Recent content by Rodrigo Schmidt

Oh, thank you! I totally forgot that.

So the statement which the proof's about is: For every linear transformation ##A##(between finite dimension spaces), the product ##A^*A## is self-adjoint. So, the proof is: ##(A^*A)^*=A^*A^{**}=A^*A## What i don't understand is why ##(A^*A)^*=A^*A^{**}##. Isn't that true only if ##A## and...

Oh, you mean something like a "spin"? I didn't tought of that. Where does it acts and why not in the center of mass? Is the tension in the string that provokes this rotation?

So, I'm really bothered with something. Let's suppose there's a simple pendulum with a rigid sphere on it's end. In order to get the motion equations I thought we could use two approaches. One would be using rigid body dynamics (torque, moment of inertia ...), the other one would be using...

So I'm having a introductory study on waves and there's something that i can't understand when dealing with reflections on a fixed end. We have the general solution for the wave equation: ## y(x,t)=f(x-vt)+g(x+vt)## Supposing that the fixed point is in the origin we have the boundary condition...

Thank you very much! It seems strange, but it's more clear to me now!

That's exactly what i tought, but the thing is that in my book and in some internet sources there are mentions of supposedly irrotational vortexes (which are also called potential vortexes), which seems very strange and confusing to me.

So, i just started an elementar study on hidrodynamics and I'm stuck with something. We have that the circulation in a closed path Γ is given by: ##C_Γ=\oint_Γ \vec v⋅\vec {dl}## And that, in a irrotational flow, ##C_Γ = 0## for any given Γ. But if we have an irrotational vortex wouldn't...

Yeah, that's what i meant. Sorry if i wasn't clear enough! English is not my mother language so, mostly when writing about math and science, my texts can get a little confusing. I will try to be more specific in the next time. Okay! Thanks for the support and knowledge shared!

Hm, i see, but isn't that the basis of the set of all polynomials? So, by being a basis, that must be a linearly independent set, and it's also infinite, so that implies in the infinite dimensionality of C°(ℝ)? That's where i want to get someday. Thanks for the inspiration!

Thanks for the knowledge shared! I hadn't tought that, that's, indeed, much simpler. So the basis of the set of all polynomials would be enough?

[mentor note: thread moved from Linear Algebra to here hence no homework template] So, i was doing a Linear Algebra exercise on my book, and thought about this. We have a linear map A:E→E, where E=C°(ℝ), the vector space of all continuous functions. Let's suppose that Aƒ= x∫0 ƒ(t)dt. By the...

Thanks for all the suggestions! I will check on all of them.

So, i am currently studying physics in a brazilian university. I am going to have a Calculus 2 course which, in Brazil, covers Ordinary Differential Equations and multi-variable differential calculus. So which challenging and rigourous books would you guys recommend for that? Thanks for the...