Recent content by richardlhp

Hi, just wondering about MO theory. Take O2 for example; O is sp2 hybridised according to VB theory. However, when drawing the MO diagram for O2, one considers the sigma overlap between the s orbital and p orbitals separately (according to the theory), rather than considering the overlap of...

Hi, can anyone kindly explain to me (assuming no knowledge of spectral theorem, but only simple linear algebra understanding) how to see the vanishing of the terms Ixy, Iyz etc., where only the terms Ixx, Iyy and Izz remain? Thanks.

Thanks so much!

Calculus of variations (HELP!) Hi all! Just a question... How should I visualise geometrically the minimising of definite integrals, and what is the significance of finding stationary points of definite integrals? (Can someone provide me with an intuitive explanation?) Thanks so much!

Yeah! Thanks a lot. Hence for a more accurate value, one can keep the higher order terms?

Hi! I am a 16 year old trying to figure out the application of taylor series. I understand most of its uses when applied to functions like e^x, sinx, cosx, but in a mechanics book, i am required to find delta-F, a finite change in a function F. Ostensibly, this appears to be a step that needs...

Hi i want to study analytical mechanics. Should i read up on differential equations and linear algebra before starting on analytical mechanics? How about electromagnetism (beyond year 1 level)? Which is better to start, electromagnetism or analytical mechanics? And how about the math? Can...

You should think of the simplest case where f(x,y) before moving on to f(x,y,z...).

I think that it is not the tangent plane but the level curve that the gradient is perpendicular to, i.e. when the function is at a certain value. For e.g. a function of x and y then the level surface is not that tangent to the function, but an arbitrary curve formed by the function on any value...

http://www2.seminolestate.edu/lvosbury/images/Sect127No10Pic2.gif Can someone help me visualise and tell me how the gradient vector is going to look like if I plot this function on a contour plot?

Thanks for your help. So can i say that the gradient vector shown on the contour plot is just a projection of the actual vector in euclidean space to the xy plane?

Hi I am 16 and i am starting to learn analytical mechanics but i have just realized that i do not have enough math to do it. I have done basic calculus, but i also recommend you to do the same as i am doing, which is to learn up on multivariable calculus, differential equations and linear...

IMPORTANT! ---- what is the geometric intepretation of the gradient vector? Assume the situation in which I have a slope, a component of a function dependent on x and y, which is at an angle to the xy plane. The gradient vector would be perpendicular to the tangent plane at the point in which i...