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Differential Geometry Answers


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Determine the square of the arc element for the curvilinear coordinate system
(u,v,w) whose coordinates are related to the Cartesian coordinates as follows:
x = 3u + v − w; y = u + 2v + 2w;z = 2u − v − w.
Coordinates whose curves are mutually perpendicular at each point are called …………
Cylindrical Coordinates
Spherical Coordinates
Orthogonal Curvilinear coordinates
Ellipsonic Cylindrical Coordinates
Given that
, find
1)Find the point of maximum curvature on the graph of y=e^(x)
2)Find the minimum and maximum curvatures of the ellipse r(t)=(acost,bsint),0<=t<=2pi, where a>b
Find the slope of c(t)=(t/2,(t^(2)/4) -t) at t=2
find a vector parametrization v(t),t (0,3) of the path(or loop) ABCA where A(1,0,1),B(1,1,0),C(0,1,1)
Find the Bezier curve where the control points are P(2,3),P1(2,0),P2(3,1),P3(4,4)
A curve has the equation y = x/16 * (5-x)^4. Calculates the values of x for which dy/dx =0 . Given that a small change,p,is made in the x-coordinate at the point (4,0.25), calculate,in terms of p, the approximate change in the y-coordinate .
find the tangent line of the curve at the points t=+1,-1,0
let r(s)=(x(s),y(s),0) be a unit speed curve prove that K=|x'y''-x''y'|