# Questions tagged [differentiation]

Differentiation is the set of techniques and results from Differential Calculus, concerning the calculation of derivatives of functions or distributions.

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### What is the instant velocity?

The velocity is the variation rate of the position correct? So does it make sense to talk about velocity without time?
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1 vote
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### Currently self-studying QFT and The Standard Model by Schwartz and I'm stuck at equation 1.5 in Part 1 regarding black-body radiation

So basically the equation is basically a derivation of Planck's radiation law and I can't somehow find any resources as to how he derived it by adding a derivative inside. Planck says that each mode ...
1 vote
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### Non-parallel light diffraction

Does light (and in general any kind of wave) diffract only when the wave fronts are parallel? Like if you did the double slit experiment when the waves were coming from a point source close to the ...
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1 vote
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### Covariant derivative with an upper index in terms of Christoffel symbols

I have encountered expression $$\frac{1}{2}\left(2 \dot{g}_{\mu}{}^{\lambda ; \mu}-\dot{g}_{\mu}{}^{\mu ; \lambda}\right)$$ in a GR paper. Here we assume to be working with the de Sitter metric $g$ ...
• 1,032
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### Why while solving some specific problems like this we need the second-order variation like this one?

Consider a string which is fixed at both ends and we are giving it a small amplitude by tauting it and moving to and from. If someone wants to derive the wave equation of the string, they would first ...
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### Covariant derivative, directional derivative, and curvature tensor

I'm confused about how to connect those three things together, so hopefully the question doesn't end up vague. The main problem is understanding how the curvature tensor is a commutator of covariant ...
• 662
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### Find the curl if the vector field depends on a parameter

Given the following vector, \begin{align} F(x(t),y(t),z(t)) &= \begin{bmatrix} \omega_1^2 x_o\cos(\omega_1 t) \\ \omega_2y_0\sin(\omega_2 t)\\ 0\\ \...
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### Limit of $d\rightarrow 4$ of a function in Peskin & Schroeder
In Peskin & Schroeder section 12.1 equation 12.15 we compute the function $$\frac{-3\lambda^2}{(4\pi)^{d/2} \Gamma(\frac{d}{2})}\frac{(1-b^{d-4})}{d-4}\Lambda^{d-4}$$ Now when we take the limit \$...