In Calculus I and in most of Calculus II we concentrated on
functions of one variable. In Calculus
III we will extend our knowledge of calculus into functions of two or more
variables. Despite the fact that this
chapter is about derivatives we will start out the chapter with a section on
limits of functions of more than one variable.
In the remainder of this chapter we will be looking at differentiating
functions of more than one variable. As
we will see, while there are differences with derivatives of functions of one
variable, if you can do derivatives of functions of one variable you shouldn’t
have any problems differentiating functions of more than one variable.
Here is a list of topics in this chapter.
Limits
Taking limits of functions of several
variables.
Partial Derivatives In this section we will introduce the idea of
partial derivatives as well as the standard notations and how to compute them.
Interpretations of Partial Derivatives Here we will take a look at a couple of
important interpretations of partial derivatives.
Higher Order Partial Derivatives We will take a look at higher order partial
derivatives in this section.
Differentials In this section we extend the idea of
differentials to functions of several variables.
Chain
Rule Here we will look at the chain rule for
functions of several variables.
Directional Derivatives We will introduce the concept of directional
derivatives in this section. We will
also see how to compute them and see a couple of nice facts pertaining to
directional derivatives.