Recent content by Vicfred

Hi, I've been studying mathematics for some years and now for some reasons I have to study introductory subjects in physics. I've looking at some books but the mathematics they use is very basic, are there some books on classical mechanics, thermodynamics, fluids, electromagnetism and optics...

ok, my teacher solved the vector laplacian in class (and after 5 pages of my notebook) we got \nabla^2 \left[ \vec F(r)\right] = \frac{2}{r}\frac{d \vec F}{dr} + \frac{d^2 \vec F}{dr^2} then my teacher said that it was a shorter way to find it but it was more complicated now I'm intrigued hmm...

\frac{\partial }{\partial x}(\frac{du(r)}{dr}\frac{x}{r}) = u\frac{dr}{dr} \frac{x}{r} = \frac{\partial}{\partial x}\frac{ux}{r} = \frac {r(u{\frac{\partial x}{\partial x}} + x\frac{\partial u}{\partial x}) + (ux)\frac{\partial r}{\partial x}}{r^2}

\frac{du(r)}{dr}\frac{\partial}{\partial x}\frac{x}{r} + \frac{x}{r}\frac{\partial}{\partial x}\frac{du(r)}{dr}? hmmm...

ok, from that proof I've got \nabla^2\vec{F}(r) = \nabla^2 {u} \hat e_x + \nabla^2 {v} \hat e_y + \nabla^2 {w} \hat e_z \nabla^2 {u} = \nabla \cdot \left[ \nabla u \right] \nabla u = \frac{\partial r}{\partial x} + \frac{\partial r}{\partial y} + \frac{\partial r}{\partial z} = \frac{x}{r} +...

I got \frac{\vec r}{r} \times \frac{d}{dr} \vec F(r)

I already had the gradient, the divergence and the scalar laplacian, what I can't find still is the curl and the vector laplacian for the curl I have this, I'm not sure if it's correct. \left(\frac{d}{dr} F_{z}(r)\frac{\partial y}{\partial r} -\frac{d}{dr} F_{y}(r)\frac{\partial z}{\partial...

I'm trying to find an equation like this: \nabla\left[F(r) \right] = \frac{d}{dr}F(r) \frac{\vec r}{r} \nabla\cdot\left[ \vec F(r) \right] = \frac{d}{dr}F(r) \cdot \frac{\vec r}{r} {\nabla}^2 \left[\vec F(r) \right] = 2 \frac{d}{dr}F(r) + \frac{d^2}{dr^2}F(r) hmm sometimes I say rotational...

if someone have the equations for that rotational post it that way at least I'd know what I have to get...

ok then \frac{\partial}{\partial y} F_{z}(r) = \frac{d }{d r} F_{z}(r) \frac{\partial r}{\partial z} ?

Ok, thanks I'll try it, it's too late here (3:55am), for the vector laplacian I think I'll have to do a BIG matrix... I guess I'll have to learn something about linear algebra... Thanks for your help.

yes, \vec{F}(r) is an arbitrary vector function in cartesian form that depends of x, y and z. Maybe I was wrong to say that r = \sqrt{x^2+y^2+z^2} maybe \left( \frac{\partial}{\partial y}\vec F_{z}(r)-\frac{\partial}{\partial z}\vec F_{y}(r)\right)\hat{i} + \left( \frac{\partial}{\partial...

Well, today I started to learn about spherical and cylindrical coordinates and I still don't know how to transform nabla, dot or vector product to another coordinate system... is that necessary to solve this problem?

Homework Statement I want to calculate \nabla\times[\vec{F}(r)] and \nabla^2[\vec{F}(r)] where F if a function that depends of r, and r = \sqrt{x^2+y^2+z^2} Homework Equations 1)\nabla \times \vec A = \left|\begin{matrix} \mathbf{\hat{i}} & \mathbf{\hat{j}} & \mathbf{\hat{k}} \\ \\...