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Matemáticas para la universidad, 3: Cálculo tensorial: continuación. Historia de la Relatividad General by Villalba, Juan

Matemáticas para la universidad, 3: Cálculo tensorial: continuación. Historia de la Relatividad General

by Juan Villalba
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Book cover type: Paperback
  • ISBN13: 9798614217303
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Publication Date:
  • Pages: 162
  • Original Price: USD 37.25
  • Language: Spanish
  • Edition: N/A
  • Item Weight: 245 grams
  • BISAC Subject(s): Geometry / Differential

Una de las principales dificultades que tal vez encuentren los estudiantes del cálculo tensorial es: cómo desarrollar una ecuación tensorial "abreviada" por medio de la notación de índices, para volver a obtener a partir de ella, el sistema de ecuaciones que permite hacer la transformación de coordenadas de unos sistemas a otros.Por ese motivo este número está dedicado a considerar, lo que podríamos llamar, las reglas fundamentales que hay que seguir al hacerlo.Se empieza a explicar también, que además de los vectores y cuadrivectores que ya hemos considerado, hay tensores de mayor orden, o de rango mayor, puesto que hay magnitudes físicas que requieren ser representadas por esas expresiones matemáticas mayores.Se trata en primer lugar el caso más sencillo: el de un tensor de 2 orden, y se muestra cual es la regla de transformación de coordenadas para dicho tensor, al pasar de un sistema a otro, es decir, cómo se calcula el valor de las componentes del tensor en un sistema de coordenadas, a partir de los valores conocidos de tales componentes en otro sistema, pues el tensor, al representar una magnitud física, sigue siendo la misma entidad, pero los valores de las componentes, como ya sabemos, y es fácil de entender, son distintos en sistemas de coordenadas diferentes, pero el tensor tendrá el mismo valor en cada "punto" de la variedad en que se encuentre, en todos los sistemas.Se muestra cómo obtener la ley de transformación, y se ilustra con ejemplos, así como también se ilustran con ejemplos las reglas a seguir para desarrollar una ecuación tensorial.Además de la importancia de los aspectos del cálculo tensorial que se tratan, esenciales para poner un buen fundamento para las consideraciones que seguirán, este número contiene un rasgo especial: incluye una exposición de los descubrimientos y el desarrollo de las ideas que llevaron a la formulación de la Relatividad, proporcionando así una comprensión de los conceptos de la teoría que servirá de guía para comprender en profundidad los aspectos de las matemáticas que se explicarán en los próximos números.Se consideran también las razones para usar "matrices y determinantes" cuando hay que tratar con sistemas de ecuaciones grandes, lo que es habitual en el estudio científico del mundo real, y se empieza a explicar cómo se deriva un "determinante", algo que tendrá importancia al proseguir el estudio de las matemáticas de la Relatividad General.

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