Recent content by praharmitra

I am doing some calculation and am now stuck with an integral of the form \lim_{r \to \infty} \int_{-1}^1 dt f(t) e^{i r (t-1)} for some function f(t). I don't know what the exact form of f(t) is. Is there any way to address this integral? Similar to the saddle-point method perhaps...

How would one do the following sum? \sum\limits_{n=1}^\infty n e^{- \epsilon~n^2}

I am assuming the tilde above an object implies taking a transpose. If that is the case, then M is indeed a symmetric matrix. One can see this by looking at the Lagrangian. Since the Lagrangian is a number, we can take a transpose of L and we'll get back the same number, i.e. L^T=L, this will...

OK. So I was thinking right! Thanks a lot :)

This is confusing me more than it should. A curve in space is given by x^i(t) and is parameterized by t. What is the tangent vector along the curve at a point t= t_0 on the curve?

Hi guys, I figured out the problem with the question. There is not enough information to solve this problem. You can see this by doing the following construction. Draw the line AD first (This can be any length, for this argument atleast). Now draw the two equal angles BAD and DAC on either side...

Well, but with that construction AD will not be the angle bisector of angle A.

Hey guys, This is NOT homework. I remember solving this question many years ago (at least 10 years ago). I am trying to recall the solution again and am just not able to. The question is - In a triangle ABC, AD is the angle bisector of angle BAC. AB = CD. Prove that angle BAC = 72 degrees...

So I know that the Hodge dual of a p-form A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p} in d dimensions is given by (*A)^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}} = C\epsilon^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}\mu_1 \mu_2 \cdot \cdot \cdot \mu_p}A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p} where C...

Is the following the definition of wedge product in tensor notation? Let A \equiv A_i be a matrix one form. Then A \wedge A \wedge A \wedge A \wedge A = \epsilon^{abcde}A_a A_b A_c A_d A_e ? in 5 dimensions. This question is in reference to the winding number of maps.

The first three equations you've written down are correct. The answer is indeed pi/5. Check your calculation again. If you still don't find your mistake, write down your step by step solution, and i'll tell you where you're going wrong.

You are right by guessing Law of sines. Why don't you show what work you've done till now and where exactly you're stuck?

The equations of motion are of the form \ddot{x} = -\frac{\partial V}{\partial x} From this you can read off V. Now that you have the function V(x), what are the conditions for such a function to have a minimum at x=0 ?

You can prove this using induction. Using the usual induction techniques, define f(n) = \sum\limits_{k=1}^{k=n}\left(\frac{1}{2k-1} - \frac{1}{2k}\right) . You want to show f(n) = \sum\limits_{k=1}^{k=n} \frac{1}{k+n} . You've already shown that this is true for n=1. Assuming the statement is...

Thanks Sam. I'll do some calculations with this definition and come back if I have further clarifications.