Abstract
This chapter describes triple integrals, cylindrical coordinates, spherical coordinates, center of gravity, moments of inertia, line integrals, Green's theorem, and surface integrals. The main theoretical fact is triple integral exists if Δ(x) is continuous and the boundary D is not too complicated. The main practical fact is that integral can be evaluated by iteration. Cylindrical coordinates are designed to fit situations with rotational (axial) symmetry about an axis, usually taken to be the z-axis. Spherical coordinates are designed to fit situations with central symmetry. It is convenient to fit a frame of three mutually perpendicular vectors to cylindrical coordinates just as the frame i, j, k fits rectangular coordinates. At each point (r, θ, z) of space attach three mutually perpendicular unit vectors u,w,k.
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