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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 infinitesimal displacement?

This section is from the Openstax University Physics: Volume 1 online textbook. In physics, work is done on an object when energy is transferred to the object. In other words, work is done when a ...
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Acceleration of speed of light [on hold]

If we consider the equation "$E=mc^2$" and if we differentiate the equation with respect to time, e.g. $$\frac{\mathrm dE}{\mathrm dt}=m\frac{\mathrm dc^2}{\mathrm dt},$$ we will get after ...
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Differentiation of metric tensor in new coordinate

I want to understand the explicit meaning of $g_{\mu'\nu',\lambda}=0$ where unprimed coordinates are coordinates of the the original coordinate systems and primed ones are for new coordinate system. ...
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Differentiation of the determinant $g$

Let $g$ be the determinant of the metric tensor. I want to derive the following equation $g_{,\nu}=gg^{\lambda \mu}g_{\lambda \mu,\nu}$. It is said that $gg^{\lambda \mu}$ is a cofactor, but I can't ...
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Fractional differential equations and Physics [duplicate]

Are the "fractional differential equations" have any real significance in respect to physics? or are they just stilted math?
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What was the real need of the operators of divergence and curl?

As I'm advancing my study in Electromagnetism I'm getting introduced to more mathematical operators which are exclusively used in Electromagnetism and Fluid Dynamics only. Let me try to explain ...
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(Physics version of) Taylor expansion. In the the context of deriving a Lie groups generators (a Lie algebra from a Lie group)

Statement which I'm confused about: "Consider some n-dimensional Lie group whose elements depend on a set of parameters $\alpha = (\alpha_1 ... \alpha_n)$, such that $g(0) = e$ with e as the identity,...
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Computing total derivative of Kinetic Energy w.r.t time

I am confused as to how to take the total derivative $\frac{dKE}{dt}$, where $KE$ is the kinetic energy. I know that $KE = 1/2 *m * \dot{\vec r} \cdot \dot{\vec r}$. From here, if I take derivative ...
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Derivation of Perturbation Terms in Thermodynamic Perturbation Theory

In the "A critical evaluation of perturbation theories by Monte Carlo simulation of the first four perturbation terms in a Helmholtz energy expansion for the Lennard-Jones fluid" paper by T. van ...
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Did R. Feynman know about the different notations for exact and inexact differentials? [closed]

I remember reading a long time ago, the story of a student taking R. Feynman for responsible of her (I think it was a woman, not sure though) fail at an exam of physics because what was written in her ...
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If $dQ_p = dU_p + pdV = dH_p$, then how can $dQ_p / dT = \partial H_p / \partial T$

In the book of Kondepudi & Prigogine, Modern Theormodynamics, at page 65, (under constant pressure) $$dQ_p = dU_p + pdV = dH_p,$$ where $H_p$ is the entalpy at the constant pressure $p$. ...
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What is $\frac{d}{d\psi}\langle\psi| \hat{O} | \psi\rangle$?

I would like to know what is the derivative of an expectation value with respect to the molecular state $$\frac{d}{d\psi}\langle\psi| \hat{\mathbf{O}} | \psi\rangle$$ Note that here $|\psi\rangle$ ...
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The equation of motion for a scalar field in curved spacetime in terms of the covariant derivative

The equation of motion for a scalar field in curved spacetime \frac{\partial\mathcal{L}}{\partial\phi}=\frac{1}{\sqrt{-g}}\partial_{\mu}\left[\sqrt{-g}\frac{\partial\mathcal{L}}{\partial\left(\...
Meaning of time derivative of the Lorentz factor $\gamma$?
This question about the Lorentz factor $\gamma$ in special relativity. I know what $\gamma$ means and how to drive. I'm wondering if I have time derivative of $\gamma$, what dose it mean conceptually?