The second paper, 'Modeling shell morphology of an epitoniid species with parametric equations
,' dealt with mathematically modelling marine species and noted the significance of the method in differentiating each group of specie.
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.
After solving these equations, the parametric equations
x (t) and y (t) (where x and y are spatial coordinates and t is the time) result from exponential functions.
The main problem of this description is that the solution to higher-order parametric equations
usually, except for rare cases, does not exist.
The parameters estimates presented in table 3 have also been used to build estimated Lorenz curve by applying parametric equations
given in Table 1.
Then, the obtained parametric equations
are illustrated in Figure 1 and 2:
It will filter and adjust the design recording, clear sequence of steps for each operation (including feature selection, feature positioning, assembly sequence, etc.), determine interaction method between Design Navigation and designers, define the types of design parameters (CAD input, Design Navigation default, parametric equations
or geometric constraints) and so on.
Finally, an adventurous student may wish to perturb the coefficients in the parametric equations
and determine the manner in which the loop points change.
The topics are fundamentals, the unit-circle and right-angle approaches to trigonometric functions, analytic trigonometry, polar coordinates and parametric equations
, vectors in two and three dimensions, conic sections, and exponential and logarithmic functions.
The piece is based on a set of parametric equations
that create a deltoid, a type of hypocycloid which looks like a triangle with concave sides.
The parametric equations
of straight families which are passing through current point [P.sub.C] (x (t), y (t), z (t)) and fixed points (nodes) [N.sub.1], [N.sub.2] and [N.sub.3] are determined with the aid of relations (1)