265L04 - LESSON 4 Other Coordinate Systems READ: Section...

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LESSON 4 Other Coordinate Systems READ: Section 13.7 NOTES: Recall that besides the commonly used Cartesian coordinates, points in the plane can be described using polar coordinates. The two main advantage of polar coordinates are (1) some curves which have very complicated Cartesian equations have very simple polar equations and (2) many difficult integrals can be recast in polar coordinates where they become routine. In 3-space, there are two coordinate systems in addition to the Cartesian system we have been using so far. These system offer the same two advantages as polar coordinates in the plane. In this section, the discussion centers on the types of surfaces that can be neatly described in these alternative systems. Applications to integration will appear in Chapter 16. Of the two new coordinate systems for 3-space described in this section, the cylindrical coordinate system is the one most often used in real life, and, happily, it is also the easier of the two to visualize. If ( x,y,z ) are the Cartesian coordinates of a point in 3-space, then cylindrical coordinates of that point are obtained by replacing the x and y coordinates by their polar equivalents. If it has been a while since you’ve worked
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This note was uploaded on 02/24/2011 for the course MATH 265 taught by Professor Jerrymetzger during the Winter '11 term at North Dakota.

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265L04 - LESSON 4 Other Coordinate Systems READ: Section...

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