# 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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### I need an explanation for the time derivative omissions in Landau’s Mechanics: Chapter 1 [closed]

So I have been self-studying Landau and Lifshitz’s Mechanics for a little bit now, and I have been working through the problems, but Problem 3 is giving me some trouble. I solved the Lagrangian ...
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### What happens if we differentiate spacetime with respect to time? [closed]

Essentially, what would differentiating space-time with respect to time provide us with? What are the constraints associated with such operations? Is it possible to obtain a useful physical quantity ...
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### Changing coordinate system [migrated]

Someone please explain how did we get second term in equation 2.15.
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### Differential form of Lorentz equations

A Lorentz transformation for a boost in the $x$ direction ($S'$ moves in $+x$, $v>0$) is given by: $$t'=\gamma\left(t-v\frac{x}{c^2}\right),~x'=\gamma(x-vt)$$ In the derivation of the addition of ...
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### Covariant Directional Derivative

How is the covariant directional derivative $\frac{D}{d\lambda}=\frac{dx^{\mu}}{d\lambda}\nabla_{\mu}$ in GR related to acceleration? I am motivated to ask this question because I’ve seen it stated ...
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### Solving divergence and curl equations numerically

I've recently come to learn about Jefimenko's general solution for Maxwell's equations as well as the FDTD method in electromagnetic optics, and that has got me thinking whether I myself can solve ...
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### How does the chain rule work in sound wave analysis using fluid mechanics? $\tfrac{d x}{dt}\neq v$?

Context: I am reading Landau & Lifshitz's book on Fluid mechanics. Specifically its section on Sound waves. In section 101, the book's authors discuss about nonlinear traveling waves in one ...
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### What's the physical meaning of Curl of Curl of a Vector Field?

The curl of curl of a vector field is, $$\nabla \times (\nabla \times \mathbf{A}) = \nabla (\nabla \cdot \mathbf{A}) - \nabla^2 \mathbf{A}$$ Now, curl means how much a vector field rotates ...
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### Deriving Klein-Gordon equation from Euler-Lagrangian equation: Taking partial derivative inside [duplicate]

Lagrangian for Klein-Gordon equation is given by $$L=\frac{1}{2}\partial_\mu \phi \partial^\mu\phi - m^2\phi^2/2.$$ To derive Klein-Gordon Equation I have to Compute derivative in Euler-Lagrange ...
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### How to calculate the final position of a particle under variable accelaration and its instantenous velocity?

I'm a first-semester physics student who was recently on a train. On a screen, it said the instantaneous velocity of the train was 176 km / h. We had 4 min left until our destination. I wanted to ...
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