James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

16 Vector Calculus 1067
Parametric surfaces, which
are studied in Section 16.6,
are frequently used by
programmers in creating the
sophisticated software used in
the development of computer
animated films like the Shrek
series. The software employs
parametric and other types of
surfaces to create 3D models
of the characters and objects
in a scene. Color, texture, and
lighting is then rendered to
bring the scene to life.
Everett Collection / Glow Images
In this chapter we study the calculus of vector fields. (These are functions that assign vectors
to points in space.) In particular we define line integrals (which can be used to find the work
done by a force field in moving an object along a curve). Then we define surface integrals (which
can be used to find the rate of fluid flow across a surface). The connections between these new
types of integrals and the single, double, and triple integrals that we have already met are given
by the higher-dimensional versions of the Fundamental Theorem of Calculus: Green’s Theorem,
Stokes’ Theorem, and the Divergence Theorem.
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.