Recent content by Kuma

I figure I can parameterize it no problem but the question literally asks what I said. Find an orientation preserving parameterization. What does that mean?

Homework Statement If I have been given a surface x = 12 − y^2 − z^2 between x = 3 and x = 8, oriented by the unit normal which points away from the x–axis. I want to find an orientation preserving parameterization. Homework Equations The Attempt at a Solution I know...

I saw your first reply :) But why project it to the xy plane as opposed to any other (yz, xz)? How would I know which plane to project it to?

Oh okay. So here's another question. If you have a sphere for example then outward vectors could be considered as the x,y, and z axes. But if you have a plane, it has to specify either upward or downward then? Also this brings me back to my confusion of each component of the normal when it is...

Wait what...? :( Well what does this mean then Also note that in order for unit normal vectors on the paraboloid to point away from the region they will all need to point generally in the negative y direction. On the other hand, unit normal vectors on the disk will need to point in the...

Thanks for the replies. See his first and second example here: http://tutorial.math.lamar.edu/Classes/CalcIII/SurfIntVectorField.aspx On the first example he uses the y-component and I'm kind of confused about trying to figure out what outward and inward means first off, and which...

Homework Statement I'm a bit confused as to how to determine which component must be positive or negative if the question gives you a surface and says the normal vector is pointing outward or inward. Some surfaces have it so that the z component is positive if n is pointing outward and...

Homework Statement I need to show that the yield curve defined by r(t) = 1/t integral r(s) ds from 0 to t is a nondecreasing function iff: P(αt) ≥ (P(t))^α, for all 0<=α<=1 , t>= 0 and P(t) is defined as: P(t) = exp{-integral r(s) ds from 0 to t} and r(s) is the spot rate...

Homework Statement Here is the surface I need to parameterize. It is a solid of revolution. Homework Equations The Attempt at a Solution So since its a piecewise function, I can define it as follows (x-2)^2 + z^2 = 1, 1<x<2 z = -x+3, 2<x<3 z = x-3, 2<x<3 I know...

Right. When the surface is curved the cross product of the tangents shouldn't be 0.

It shouldn't make a difference. Do i just plug in the endpoints of u and v? ie would (0,0) work? I get (0,0,0) if I use that point. Not a vector...

Homework Statement Given a parameterized surface: C(u,v) = (3 cos u sin v, 2 sin u sin v, cos v) 0<u<2pi, 0<v<pi I have to find a normal vector to that surface. Homework Equations The Attempt at a Solution So tangent vectors can be Tu = (dx/du, dy/du, dz/du) and Tv =...

Homework Statement I have some questions similar to this one. I have to just provide reasoning as to why this can or cannot be evaluated using greens theorem. given f = x/sqrt(x^2+y^2) dx + y/sqrt(x^2+y^2) dy, and the curve c is the unit circle around the origin. Why can/cannot the integral...

It says that 1n is a vector of 1's so shouldn't 11' = n?

Homework Statement Hi there I'm trying to solve this question: Homework Equations The Attempt at a Solution I figured i should just multiply them together and show that you get the identity matrix, but I'm having trouble cancelling out some of the terms. I'm not sure if I...