They cover preparation for calculus; limits and their properties; differentiation; applications of differentiation; integration; differential equations; applications of integration; integration techniques and improper integrals; infinite series; conics, parametric equations, and polar coordinates
; vectors and the geometry of space; vector-valued functions; functions of several variables; multiple integration; and vector analysis.
The transverse wave function [f.sub.[rho], [phi]](z) with fixed polar coordinates
[rho],[phi] satisfies additional Ben Daniel Duke boundary condition at the bottom of the layer with the coordinate z = 0 and at each point of the top of the layer z = d ([rho], [phi]).
Given a point p, the shape context of p is defined as a coarse histogram of the relative polar coordinates
of the other points, written as
then after deformation, if we will use polar coordinates
R, [alpha], where R = r - u and the formula for determining the curvature, we will get:
The RE is parameterized and represented in polar coordinates
and given in the following form:
and the relations of [[phi].sub.i], i = 1, ..., n - 1, are the same as those in the case of usual polar coordinates
. For calculating the Jacobian, we refer to the proof of Theorem 3.1 in  that can be extended to the n-dimensional case.
In this section, the design variables and mathematical model which influence the performance of ACO are constructed under polar coordinates
. Moreover, main objective is improvement by considering a relative position relationship of machines.
If amplitude spectra (computed by means of the discrete Fourier transform) are transformed to polar coordinates
, only a half of the domain on the angular axis is sufficient.
In Figure 2, we represent the force exerted by an infinitesimal mass dM of the disk on the mass m using polar coordinates
. Because of the symmetry of the disk with respect to the axis passing between its center and the mass m, we need to compute the projection of the force exerted by the infinitesimal mass dM on this axis.
Our measurements were performed in polar coordinates
and the image was conveniently drawn in Cartesian coordinates