Obra esta dise�ada para ser el texto de un curso de c�lculo multivariable, por lo que puede considerarse como una continuaci�n de nuestros textos Calculo Diferencial y Calculo Integral. Este texto, junto a los dos t�tulos antes mencionados, cubren todo, o casi todo el contenido de C�lculo requerido en los programas superiores de Ciencias e Ingenier�a.

Se ha buscado equilibrar la teor�a, la pr�ctica y las aplicaciones. Cada tema es acompa�ado de numerosos ejemplos. Cada secci�n es reforzada con una selecci�n de problemas resueltos.

Los problemas t�picos y de relevancia, son desarrollados con todo detalle. La gran mayor�a de teoremas son presentados con su respectiva demostraci�n. Adem�s, a lo largo de toda la obra, son resaltados ciertos aspectos hist�ricos.

CONTENIDO

Cap�tulo 1. Vectores y geometr�a anal�tica 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 cil�ndricas, cuadr�ticas y superficies de revoluci�n.

-Coordenadas cil�ndricas y esf�ricas.

Cap�tulo 2. Funciones vectoriales

-Funciones vectoriales de variable real.

-Derivadas e integrales de funciones vectoriales.

-Longitud de arco y cambio de par�metro.

-Vector tangente, vector normal y vector binormal.

-Curvatura, torsi�n y aceleraci�n.

-Las leyes de Kepler.

-Superficies param�tricas.

Cap�tulo 3. Derivadas parciales

-Funciones de dos o m�s variables.

-L�mites y continuidad.

-Derivadas parciales.

-Funciones diferenciables, plano tangente y aproximaci�n lineal.

-La regla de la cadena.

-Derivadas direccionales y gradiente.

-M�ximos y m�nimos de funciones de varias variables.

-Multiplicadores de Lagrange.

-F�rmula de Taylor para funciones de dos variables.

Cap�tulo 4. Integrales m�ltiples

-Integrales dobles sobre rect�ngulos.

-Integrales dobles sobre regiones generales.

-Volumen y �rea con integrales dobles.

-Integrales dobles en coordenadas polares.

-Aplicaciones de las integrales dobles.

-Area de una superficie.

-Integrales triples.

-Integrales triples en coordenadas cil�ndricas y esf�ricas.

-Cambio de variables en integrales m�ltiples.

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