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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Infinitesimally small time intervals

When saying that in a small time interval $dt$, the velocity has changed by $d\vec v$, and so the acceleration $\vec a$ is $d\vec v/dt$, are we not assuming that $\vec a$ is constant in that small ...
1 vote
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Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

When we want to find the total charge of an object or total mass, usually we start off with a setup such as: $$m = \int dm \:\;\:\text{or} \:\;\:q = \int dq$$ in which we then use (and to keep it ...
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Why is instantaneous velocity tangent to trajectory?

Trajectory is the path of an object through space as a function of time. However, in many trajectory plots, when the movement is planar, a horizontal position axis and a vertical position axis are ...
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In Radius of Curvature calculation why do I have to assume $\text{d}^2x/\text{d}t^2=0$?

Recently, I was calculating the radius of curvature of projectile trajectories at certain points. There are two ways to do the same: Given the velocity and acceleration of the particle at some point, ...
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What is the meaning of $\nabla _{\mu}\nabla _{\nu}\phi(r)$ in general relativity?

I know the covariant derivative of a tensor is $$\nabla_{\mu} V_{\nu}=\partial_\mu V_\nu-\Gamma_{\mu\nu}^{\lambda}V_{\lambda}$$ Now I want to obtain $\nabla_{\mu}\nabla_{\nu}\Phi(x)$ where $\Phi(x)$...
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What does $\delta/\delta t$-derivative represent in tensor calculus?

Some texts, such as Pavel Grinfeld's, talk about a $\delta/\delta t$-derivative whose role (in trajectory analysis of particles using tensor calculus) is pretty obscure to me. For example, the ...
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What is the instant velocity? [duplicate]

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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