Calculo 2 De dos variables_9na Edición - Ron Larson

15 Vector Analysis
Vector Analysis
Análisis vectorial
In In this chapter, you will study vector
En fields, este line capítulo se estudiarán los campos
vectoriales, In this integrals,
chapter, and integrales you
to de will surface
línea study integrals.
to e integrales vector
You will de fields, learn
superficie. line to
integrals, use these to Se aprenderá and as
a surface determine
usarlos integrals.
real-life quantities para
determinar You will such
learn cantidades to use as en these surface area,
la vida to real, determine
mass, flux, como
el real-life work,
área de quantities and energy.
una superficie, such masa, surface flujo, trabajo
In mass, y this energía.
flux, chapter, work, you and should energy.
learn the
En following.
In este this capítulo, chapter, se you aprenderá: should learn the
■ following.
How Cómo to to dibujar sketch un a a campo vector vectorial, field, determine
deter-
whether minar si a es a conservativo, is encontrar una
area,
In
■ How to vector
sketch field
a is
vector conservative,
field, determine
find función a a de potencial, el rotacional y la
divergencia.
whether potential function,
a vector find (15.1)
field is curl,
conservative,
and
find divergence.
find (15.1)
a potential function, find curl, and
■ How Cómo find to divergence. to encontrar find a a piecewise una (15.1) parametrización
smooth
parametrization, continua por secciones, write escribir y evaluar a
■ una
How to find
de
a línea
piecewise and evaluate y utilizar
smooth
a
line integral, el teorema
de parametrization, and use Green’s
Green. (15.2, 15.4) write Theorem.
and evaluate a
(15.2, 15.4)
Cómo
line integral, usar el teorema
and use
fundamental
Green’s Theorem.
de
■■ How to las
(15.2, to integrales
15.4) use the Fundamental Theorem
de línea, la independencia
of of Line of ■
■ de How Integrals,
la trayectoria to independence
use the y Fundamental of
la conservación Theorem
path,
■
de
and energía. of conservation
Line (15.3) Integrals,
of of independence energy. (15.3)
of path,
■ How Cómo and to conservation to dibujar sketch una a a parametric superficie of energy. paramétrica, surface,
(15.3)
find encontrar a a set of un conjunto de ecuaciones to
■ How set
to of
sketch parametric equations
a parametric to
surface,
represent paramétricas find a set
a a surface,
of parametric representar find a a
equations normal una super-
vector,
to
find ficie, represent
a a determinar tangent a surface, plane, un vector and
find find
a normal, normal the un area
vector,
of of plano find
a a parametric a tangente y surface.
plane, el área and de (15.5)
find una superficie the area
■■ How paramétrica.
of a to parametric to evaluate (15.5) a surface. a surface (15.5)
integral,
■
determine Cómo evaluar the una integral of de a superficie,
■ How to evaluate orientation of
a surface a
integral,
surface,
evaluate determinar a a la orientación de una superficie,
determine flux integral,
evaluar
the una
orientation and use
integral de
of the
flujo
a surface,
Divergence Theorem. y usar
el
evaluate
teorema
a
de
flux (15.6,
la
integral, 15.7)
divergencia.
and (15.6,
use the
15.7)
■■ How Divergence to to use Stokes’s Theorem. Theorem (15.6, to 15.7) to evaluate
■ Cómo utilizar el teorema de Stokes para
a a line or a ■ evaluar How integral or
to una use integral Stokes’s a surface integral
de Theorem and
línea o superficie to evaluate
how to to to y a cómo line use
integral curl to
usar el rotacional or analyze
a the
surface motion
para integral analizar andel
of of a a movimiento how rotating liquid. use curl (15.8)
de un to líquido analyze que the gira. motion (15.8)
of a rotating liquid. (15.8)
■
NASA
While on on the ground awaiting liftoff, space shuttle astronauts have access to to a a
NASA
Mientras basket and is to as far While on esperan slide
the wire
ground el despegue system
awaiting en that liftoff, tierra, is designed space los astronautas to
shuttle move astronauts del them transbordador as far
have away access espacial from the
to a
■■
tienen shuttle as in an of by
basket acceso as possible
and slide a un wire sistema in an emergency
system alámbrico situation.
that is de designed canasta Does to y move tobogán the amount
them diseñado of
as work
far away para done transportarlos
the for ■ shuttle lo gravitational más as lejos possible posible force field
by
from the
in an del emergency transbordador vary for different situation. en una slide Does situación wire paths
the amount de emergencia. between two
of work done ¿La fixed
cantidad by
de points? the trabajo (See
gravitational realizado Section force por 15.3, field campo Exercise vary de for fuerza 39.)
different gravitacional slide wire varía paths para between diferentes two fixed trayectorias
points? entre (See dos Section puntos fijos 15.3, del Exercise tobogán 39.) alámbrico? (Ver la sección 15.3, ejercicio 39.)
In En In Chapter el capítulo 15, 15 you se will combinará combine el your conocimiento knowledge of of de vectors vectores with con your el knowledge del cálculo of of integral. La calculus. sección Section 15.1 introduce 15.1
campos introduces vectoriales, as of In Chapter fields, como los que muestran arriba. Ejemplos de campos vectoriales incluyen campos de velocidad,
fields, campos and electromagnéticos y campos gravitacionales.
15, you such
will combine as those shown
your knowledge above. Examples
of vectors of
with vector
your fields
knowledge include velocity
of integral fields,
calculus. electromagnetic
Section 15.1
introduces gravitational fields.
vector fields, such as those shown above. Examples of vector fields include velocity fields, electromagnetic
fields, and gravitational fields.
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