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by Jorge Saenz (Author)
Obra diseñada para ser el texto de un segundo o un tercer curso de Cálculo, para estudiantes de ciencias o ingeniería.
Este texto, junto al libro Cálculo Diferencial, cubren todo, o casi todo, el contenido del cálculo de una variable.
Se ha buscado equilibrar la teoría, la práctica y las aplicaciones. Cada tema es acompañado de numerosos ejemplos. Cada sección es reforzada con una selección de problemas resueltos. Aquí, los problemas típicos y de relevancia, son desarrollados con todo detalle. La gran mayoría de teoremas son presentados con su respectiva demostración. Además, a lo largo de toda la obra, son resaltados ciertos aspectos históricos.
CONTENIDO:
Capítulo 1. La integral indefinida
-La antiderivada.
-Integración por sustitución.
-Integración por partes
Capítulo 2. Otras tecnicas de integración
-Integrales de productos trigonométricas.
-Sustitución trigonométrica.
-Integrales Hiperbólicas.
-Integración por fracciones parciales: Casos I y II.
-Integración por fracciones parciales: Casos III y IV.
-Integrales racionales de seno y coseno. Sustitución de Weirerstrass.
-Algunas integrales irracionales.
-Ecuaciones diferenciales elementales.
Capítulo 3. La integral definida
-La notación sigma.
-Área.
-La integral definida.
-Área entre curvas.
-Valor medio para integrales.
-Integración numérica.
Capítulo 4. Aplicaciones de la integral definida
-Volumen. Método de las rebanadas.
-Volumen de un sólido de revolución. Métodos del disco y de las arandelas
-Volumen. Método de los tubos cilíndricos.
-Longitud de una curva plana.
-Área de una superficie de revolución.
-Momentos y centros de masa.
-Trabajo.
-Presión y fuerza hidrostática.
Capítulo 5. Integrales impropias y algunas funciones especiales
-Introducción.
-Integrales impropias de primera especie: Límites de integración infinitos
-Integrales impropias de segunda especie: Integrandos infinitos
-Criterios de convergencia para integrales impropias.
-La función gamma.
-La función beta.
-Transformada de Laplace.
Capítulo 6. Ecuaciones paramétricas
-Ecuaciones paramétricas.
-Pendiente y concavidad de curvas paramétricas.
-Longitudes, áreas, volúmenes y curvas paramétricas
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