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In this section we will be looking at parametric equations
and polar coordinates. While the two
subjects don’t appear to have that much in common on the surface we will see
that several of the topics in polar coordinates can be done in terms of
parametric equations and so in that sense they make a good match in this
chapter.
We will also be looking at how to do many of the standard
calculus topics such as tangents and area in terms of parametric equations and
polar coordinates.
Here is a list of topics that we’ll be covering in this
chapter.
Parametric Equations and Curves 
An introduction to parametric equations and
parametric curves (i.e. graphs of
parametric equations)
Tangents with Parametric Equations Finding tangent lines to parametric curves.
Area
with Parametric Equations Finding the area under a parametric curve.
Arc Length with Parametric Equations Determining the length of a parametric curve.
Surface Area with Parametric Equations Here we will determine the surface area of a
solid obtained by rotating a parametric curve about an axis.
Polar Coordinates We’ll introduce polar coordinates in this
section. We’ll look at converting
between polar coordinates and Cartesian coordinates as well as some basic
graphs in polar coordinates.
Tangents with Polar Coordinates Finding tangent lines of polar curves.
Area
with Polar Coordinates Finding the area enclosed by a polar curve.
Arc Length with Polar Coordinates Determining the length of a polar curve.
Surface Area with Polar Coordinates Here we will determine the surface area of a
solid obtained by rotating a polar curve about an axis.
Arc Length and Surface Area Revisited In this section we will summarize all the arc
length and surface area formulas from the last two chapters.