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HOMOTECIA Nº 6-15 Junio 2017 HOMOTECIA Nº 6 – Año 15 Martes, 1º de Junio de 2017 1 Entre las expectativas futuras que se tienen sobre un docente en formación, está el considerar como indicativo de que logrará realizarse como tal, cuando evidencia confianza en lo que hace, cuando cree en sí mismo y no deja que su tiempo transcurra sin pro pósitos y sin significado. Estos son los principios que deberán pautar el ejercicio de su magisterio si aspira tener éxito en su labor, lo cual mostrará mediante su afán por dar lo bueno dentro de sí, por hacer lo mejor posible, por comprometerse con el porvenir de quienes confiadamente pondrán en sus manos la misión de enseñarles. Pero la responsabilidad implícita en este proceso lo debería llevar a considerar seriamente algunos GIACINTO MORERA (1856 – 1907 ) aspectos. Obtener una acreditación para enseñar no es un pergamino para exhib ir con petulancia ante familiares y Nació el 18 de julio de 1856 en Novara, y murió el 8 de febrero de 1907, en Turín; amistades. En otras palabras, viviendo en el mundo educativo, es ambas localidades en Italia. asumir que se produjo un cambio significativo en la manera de Matemático que hizo contribuciones a la dinámica. participar en este: pasó de ser guiado para ahora guiar. No es que no necesite que se le orie nte como profesional de la docencia, esto es algo que sucederá obligatoriamente a nivel organizacional, Giacinto Morera , hijo de un acaudalado hombre de pero el hecho es que adquirirá una responsabilidad mucho mayor negocios, se graduó en ingeniería y matemáticas en la porque así como sus preceptores universitarios tuvieron el compromiso de formarlo y const ruirlo cultural y Universidad de Turín, Italia, habiendo asistido a los académicamente, él tendrá el mismo compromiso de hacerlo con cursos por Enrico D'Ovidio, Angelo Genocchi y sus discípulos, sea cual sea el nivel docente donde se desempeñe. Francesco Siacci. Consider ó Siacci no sólo su Como consecuencia, deberá considerar lo siguiente: permanecer "maestro" en ciencia y sino también su maestro cinco o más años en la institución universitaria o pedagógica de acerca de la vida. Morera amplió su s conocimientos donde egrese, no lo hará definitivamente un erudito ni el mejor docente en la disciplina en la cual se ha formado. El de matemáticas, primero en la Universidad de Pavía , conocimiento disciplinario que posee (contenidos temáticos y Italia, bajo la dirección de Eugenio Beltrami y Felice didáctica), por ahora solo es una pequeña parte del conglomer ado Casorati, luego en la Universida d de Pisa bajo la total que existe del mismo y para adquirir más de éste, la solución dirección de Enrico Betti y Ulisse Dini y finalmente está en estudiar e investigar más. La realización exitosa de la transposición didáctica del conocimiento disciplinario que en Leipzig con Adolph Meyer y Felix Klein. domina será una consecuencia natural de su propia acción; y e l Ganó el concurso para el cargo de profesor de final exitoso se posibilitará cuando muestre su intención de ayudar a sus discípulos en transformarse en seres virtuosos, a la mecánica racional en la Universidad de Génova, par que conscientemente intenta también él llegar a serlo. Los donde se quedó y vivió durante catorce años. En valores estarán siempre presentes en el contexto de su vida pero Génova fue también profesor de física matemática, para llegar a ser virtuoso tiene que practicarlos. Deberá practicar convirtiéndose luego en Decano de la Facultad y en valores para ser ante sus estudiantes ejemplo de virtud y a la vez, debe promover en estos jóvenes su práctica para que lleguen a ser Rector de la Universidad. personas buenas, buenos ciudadanos, mejores seres hum anos. En En 1900 se fue a la Universidad de Turín donde cuanto a lo organizacional, serán las vivencias laborales en la institución educativa donde se harán mejores docentes; con la enseñó mecánica avanzada y racional, tanto en la práctica del ensayo y del error crecerán en el tiempo como Universidad como en la escuela Po litécnica. Allí, gestores administrativos y organizativos de la educación. La como lo había sido en Génova, fue nombrado decano responsabilidad y la honestidad personal deberán caracterizar su de la Facultad de Ciencias. Fue miembro de la profesionalidad. Por ahora, ante la coyuntura sociopolítica que da Academia de Ciencias de Turín y de la Accademia la performatividad actual a Venezuela, pareciera que se está hablando de un sueño, de un reto difícil, de una utopía, pero es dei Lincei. una posibilidad que no se debería dejar de intentar con sencillez, Somigliana describió a Morera como un "correcto y sin engreimientos, con vocación, con pasión y deseo por educar, por el bien de la sociedad y el de la humanidad. Por ello aceptar cuidadoso hombre ", un "profesor e ficaz" y escribió la