Apr 25, 2015 · This parameterization looks qualitatively different from the trigonometric parameterization $\gamma (t)$ above, but they are related by a clever and important change of variable related to …

Aug 2, 2018 · What is the difference between parameterization and change of variables? How do I know when I'm doing one or the other? Also, under which one of these does "transformations" and …

One of the conditions that sub-manifolds have to fulfill is to be the image of a map with a constant rank derivation (equal to the dimension of the domain). Hence having a regular curve, by knowing the …

Apr 28, 2017 · How do I parametrize a triangle with vertices $A(1,1)$, $B(2,2)$ and $C(1,3)$? I have tried working with the equations of the lines that form it but am not completely ...

Dec 7, 2019 · Try cillindrical coordinates i.e. use polar coordinates to describe the xy x y plane and let z z depend on them. Let x = r cos θ, y = r sin θ, z = z x = r cos θ, y = r sin θ, z = z then the …

Feb 20, 2017 · How to find parameterization if 2 points are given? Ask Question Asked 8 years, 11 months ago Modified 8 years, 11 months ago

Parameterization is necessary to capture what your curve actually is but the particular parameterization used doesn't matter. If you setup the same line integral with two different parameterizations, those …

Question: Consider the parameterization of the unit circle given by x=cos (3t^2-t), y=sin (3t^2-t) for t in (-infinity, infinity). Describe in words and sketch how the circle is traced out, and use this to answer the …

Oct 17, 2014 · What is the appropriate parametric equation of the boundary of a square? For example, the unit circle has a parametric equation $x(t)=\\cos(t)$ and $y(t)=\\sin(t)$.

You can guarantee this if you pick a special parameterization, the arc-length parameterization. Intuitively it corresponds to having velocity a unit vector everywhere, and things that you compute from the arc …