Mathematical prerequisites for studying introductory Quantum Mechanics are basics in complex numbers, fourier analysis, differential equations and linear algebra. I think it is also necessary to have ...

India: The Indian Institute of Science is quite good. (A lot better than the IITs, at least in the sciences) Europe: ETH Zurich, University of Basel, German universities like Technical University ...

There's a fantastic resource called by the National Programme on Technology Enhanced Learning. Check it out at http://nptel.iitm.ac.in/. They have a youtube channel as well http://www.youtube.com/...

I think there is some debate about this, at least according to Steven Strogatz. I paraphrase a part of his lecture that I'm watching: Even systems with perfectly known, perfectly deterministic laws, ...

A tensor is a generalization of the notion of scalars and vectors. A tensor of rank 0 is a scalar (it has $3^0$ compenent), while a tensor of rank 1 is a vector (which has $3^1$ components). In ...

Assuming 1 particle ($i$=1), and the mutually orthogonal Cartesian co-ordinates ($x$,$y$,$z$), the applied force is given by : $${\bf F^{a}=\bf F_x^{a}+\bf F_y^{a}+\bf F_z^{a}}\tag1$$ Now, we have ...
This is what I get: Using conservation of energy, velocity from the top of the loop as a function of $\theta$ is $\sqrt{2gr(1 - \cos(\theta))}$. Distance traveled is arc length, which is $rd\theta$. ...