Recent content by GoutamTmv

Thanks. Is there, then, an easy way to find the partial fractional decomposition of the infinite product?

Hello everyone, I came across this identity while browsing Wikipedia, and I decided to try to prove it for myself. ( It was discovered by S Ramanujan) \int_0^\infty \cfrac{1+{x}^2/({b+1})^2}{1+{x}^2/({a})^2} \times\cfrac{1+{x}^2/({b+2})^2}{1+{x}^2/({a+1})^2}\times\cdots\;\;dx =...

Hmm, I see. Well both of us have the e-book actually. He's gone through the book (not worked through it). He feels the need to master ODE's before this, and for that he wants a quick and dirty tutorial, just enough to get him through.

He wants teach himself using Gelfand and Fomin's book. G & F's book is rather theoretical (lot of proofs) with a few applications to physics ( it covers the Hamilton-Jacobi equation, and the principle of least action, for example). Its tone is formal, if that's what you mean.

Hello all, A friend of mine has recently developed an interest (rather, an obsession) with the Calculus of Variations. He's familiar with linear algebra and also with the contents of Spivak's "Calculus on Manifolds", and is now looking for the shortest path to Gelfand and Fomin's "Calculus of...

Gelfand and Fomin contains a treatment of the Hamilton-Jacobi Equation, which is a partial diffrential equation. So would it not be better for the OP to develop familiarity with PDE's as well? Or am I just plain wrong?

Alright, I will check into those books. Thank you everyone :) Sorry for the late reply by the way.

Well, it seems extremely interesting to me. I would love a theoretical approach. And if I must, then I don't mind learning the pre-requisites :)

It is "Calculus" By Michael Spivak. I am unable to post the link to it at the moment. However, if I can learn, which text is the best for self learners?

Hey guys, Is it possible to learn, (at least) elementary Fourier analysis, after completing Spivak's "Calculus"?. If not, what more is there to learn before one can begin Fourier analysis?

Well then, what would be the minimum knowledge required to understand the proof? Thanks in advance

Hey guys, I would like to know whether there exists a proof for the Lindemann-Weierstrass Theorem that uses only the tools and techniques of elementary analysis. If such a proof does not exist, I would like to know what would be the mathematical knowledge required to understand the proof.