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Unformatted text preview: Defn. Spherical Coordinates A point P in spherical coordinates is ( ρ, φ, θ ) where 1. 2. 3. 7 Equations Relating Spherical, Cylindrical and Rectangular Coordinates Example Convert z = p x 2 + y 2 to spherical coordinates. Graphing Examples 1. ρ = 3 2. θ = 3 π 4 3. φ = 3 π 4 4. φ = π 8 Spherical Triple Integrals Defn. Spherical Triple Integral A spherical triple integral on a surface D is where D is given in spherical coordinates. 9 Tips 1. 2. 3. 10 Example 1 Find the volume bounded by x 2 + y 2 = z 2 and x 2 + y 2 = 4. 11 Example 2 Evaluate ZZZ E y dV where E is the hollow sphere whose outside radius is √ 2 and inside radius is 1. 12 Do. Find the volume bounded above by x 2 + y 2 + z 2 = 4 z and below by x 2 + y 2 = z 2 . 13 Evil Example  If this is clear to you, then you’re awesome. Convert Z π 2 Z √ 3 1 Z √ 4r 2 1 r sin θ dzdrdθ to spherical coordinates. 14...
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This note was uploaded on 03/03/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.
 Spring '03
 MECothren
 Integrals, Multivariable Calculus, Cone, Polar Coordinates

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