Recent content by squire636

Nope, that's what I have, I just factored out an a^2 from inside the square root.

Homework Statement http://imgur.com/gLLVSuA Homework Equations The Attempt at a Solution Part a is simple. The first step is to find the complex potential. I wasn't 100% sure, but it seems like I need to add an image of the source, so I added an additional source located at...

I think I figured it out, thanks so much!

Would I do something along these lines? ln(z+a) ln(r*e^iθ + a) ln(r*cos(θ)+i*r*sin(θ) + a) ln((r*cos(θ)+a) + i*r*sin(θ)) And then try to find a new r and θ in order to put this back into the form of r*e^iθ ? That doesn't seem to me like it will be possible, and I can't find the...

I'm sorry I don't quite follow you, could you explain in more detail? I'm unfamiliar with that notation. Thanks.

I tried that, but still did not make any progress. ln(z+a) - ln(z-a) ln(r*e^iθ + a) - ln(r*e^iθ - a) Now what? I can't split it up into ln(r)+iθ anymore.

Homework Statement a. Determine the complex potential for two equal counter-rotating vortices with strength \Gamma, the positive one located at z=-a and the negative one at z=a. b/ Show the shape of the streamlines for this case. Homework Equations z = x + iy = r*e^(i\theta) W(z)...

We're allowed to use pretty much whatever we want, as long as I understand it and it makes sense.

Homework Statement Simplify the following, where A and B are arbitrary vector fields: f(x) = ∇\bullet[A \times (∇ \times B)] - (∇ \times A)\bullet(∇ \times B) + (A \bullet ∇)(∇ \bullet B) I know that the correct solution is A \bullet ∇2B, according to my professor. However, I can't...

Homework Statement ∫ ∂k(gixiεjklxl dV Can anyone make sense of this? I know I'll need to apply the chain rule when taking the derivative, but I'm not quite sure how to proceed. Also, this is part of a larger problem where g is a gravity vector existing purely in the -z direction, but I...

In case you're still around and feel like helping more (it'll be greatly appreciated), I can use the commutative property of the dot product to write the third one as the following: (∂juj) xk/√(xixi) How do I take the derivative of u in this case?

Looks to me like we can just replace it with the kronecker delta δik, since it is 0 when the indices are different, and 1 when the indices are the same. This also takes care of combining the xi and xk terms like I wanted to. Thanks so much for your help, this finally makes some sense. Index...

Okay I follow you there, and I think I see what is going to happen, but I'm not sure if my math is working correctly. The product rule for ∂i(xkxk) = xk * 2∂i(xk) This makes the second term become: -xi(xjxj)-3/2xk ∂i(xk) If we can somehow combine the xi and xk term, we should be able...

I must really be missing something. From there, using the product rule to take the derivative, we would get: ∇.n = (1/√(xjxj))*∂ixi + xi*∂i*(1/√(xjxj)) Since we've already shown that ∂ixi = 3, the first term becomes simply: 3/√(xjxj) Using the chain rule, the second term would...

The divergence of v is δivi. In my situation, I'm trying to take the divergence of vector: n = x/r = x/√(xjxj) My "vi" in this case would be xi/√(xjxj) So (∇ . n)i = δixi/√(xjxj) Is this correct? What next? Thanks so much for your help, by the way.