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Métodos matemáticos de la ingeniería by Mariaca Gaspar, Carlos Roman

Métodos matemáticos de la ingeniería

by Carlos Roman Mariaca Gaspar , Jesús de la Cruz Alejo , Pedro Romano Aportela
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Book cover type: Paperback
  • ISBN13: 9781980214854
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Publication Date:
  • Pages: 188
  • Original Price: USD 17.99
  • Language: Spanish
  • Edition: N/A
  • Item Weight: 332 grams
  • BISAC Subject(s): Teaching / Subjects / Mathematics

La modelación de un sistema físico generalmente se da en forma de una ecuación diferencial y, por lo tanto, la solución de éstas nos representan la evolución del propio sistema. En este texto estudiaremos la teoría concerniente a las ecuaciones diferenciales ordinarias de primero y segundo orden, analizando de manera detallada los diferentes métodos de solución y sobre todo las aplicaciones en diferentes áreas de la ingeniería. Este libro tiene por objetivo dar las bases teóricas suficientes para que el lector pueda continuar sus estudios en las aplicaciones a los sistemas de ecuaciones diferenciales no lineales, tópico de interés fundamental en el estudio de teoría de control y en el análisis de los sistemas dinámicos. En el capítulo 1 se estudian las ecuaciones diferenciales de primer orden y de primer grado, en particular a las ecuaciones de variables separables, homogéneas, exactas, lineales y de Bernoulli. En el capítulo 2 se estudian a las ecuaciones diferenciales de segundo orden, y con el fin de darle un mayor contenido físico a la teoría, este estudio se hace a través del análisis del oscilador armónico considerando varias características como es el caso de un oscilador amortiguado, sobre amortiguado y forzado. En el capítulo 3 se estudia de manera exhaustiva la transformada de Laplace directa e inversa y su aplicación directa en la solución de ecuaciones diferenciales, sistemas de ecuaciones y la solución de ecuaciones integro diferenciales. En el capítulo 4 se estudian los conceptos básicos del análisis clásico de Fourier, así como el cálculo de los coeficientes de las series de Fourier en problemas donde se aprecia la metodología y como se puede simplificar los cálculos usando propiedades de las funciones.

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