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Mathematical Modeling and Statistical Inference
Published in Gerald L. Schneberger, Adhesives in Manufacturing, 2018
Before continuing, it may be necessary to illustrate the meaning of two of the mathematical terms which we will be using. We define a family of curves as a set of curves, all of which are defined by the same basic equation. For instance, the single equation y = mx + b defines a whole family of straight lines. In this case the slope m and the y-intercept b are referred to as parameters. Different choices for m and b produce different lines, but all are members of the same family.
The Nature of Differential Equations. Separable Equations
Published in George F. Simmons, Differential Equations with Applications and Historical Notes, 2016
We have seen that the general solution of a first order differential equation normally contains one arbitrary constant, called a parameter. When this parameter is assigned various values, we obtain a one -parameter family of curves. Each of these curves is a particular solution, or integral curve, of the given differential equation, and all of them together constitute its general solution.
The Object-Oriented Approach
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
A first reading of the problem description shows that the program is to draw geometrical figures of four different types: line, rectangle, circle, ellipse, and parabola. We also notice that circle, ellipse, and parabola belong to a family of curves called the conic sections. These are obtained by sectioning a right-circular cone, as shown in Figure 28.5.
Multiple-contact thermoelastic oscillations
Published in Journal of Thermal Stresses, 2018
P. D. Howell, J. R. Barber, J. R. Ockendon
Next we perform an analogous calculation for negative double roots by letting in Eq. (40), resulting in the parametric representation For fixed h and , Eq. (54) parameterizes a family of curves in the -plane, of which the lowest branch is the relevant one corresponding to the dominant growth rate. We therefore consider values of , where satisfies the transcendental equation