14.7 Day 2 Triple Integrals Using Spherical Coordinates and more applications of cylindrical...
-
Upload
bertha-phillips -
Category
Documents
-
view
245 -
download
1
description
Transcript of 14.7 Day 2 Triple Integrals Using Spherical Coordinates and more applications of cylindrical...
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
Conversions between Spherical and other Coordinate systems
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
Example 4
Example 4 Solution
Example 4 explanation
Problem 22
Problem 22 Solution
(the really sad part of this example is that the example provided by the teacher is also incorrect)
Problem 14 (spherical coordinates only)
Convert the integral from rectangular to spherical coordinates
Problem 14 (spherical coordinates only)
Problem 14 Solution (cylindrical)(from yesterday)