Recent content by Gear.0

Sorry for such a basic question, but I don't know what they mean by the O, o, and ~ in a book I am reading. I'll write out the whole thing to show what I am asking about as well as to give context. Those symbols appear in ii) and iii) below. Also note that I wrote them here as having a...

That makes perfect sense, thanks! It is zero so that the two integrals are equal in this case. My problem was not really knowing how to apply green's theorem to something that doesn't resemble a curl. But instead of completely simplifying \nabla\cdot\left( w\nabla w\right) if I do it up to this...

But I don't have anything with in the equation \int_{R}\nabla}\cdot\left(w\matbf{\nabla}w\right)dxdy I tried it anyway and I got that it can be rewritten as: \int_{R}\left\| \nabla w\right\|^{2}dxdy + \int_{R}w\nabla^{2}w dxdy The term on the left is exactly what I want but I don't know...

I must sincerely apologize, the original equation should have had a square in there on the first integrand: \int_{R}\left\| \nabla w\right\|^{2} dxdy = \oint_{C}w\frac{\partial w}{\partial N}ds But thanks for the help, I will try your suggestions with this corrected equation.

I'm sorry, I'm really trying to get this but I just don't see how writing eq(1) as \int_{R}\left( \nabla\cdot\nabla w\right) dxdy = \oint_{C}\frac{\partial w}{\partial N}ds will help. I tried doing it and writing this next to the form I want to get: \int_{R}\left\| \nabla w\right\| dxdy =...

Homework Statement Show that for a solution w of Laplace's equation in a region R with boundary curve C and outer unit normal vector N, \int_{R}\left\| \nabla w\right\| dxdy = \oint_{C}w\frac{\partial w}{\partial N}dsHomework Equations The book goes through the steps to show that the following...

Basically I have most of my classes required to graduate, but due to the lack of availability of some classes it will still take me about 3 more semesters after the current semester. So I was considering double majoring with math, so it would be physics + math major. Since I was already a...

Homework Statement This isn't directly a homework question, but a response will really help me on my homework. How does one calculate the quadrupole moment, when given two point dipole moments? I would know how to proceed had I been given a system of 4 charges, which is essentially the same...

It seems to me that the solution should actually be pretty simple.. I hope I am understanding correctly. But if your formula for the jerk at any time t is given as J = J_{0}^{t} is that correct? Then you can find the exact values of acceleration, velocity, and distance at any time t also...

Yes that is exactly right. The reason I said to look at the volume of water as x*V, because then you can see that (volume of water)/(volume of ice) is equal to the submerged fraction of the ice. Volume of water = x*V Volume of ice = V (volume of water)/(volume of ice) = x and x is the fraction...

Those quantities you don't need will cancel out. It's often hard to see this right away, the best thing to do is to just start solving it manipulating the unknown quantities as variables and just hope for the best. In this case, you should write out an equality for what you do know. A hint...

You are right again, man I can't believe I'm making all these stupid mistakes. I'm still just an undergraduate so maybe I shouldn't be helping you lol. But, if you'll permit me to give it another shot I'd like to write everything out in detail, hopefully that will force me to think more about it...

I apologize, I made a horrible mistake. Everything I did applied to half the distance. So when I was talking about half the distance it was really a fourth lol, sorry about that. However, the final equation still describes the maximum acceleration needed except that 'd' is now 1/2 the distance...

It's been a while since the OP has replied so I don't think he will mind if we continue this alternate discussion here. I think I understood you correctly. It's simply a matter of finding all the integrals. So you have a constant jerk (let's say jerk has the value 'A', this gives the equation...

You need to understand that in order to see a focused image, the eye must converge all the rays from the object to basically a single point at the back of the eye. If the light rays diverge, or converge at a point slightly ahead or behind the back of the eye then the image will appear blurry...