In this section we will be looking at parametric equations and polar coordinates. While the two subjects dont 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.
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. Well introduce polar coordinates in this section. Well 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). 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.
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 well be covering in this chapter.
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