14.7 day 2 triple integrals using spherical coordinates and more applications of cylindrical...
DESCRIPTION
Converting the differential (finding the Jacobian) dxdydz=ρ sinφ dρdφdθ 2 Why? To find volume of the box at the left, use V=lwh V = dρ * ρdφ * rdθ (the r is from cylindrical coordinates) From chapter 11 r = ρsin φ Hence dxdydz=ρ sinφ dρdφdθ 2TRANSCRIPT
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14.7 Day 2 Triple IntegralsUsing Spherical Coordinates
and more applications of cylindrical coordinates
This is a Klein bottle, It is a 4 dimensional objected depicted here in 3 dimensions
This object has only 1 side.
More information about the Klein bottle can be found athttp://www-maths.mcs.standrews.ac.uk/images/klein.html
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Conversions between Spherical and other Coordinate systems
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Converting the differential(finding the Jacobian)
dxdydz=ρ sinφ dρdφdθ 2
Why? To find volume of the box at the left, use V=lwhV = dρ * ρdφ * rdθ(the r is from cylindrical coordinates)From chapter 11r = ρsin φ
Hence dxdydz=ρ sinφ dρdφdθ 2
![Page 4: 14.7 Day 2 Triple Integrals Using Spherical Coordinates and more applications of cylindrical coordinates This is a Klein bottle, It is a 4 dimensional](https://reader036.vdocuments.mx/reader036/viewer/2022081422/5a4d1b7d7f8b9ab0599b9d13/html5/thumbnails/4.jpg)
Example 4
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Example 4 Solution
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Example 4 explanation
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Problem 22
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Problem 22 Solution
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(the really sad part of this example is that the example provided by the teacher is also incorrect)
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Problem 14 (spherical coordinates only)
Convert the integral from rectangular to spherical coordinates
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Problem 14 (spherical coordinates only)
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Problem 14 Solution (cylindrical)(from yesterday)