This document is a collection of detailed lecture notes from a university-level course on Multivariable Calculus and Physics. It covers essential topics including lines, planes, and surfaces, projectile motion, limits, partial derivatives, optimization, and integration techniques in various coordin...
Math 210 Lecture 13: Triple integrals in
cylindrical and spherical coordinates
Daniel Ingebretson
University of Illinois at Chicago
July 10, 2024
,Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
,Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
Polar coordinates (r , θ) in the xy -plane, and Cartesian
coordinate z along the z-axis.
, Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
Polar coordinates (r , θ) in the xy -plane, and Cartesian
coordinate z along the z-axis.
Conversion:
y
r 2 = x 2 + y 2, x = r cos θ, y = r sin θ, tan θ = .
x
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