Unformatted text preview: 2 ) f 2 ( x 1 ,x 2 ) f 3 ( x 1 ,x 2 ) . Often we shall be sloppy and simply write F ( −→ x ) = f 1 ( x 1 ,x 2 ) f 2 ( x 1 ,x 2 ) f 3 ( x 1 ,x 2 ) . We cannot draw (or imagine drawing) the “graph” of a mapping F : R n → R m if m + n > 3, but we can try to picture its action by looking at the images of various sets. ±or example, one can view a change of coordinates in the plane or space as a mapping: speciFcally, the calculation that gives the rectangular coordinates of a point in terms of its polar coordinates is the map P : R 2 → R 2 from the ( r,θ )plane to the ( x,y )plane given by P ( r,θ ) = b r cos θ r sin θ B . We get a picture of how it acts by noting that it takes horizontal ( resp . vertical) lines to rays from ( resp . circles around) the origin (±igure 4.1 )....
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 Spring '08
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 Calculus, Transformations, Vectors, Coordinate system, Polar coordinate system

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