Recent content by Castilla

Let's suppose we have a function r that parametrizes a surface S in R3, taking as domain a flat region R in R2. I see in many books that in the statement of Stokes Theorem they say that the parametrizacion of the boundary of R must give counter-clockwise direction to said boundary. But I...

Hallsoftivy, I am afraid I am getting a bit confused. Classical Stokes theorem states an equation with a surface integral in one side and a line integral in the other side. Line integrals depend on the orientation of the curve. Let's say that function α parametrizes that curve in one...

I understand that this conventions about orientation of surface and edge have only one reason, that of treating equivalently either side of the surface. But I found this in a webpage: It turns out, that if we parametrize a surface S starting from a domain D in R2 whose boundary curve C is...

Hello, Chiro. Up to my limited knowledge, a coordinate system follos the RHR when: - the thumb points in direction of positive y, - second finger points in direction of positive z and - third finger points in direction of positive x. But I can't see how this would help me to see that...

I was referring to fixed numbers. Differentiating under the integral sign is also valid with improper integrals ("infinity" in the limit of integration) but in that case you need more requisites. Uniform convergence, I believe.

Let S be the integral sign. Suppose you have Sf(x,y)dy, with constant limits of integration. You want to justify d/dx S f(x,y)dy = S d/dx f(x,y)dy. If the partial derivative w.r.t. x of f(x,y) is continuous in a compact set, that is enough justification, though maybe not necesary. That...

Consider a function Q, from some set D in R2 to some set in R3. Suppose Q parametrizes a surface S. Orientation of the edge of the surface must be compatible with orientation of the surface. I read that if the parametrization of the Boundary of the domain D give it anticlockwise direction...

Excellent explanation. Thank you.

Just one question. Looking at both answers, basically the same, it seems that I need that the functions g and p to be bounded. So I would need not only that g and p are continuous, but also that they're continuous in a compact set? thanks again!

Thank you, stanley and micromass. You enlightened my mind.

I know this must be easy, but... Say real functions g(x) and p(y) are continuous and f(x,y) = g(x)p(y). How to proof rigorously the continuity of f in a point (x1,y1)? In other words, how to obtain l g(x)p(y) - g(x1)p(y1) l < epsilon (for any epsilon). I can prove that l g(x)p(y1) -...

I found this description of "betrayal to the country" in a peruvian legally-oriented web page: "To favour the external enemy during war, supplying him with any data, procedure, issue, document or object that may be used to damage the national defense". Obviously, it does not apply to Van der...

There is a mistake in previous posts. In Peru, death penalty applies only "in case of betrayal to the country during a war with an external enemy". I am peruvian.

Probably I have been unclear with my statement. I draw a smooth curve in the plane xy. I know its length, it is L. I "build" a fence over it, reaching the same height H for every point of the curve. It is pretty obvious that this fence has area LH, but what is the rigorous justification...

Thanks, but if the length of the curve at the base is L and the constant heigth is H, the area of this waving flag, according to your procedure, would be (Integral) [f(x) + H]dx - (Integral) f(x)dx = (Integral) Hdx. And that is not LH, which is the obvious area of a flag of length L and...