Recent content by Alteran

Hello, I cannot download solutions via emule - sources are 0 :( I will be very appreciate, if someone will send them to me. My email is neoliten@hotmail.com. Thank you.

Thanks for support. I think now I can catch what is going on. I was little bit confused :blushing:

Yes, exactly - "Prove that for the surface f-1(0), all tangent planes pass through the origin". I have found tangent planes for this surface, but how to show that they are passing through the origin? I need to show, that these planes are defined in (0,0,0)? or something else?

The problem from Differential Geometry: Let \gamma : R -> R is smooth function and U = {(x,y,z) \in R^3 : x \ne 0} - open subset. Function f : U -> R is defined as f(x,y,z) = z - x\gamma(y/x) and this is smooth function. Proof that for surfaceS = f^{-1}(0) all tangent planes passing...

Yes, rank of Jacobian matrix is equal to 3, so these vectors are linearly independent. Looks like they are basis vectors. Thanks for support.

Jacobian matrix is known, so I believe I can computate these derivatives by using that matrix, by summarize each row in columns (there are 3 columns denoted to each u_n and 4 rows denoted to f_m(u)). By that procedure I will get 3 vectors, and they will be the basis of tangent space?

ok, may be I did not specified extra data: so: u=(u_1, u_2, u_3) and specifically f_1(u)=sinu_1 sinu_2 sinu_3 f_2(u)=cosu_1 sinu_2 sinu_3 f_3(u)=cosu_2 sinu_3 f_4(u)=cosu_3 So basis of my tangent space will be a set of 3 vectors, tangent vector, normal vector, binormal vector? or I am...

Stuck with problem: There is a local surface \alpha(u) = (f_1(u), f_2(u), f_3(u), f_4(u)) \in R^4. I need to find basis vectors of tangent space on that surface in some point p. It is not difficult to calculate tangent space for that surface, we should choose some curve on the surface and...

As I understand we derive the matrix from the system, then we calculate det(A-xI) and we get cubic equation and then roots: 1, -2, -2 which are eigenvalues. I got an equation: -x^3-3x^2+4 = 0 so roots are indeed: 1, -2, -2. How to create eigenvectors? I belief that we need so called...

In order to find streamlines for vector field, we need to solve this system of differential equations: \frac{dx}{dt} = -x+y+z \frac{dy}{dt} = x-y+z \frac{dz}{dt} = x+y-z where x(0) = a y(0) = b z(0) = c I have used Mathematica in order to find solutions for these equations and it...

The question should be very easy, its from topics of Differential Geometry, I just want to make sure that I understands it right :shy: . My question is: in R^3 we have vector field X and for every point p(x,y,z) in R^3 space, vector field X(p) = (p; X_x(p), X_y(p), X_z(p)) has: X_x(p) =...

Thank you for your support. The best thing that helps here is counting inversions. That way I can definitely say, is list in increasing order or not and calculate quality of that increasing: we have maximum number of inversions that could be (if list consist of unique items and sorted) and we...

About first set: if we will look to this as a whole, then it will increase from 45 to 149. I want to know is it really incresing that way (derive sort of a coeff of that increase/decrease). One solution could be to take first element and the last and compare them, but if set would be: 15 20...

Sorry, I have posted it to a wrong thread. Moderators, please, fell free to move it to statistics. Thank you.

Simple statistical question. Lets say that we have set of values: 45 40 30 36 11 10 75 102 113 125 137 140 149 you can see that it has a good tendency to increase (even if we have decrease in the middle). But in set: 68 33 21 31 7 7 13 123 21 33 67 64 29 9 5 87...