lecture16 - Lecture 16: Cylindrical and Spherical...

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Lecture 16: Cylindrical and Spherical Coordinates June 5, 2009 Lecture 16: Cylindrical and Spherical Coordinates
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Objectives 1 Convert between rectangular, cylindrical, and spherical coordinates. 2 Compute triple integrals using cylindrical coordinates. 3 Compute triple integrals using spherical coordinates. Lecture 16: Cylindrical and Spherical Coordinates
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Cylindrical coordinates Coordinates of a point given by ( r , θ, z ) Lecture 16: Cylindrical and Spherical Coordinates
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Conversion of coordinates To get from cylindrical to rectangular: x = r cos θ y = r sin θ z = z To get from rectangular to cylindrical: r 2 = x 2 + y 2 tan θ = y x z = z Lecture 16: Cylindrical and Spherical Coordinates
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Cylindrical coordinates A point is the intersection of a plane, a half-plane, and a cylinder. Lecture 16: Cylindrical and Spherical Coordinates
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ZZZ R f ( x , y , z ) dxdydz = Z β α Z b a Z s r f ( r cos θ, r sin θ, z ) rdzdrd θ where R is the “rectangle” given by
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This note was uploaded on 04/29/2010 for the course MATH 200 taught by Professor Unknown during the Spring '03 term at The University of British Columbia.

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lecture16 - Lecture 16: Cylindrical and Spherical...

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