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Calculo Vectorial
Paperback
Series: Colección de Jorge Sáenz, Book 5
ISBN13: 9789801265139
Publisher: Lightning Source Inc
Published: May 12 2016
Pages: 670
Weight: 1.94
Height: 1.34 Width: 6.00 Depth: 9.00
Language: Spanish
Obra esta diseñada para ser el texto de un curso de cálculo multivariable, por lo que puede considerarse como una continuación de nuestros textos Calculo Diferencial y Calculo Integral. Este texto, junto a los dos tÃtulos antes mencionados, cubren todo, o casi todo el contenido de Cálculo requerido en los programas superiores de Ciencias e IngenierÃa.
Se ha buscado equilibrar la teorÃa, la práctica y las aplicaciones. Cada tema es acompañado de numerosos ejemplos. Cada sección es reforzada con una selección de problemas resueltos.
Los problemas tÃpicos y de relevancia, son desarrollados con todo detalle. La gran mayorÃa de teoremas son presentados con su respectiva demostración. Además, a lo largo de toda la obra, son resaltados ciertos aspectos históricos.
CONTENIDO
CapÃtulo 1. Vectores y geometrÃa analÃtica del espacio
-Sistema tridimensional de coordenadas rectangulares.
-Vectores en los espacios de dos y tres dimensiones.
-Producto escalar.
-Producto vectorial.
-Rectas y planos en el espacio.
-Superficies cilÃndricas, cuadráticas y superficies de revolución.
-Coordenadas cilÃndricas y esféricas.
CapÃtulo 2. Funciones vectoriales
-Funciones vectoriales de variable real.
-Derivadas e integrales de funciones vectoriales.
-Longitud de arco y cambio de parámetro.
-Vector tangente, vector normal y vector binormal.
-Curvatura, torsión y aceleración.
-Las leyes de Kepler.
-Superficies paramétricas.
CapÃtulo 3. Derivadas parciales
-Funciones de dos o más variables.
-LÃmites y continuidad.
-Derivadas parciales.
-Funciones diferenciables, plano tangente y aproximación lineal.
-La regla de la cadena.
-Derivadas direccionales y gradiente.
-Máximos y mÃnimos de funciones de varias variables.
-Multiplicadores de Lagrange.
-Fórmula de Taylor para funciones de dos variables.
CapÃtulo 4. Integrales múltiples
-Integrales dobles sobre rectángulos.
-Integrales dobles sobre regiones generales.
-Volumen y área con integrales dobles.
-Integrales dobles en coordenadas polares.
-Aplicaciones de las integrales dobles.
-Area de una superficie.
-Integrales triples.
-Integrales triples en coordenadas cilÃndricas y esféricas.
-Cambio de variables en integrales múltiples.
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