Questions tagged [calculus]
Calculus is the branch of mathematics which deals with the study of rate of change of quantities. This is usually divided into differential calculus and integral calculus which are concerned with derivatives and integrals respectively. DO NOT USE THIS TAG just because your question makes use of calculus.
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In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?
Here are the equations. ($V$ represents a potential function and $p$ represents momentum.)
$$V(q_1,q_2) = V(aq_1 - bq_2)$$
$$\dot{p}_1 = -aV'(aq_1 - bq_2)$$
$$\dot{p}_2 = +bV'(aq_1 - bq_2)$$
Should ...
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Area under $v$-$x$ graph [closed]
What does area under $v$-$x$ graph, that is velocity vs displacement graph represent.
I was given a problem by my teacher where he asked us to analyse graph of $v$-$x$ where the curve was a parabola ...
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The reason for curl free [migrated]
I wonder about the reason for the idea of this, would you mind explain for me this can happen in mathematics.
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Physics Kinematics Equation $\Delta x = v_f\Delta t - \frac 12 a \Delta t ^2$ Derivation Using Calculus [closed]
I was wondering how you can derive the physics kinematics equation $\Delta x = v_f\Delta t - \frac 12 a \Delta t ^2$ algebraically. I understand where this equation comes from geometrically (when a=...
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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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Deriving OPE between vertex operator: Di Francesco Conformal Field Theory equation 6.65
How does one get Di Francesco Conformal Field Theory equation 6.65:
$$ V_\alpha(z,\bar{z})V_\beta(w,\bar{w}) \sim |z-w|^{\frac{2\alpha\beta}{4\pi g}} V_{\alpha+\beta}(w,\bar{w})+\ldots~?\tag{6.65}$$
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Why do I get two different expression for $dV$ by different methods?
So, I was taught that if we have to find the component for a very small change in volume say $dV$ then it is equal to the product of total surface of the object say $s$ and the small thickness say $dr$...
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What happens to $\frac{d}{dt}\left(\hat{v}\right)$ at the highest point a projectile reaches when launched vertically upwards?
Acceleration is given by $\dot{\vec{v}} = \frac{d}{dt}\left( v \hat{v}\right) = \dot{v} \hat{v} + v \dot{\hat{v}}$.
What happens to $\dot{\hat{v}}$ when the direction of velocity flips by $180^o$?
E....
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Taylor condition on the general formula for momentum commutator [closed]
My quantum homework asked me the following question:
Prove that for any $f(x)$ such that $f$ admits a Taylor expansion, the following is true:
$$[f(x), \hat{p}] = i\hbar\frac{\mathrm{d}f}{\mathrm{d}x}...
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Is there an "obvious" reason for why the second derivative of an antisymmetric tensor with respect to coordinates over both of its indices equal to 0?
It was kind of difficult to word the title so I'll restate the question here. My professor took it almost as a given that
$$\frac{\partial T^{\mu\nu}}{\partial X^{\mu}\partial X^\nu} = 0$$
If $T^{\mu\...
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$p(z)$ polynomial with $p(0) \neq 0 \neq p(1)$; $\int_{\partial R} \frac{p(z)}{(z-1)z^2}dz$; $R=[-1,2] \times [-1,3]$ [migrated]
Consider $p(z)$ a polynomial such that $p(0) \neq 0 \neq p(1)$ and the rectangle $R=[-1,2] \times [-1,3]$, calculate $\int_{\partial R} \frac{p(z)}{(z-1)z^2}dz$
The poles $P=\{0,1\}$ are in the ...
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Critical Points of a Wigner function
I am interested in calculating the critical points of a Wigner function
$$
W(x,p)=\frac{1}{\pi}\int_{-\infty}^\infty\left\langle x+y\middle|\rho\middle|x-y\right\rangle e^{-2ipy}\mathrm{d}y
$$
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Epidemic spreading model
I'm studying a model in the field of complex systems regarding the epidemic spreading. The model is the susceptible-infected model, i.e., there is a population of N subjects and each of them can ...
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Is this an error in deriving the Rayleigh-Jeans law? Kunstatter and Das's Symmetry SR and QM Ultraviolet Catastrophy
My question regards G. Kunstatter and S. Das, A First Course on Symmetry,
Special Relativity and Quantum Mechanics, Undergraduate Lecture Notes
in Physics, https://doi.org/10.1007/978-3-030-92346-4\_8
...
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How to understand $W=pc$ in Feynman's Lectures on physics?
Pictures below are from 34-3 of Feynman's Lectures on physics. I can't understand the red line.
The $p$ is momentum, $c$ is light speed. I can't understand the red line. I feel the author think $pc$ ...
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