Paul's Online Math Notes
[Notes]
Notice

On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.

I have spent the better part of the last year or so rebuilding the site from the ground up and the result should (hopefully) lead to quicker load times for the pages and for a better experience on mobile platforms. For the most part the update should be seamless for you with a couple of potential exceptions. I have tried to set things up so that there should be next to no down time on the site. However, if you are the site right as the update happens there is a small possibility that you will get a "server not found" type of error for a few seconds before the new site starts being served. In addition, the first couple of pages will take some time to load as the site comes online. Page load time should decrease significantly once things get up and running however.

Paul
August 7, 2018

Calculus II - Notes
 Applications of Integrals Previous Chapter Next Chapter Series & Sequences Probability Previous Section Next Section Parametric Equations and Curves

## Parametric Equations and Polar Coordinates

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.

 Probability Previous Section Next Section Parametric Equations and Curves Applications of Integrals Previous Chapter Next Chapter Series & Sequences

[Notes]

 © 2003 - 2018 Paul Dawkins