Recent content by rjvsngh

I assume you're looking for a way to see covariant vectors. Since they are identified with linear functionals on a vector space V, you could try to figure how to visualize linear functionals. (See https://en.wikipedia.org/wiki/Linear_form#Visualizing_linear_functionals) It is difficult to...

I think you're trying to get a 3D rotation from a set of Euler angles. You may be looking for http://en.wikipedia.org/wiki/Slerp. Slerp gives you a geodesic on the 3D rotation manifold (roughly a great arc on a sphere in 4D). I figure, it'll be easier if you "saw" 3D rotations as unit...

existence of partial derivatives does not imply "differentiability". in some sense, differentiability in higher dimensional spaces is a stronger condition than existence of partial derivatives. intuitively, partial derivatives only sample the function along "coordinate directions" but this is...

thanks for all these explanations. following a particular reply, i did realize my question was incorrect in the usage of terms. my question originated in something i read in "Math Analysis", Apostol, 2nd ed., in the chapter on multi-variable calculus. However, looking closely, the precise...

While I'm not quite sure of the desired equations, what you could be aiming at is like the following: Let a = dv/dt be the constant acceleration. Then integral( a dt) = integral( dv ) for suitable integral limits. Since a is constant it slips through the integral and a integral( dt ) =...

Given that the derivative of a linear function is the function itself, how do I make sense of the following: Given f(x) = x. It's derivative is g(x) = f'(x) = 1. Is g(x) the same as f(x) in some way? Or have I got this wrong in some way. Is f'(x) really the derivative of a f(x) in the sense of...