MAT 213 Lecture Notes - Lecture 20: Cartesian Coordinate System, Polar Coordinate System, Multiple Integral

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20 Jan 2018
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12. 3 double integrals in polar coordinates notes: sterling. Provide a generalization to each of the key terms listed in this section. When it comes to both polar and rectangular coordinates, the polar coordinates (which are in the form of (r, )) are quite similar to rectangular coordinates (which are in the form of (x, y)) by the following three equations: Equations r2 = x2 + y2 x = r cos y = r sin . When it comes to polar graphing, some regions can be in special cases of a polar rectangle that can be in the following form: R = {(r, ) | a r b, } Then actual polar subrectangle"s center is the following: Rij = {(r, ) | ri 1 r ri, j 1 j} The polar subrectangle"s center has the following two polar coordinates: i = 1 r . 2 (ri 1+ri ) and j = 1.

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