\/h2>\n\n\n\n
Desarrollar las expresiones<\/strong> del \u00e1rea para las coordenadas de la frontera superior<\/strong>, seg\u00fan el literal a. Cuando se tienen dos tama\u00f1os de paso iguales se usa Simpson de 1\/3.<\/p>\n\n\n I_{superior} = 40\\Big(\\frac{131+194}{2}\\Big) +100\\Big(\\frac{194+266}{2}\\Big) +<\/span>\n\n\n -30\\Big(\\frac{266+337}{2}\\Big) +66\\Big(\\frac{337+402}{2}\\Big)+<\/span>\n\n\n + \\frac{20}{3}\\Big(402+4(483)+531\\Big) +<\/span>\n\n\n +79\\Big(\\frac{531+535}{2}\\Big) +125\\Big(\\frac{535+504}{2}\\Big) + 54\\Big(\\frac{504+466}{2}\\Big) +<\/span>\n\n\n + \\frac{50}{3}\\Big(466+4(408)+368\\Big) +<\/span>\n\n\n + \\frac{20}{3}\\Big(368+4(324)+288\\Big)<\/span>\n\n\n I_{superior} = 254753,33 <\/span>\n\n\n\n
literal c<\/h2>\n\n\n\n
Realice los c\u00e1lculos para la frontera inferior<\/strong> y encuentre el \u00e1rea afectada<\/strong>. Con tres tama\u00f1os de paso iguales se usa Simpson de 3\/8.<\/p>\n\n\n I_{Inferior} = \\frac{3}{8}(190)\\Big(131+3(124)+3(143)+231\\Big) <\/span>\n\n\n +44\\Big(\\frac{231+288}{2}\\Big) = 94281,75<\/span>\n\n\n\n
\u00c1rea total afectada:<\/p>\n\n\n A_{afectada} = I_{superior} - I_{Inferior} = 254753,33 -94281,75 <\/span>\n\n\n A_{afectada} = 160.471,58 <\/span>\n\n\n\n
literal d<\/h2>\n\n\n\n
Estime la cota de error en los c\u00e1lculos.<\/p>\n\n\n\n
Considere usar las unidades en Km en lugar de metros para los tama\u00f1os de paso.<\/p>\n\n\n Error_{truncaSup} = O( 0.040^3) + O(0. 100^3)+ O( (-0.030)^3) + O( 0.066^3)+<\/span>\n\n\n + O( 0.020^5) + O(0. 079^3)+ O( 0.125^3) + O( 0.054^3)+<\/span>\n\n\n + O( 0.050^5) + O( 0.020^5)<\/span>\n\n\n Error_{truncaInf} = O( 0.190^5) + O(0. 044^3) <\/span>\n","protected":false},"excerpt":{"rendered":"
Ejercicio: 2Eva2024PAOII_T1 \u00c1rea de incendio forestal en Cerro Azul literal a Calcular los tama\u00f1os de paso dxi en cada frontera y plantear la integraci\u00f3n con f\u00f3rmulas compuestas. Usando los datos de las coordenadas de obtiene cada dxi = xi[i+1]-xi[i] De forma semejante se encuentra cada dxj, seleccionando los m\u00e9todos seg\u00fan se disponga de tama\u00f1o de […]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-p-ginas-mn-ejemplos","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[58,54],"class_list":["post-10629","post","type-post","status-publish","format-standard","hentry","category-mn-s2eva30","tag-ejemplos-python","tag-mnumericos"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10629","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=10629"}],"version-history":[{"count":3,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10629\/revisions"}],"predecessor-version":[{"id":23885,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10629\/revisions\/23885"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=10629"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=10629"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=10629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}