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Differential Geometry

Does there exist a plane targent to x^2−2y^2 +2z^2 = 8 and which passes through 2x+3y+2z = 8, x−y+2z = 5? Justify your answer.

Differential Geometry

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.

(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.

Differential Geometry

Coordinates whose curves are mutually perpendicular at each point are called …………

Cylindrical Coordinates

Spherical Coordinates

Orthogonal Curvilinear coordinates

Ellipsonic Cylindrical Coordinates

Cylindrical Coordinates

Spherical Coordinates

Orthogonal Curvilinear coordinates

Ellipsonic Cylindrical Coordinates

Differential Geometry

Given that

A=sinti+costj+tk

, find

∣∣∣d^2A/dt^2∣∣∣

7

3

2

1

A=sinti+costj+tk

, find

∣∣∣d^2A/dt^2∣∣∣

7

3

2

1

Differential Geometry

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

2)Find the minimum and maximum curvatures of the ellipse r(t)=(acost,bsint),0<=t<=2pi, where a>b

Differential Geometry

Find the slope of c(t)=(t/2,(t^(2)/4) -t) at t=2

Differential Geometry

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)

Differential Geometry

Find the Bezier curve where the control points are P(2,3),P1(2,0),P2(3,1),P3(4,4)

Differential Geometry

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 .

Differential Geometry

find the tangent line of the curve at the points t=+1,-1,0

r(s)=(s^2-1,s(s^2-1),0)

r(s)=(s^2-1,s(s^2-1),0)