crítica y practicar la autocrítica sintiendo una insegu ridad [1]: práctica, conduce a todo docente a mejorar sus métodos y estrategias para enseñar, y hasta su manera de actuar en sociedad. ... no es posible argumentar que él era muy Afortunado el educador quien encuentra entre sus discípulos uno creativo; su s pensamientos fueron en que incomoda su seguridad docente (altera su zona de confort ). general analíticos y crític os, así que él no No debe sentir miedo sino aceptar que es un reto al cual le invitan creó nuevas teorías, pero desarrolló las que superar, porque el que se suceda una incomodidad académica posiblemente sea una oportunidad para con base en su autocrítica, ya existían [... consistieron sus resultados corregir sus herramientas didácticas y hasta sus actitudes en] soluciones a los problemas complicados per sonales, creciendo así como docente y llenando su vida de y difíciles. satisfacciones . (CONTINÚA EN LA SIGUIENTE PÁGINA) "El mundo continuará como siempre, con sus altibajos. ¿Dónde buscaremos el rumbo a seguir, un sentido de orientación? No en los prejuicios que albergamos, debido a los hábitos y a la influencia de nuestra familia, nuestro país o el mundo, sino en la voz de la verdad que resuena en nuestro interior y nos orienta". PARAMAHANSA YOGANANDA en “Amante Cósmico” HOMOTECIA Nº 6 – Año 15 Martes, 1º de Junio de 2017 2 (VIENE DE LA PÁGINA ANTERIOR) Morera estudió los problemas fundamentales que se presentan en la dinámica con particular atención a la utilización del método Pfaff aplicado a sistemas Jacobianos de ecuaciones diferenciales parciales y el problema de las transformaciones de Lie de las ecuaciones canónicas de movimiento. Él desarrolló el estudio de las funciones armónicas, aplicando los resultados obtenidos por Pizzetti, encontrando una simple expresión para el campo gravitacional interno y externo de un elipsoide, para resolver el problema de Dirichlet. Estaba interesado también en la integral de Cauchy para la representación de funciones de una variable compleja, en la discontinuidad de los diferenciales de la función potencial y en la fórmula de representación de Gauss. Finalmente observamos que mejoró la prueba de la fórmula de Kirchhoff para el principio de Huygens. Referencias.- Artículos: 1. C. Somogliana, Giacinto Morera, Il Nuovo Cimento (V) XVII (1909), 191-194. 2. C. Somogliana, Giacinto Morera, Atti Acc. Sci. Torino 45 (1909-10), 573-580. GIACINTO MORERA Imágenes obtenidas de: Versión en español por R. Ascanio H. del artículo de Umberto Lucia, Sociedad Italiana de la Historia de la Matemática, sobre “Jean-Marie Duhamel” (Marzo 2006). FUENTE: MacTutor History of Mathematics. [http://www-history.mcs.st-andrews.ac.uk/Biographies/Morera.html]. HOMOTECIA Nº 6 – Año 15 Martes, 1º de Junio de 2017 3 Aportes al conocimiento Elementos Básicos del Cálculo Diferencial (23) ÍNDICE.- Límites de Funciones. Cálculo de Límites de Funciones Trigonométricas utilizando tablas. Límites Notables. Ejemplos de aplicación de los límites notables de las funciones trigonométricas. Cálculo de Límites de Funciones Logarítmicas utilizando tablas. Límite notable. Ejemplo aplicando el límite notable de las funciones logarítmicas. Límites de Funciones Exponenciales. LÍMITES DE FUNCIONES.- CÁLCULO DE LÍMITES DE FUNCIONES TRIGONOMÉTRICAS UTILIZANDO TABLAS. LÍMITES NOTABLES.- Considérense los siguientes ejemplos: 1.- Calcular Lim Sen x . x→0 Solución : Como x tiende a cero, consideremos que ∈ * para este ejemplo. Luego en estas condiciones se toman valores a la derecha y a la x E1 )0( izquierda del cero y procedemos a llenar las siguientes tablas: x > 0 ( x → 0+ ) x 1 0,5 0,1 0,01 0,001 0,0001 f( x ) = Sen x 0,017452 0,008726 0,001745 0,000174 0,000017 0,000001 x < 0 ( x → 0− ) x -1 -0,5 -0,1 -0,01 -0,001 -0,0001 f( x ) = Sen x -0,017452 -0,008726 -0,001745 -0,000174 -0,000017 -0,000001 Luego: Lim Sen x = 0 x→0 2.- Calcular Lim Cos x . x→0 Solución : x > 0 ( x → 0+ ) x 1 0,5 0,1 0,01 0,001 0,0001 f( x ) = Cos x 0,999847695 0,999961923 0,999998476 0,999999984 0,999999999 1 x < 0 ( x → 0− ) x -1 -0,5 -0,1 -0,01 -0,001 -0,0001 f( x ) = Cos x 0,999847695 0,999961923 0,999998476 0,999999984 0,999999999 1 Luego: Lim Cos x = 1 x→0 HOMOTECIA Nº 6 – Año 15 Martes, 1º de Junio de 2017 4 Sen x 3.- Calcular Lim . x→0 x Solución : x > 0 ( x → 0+ ) x 1 0,1 0,01 0,001 0,0001 0,00001 Sen x f() x = 0,841470984 0,998334166 0,999983333 0,999999833 0,999999998 1 x x < 0 ( x → 0− ) x -1 -0,1 -0,01 -0,001 -0,0001 -0,00001 Sen x f() x = 0,841470984 0,998334166 0,999983333 0,999999833 0,999999998 1 x Sen x Luego: Lim = 1 x→0 x Estos límites que hemos calculado utilizando tablas, son llamados límites notables trigonométricos , y sus valores se aplican directamente cuando se están calculando límites de funciones que involucran funciones trigonométricas.
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