January 2012
Intermediate to advanced
384 pages
8h 37m
English
Content preview from Calculus II For Dummies, 2nd Edition
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Chapter 14
Multivariable Calculus
In This Chapter
Visualizing vectors
Making the leap from two to three dimensions
Understanding cylindrical and spherical coordinates
Using partial derivatives
Sorting out and solving multiple integrals
Space, as Captain Kirk says during the opening credits of the television series Star Trek, is the final frontier. Multivariable calculus (also known as Calculus III) focuses on techniques for doing calculus in space — that is, in three dimensions.
Mathematicians have a variety of terms for three dimensions: 3-D, 3-space, and R3 are the most common. Whatever you call it, adding a dimension makes multivariable calculus more interesting and useful, but also a bit trickier than single variable calculus.
In this chapter, I give you a quick introduction to multivariable calculus, touching on the highlights usually taught in a Calculus III class. First, I show you how vectors provide a method for linking a value with a direction. Next, I introduce you to three ...
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