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In calculus, integration by parametric derivatives, also called parametric integration, [1] is a method which uses known Integrals to integrate derived functions. It is often used in Physics, and is similar to integration by substitution .
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization. [1] "
A parametric C r-curve or a C r-parametrization is a vector-valued function: that is r-times continuously differentiable (that is, the component functions of γ are continuously differentiable), where , {}, and I is a non-empty interval of real numbers.
The name Desmos came from the Greek word δεσμός which means a bond or a tie. [6] In May 2022, Amplify acquired the Desmos curriculum and teacher.desmos.com. Some 50 employees joined Amplify. Desmos Studio was spun off as a separate public benefit corporation focused on building calculator products and other math tools. [7]
Suppose that F is a static vector field, that is, a vector-valued function with Cartesian coordinates (F 1,F 2,...,F n), and that x(t) is a parametric curve with Cartesian coordinates (x 1 (t),x 2 (t),...,x n (t)). Then x(t) is an integral curve of F if it is a solution of the autonomous system of ordinary differential equations,
The second fundamental form of a general parametric surface S is defined as follows. Let r = r(u 1,u 2) be a regular parametrization of a surface in R 3, where r is a smooth vector-valued function of two variables. It is common to denote the partial derivatives of r with respect to u α by r α, α = 1, 2.
Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem and the divergence theorem, are frequently given in a parametric form. The curvature and arc length of curves on the surface, surface area , differential geometric invariants such as the first and second fundamental forms, Gaussian , mean , and principal ...
Parametric design is a design method in which features, such as building elements and engineering components, are shaped based on algorithmic processes rather than direct manipulation. In this approach, parameters and rules establish the relationship between design intent and design response.