All Questions
Tagged with calculus mathematics
92
questions
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6
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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.
- 1
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2
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85
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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 $dr$...
- 31
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11
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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 ...
- 101
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1
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74
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What does the notation $d𝜏'$ mean?
$\text{I was studying helmotz theorem and saw this notation, what does it mean? How is d}\tau' \, \text{ different from d}\tau \text{?}$
From :- David J. Griffiths-Introduction to Electrodynamics-...
- 33
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54
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When can I commute the 4-gradient and the "space-time" integral?
Let's say I have the following situation
$$I = \dfrac{\partial}{\partial x^{\alpha}}\int e^{k_{\mu}x^{\mu}} \;d^4k$$
Would I be able to commute the integral and the partial derivative? If so, why is ...
- 1
1
vote
1
answer
64
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Material to Study the Definition, Algebra, and Use of Infinitesimals in Physics [closed]
This is going to be a rather general question about suggestions on best supplementary material to properly explain the use of infinitesimals (or differentials?) for the purposes of integration or ...
0
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1
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31
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Differentiation of a product of functions
If I have three (vector)functions, all dependent on different (complex)variables:
\begin{equation}
a = X^{\mu_1}(z_1, \bar{z}_1),
b = X^{\mu_2}(z_2, \bar{z}_2),
c= X^{\mu_3}(z_3, \bar{z}_3)
\end{...
- 41
1
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1
answer
40
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Electric field at a point created by a charged object (derivation/integration process)
I was hoping someone can help me understand the math behind the electric field (electrostatics). I have gaps in my knowledge about integrals and derivatives (university moves very quickly and it has ...
- 19
2
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2
answers
114
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Consistency of perturbative theory when some of the first-order terms are smaller than second-order terms?
There is something that always puzzled me with perturbative approaches.
To my understanding perturbative approaches are often qualified in terms of the order of the perturbation considered. For ...
- 1,109
-2
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2
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59
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Can the different differentiation notations be equated and do they have an integral definition? [closed]
Are these all equivalent and is there an extension of this to other notation?
Does anyone have a clear and concise chart equating the different notation dialects?
I am also curious if there are more ...
1
vote
3
answers
205
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Why does a particle initially at rest at origin with acceleration as square of its $x$ coordinate ever move?
Consider a particle initially at rest at origin, with acceleration, $a$, such that $ a(x)=x^2$.
Since the particle is at origin, initial acceleration would be 0. It's also at rest initially. Its $x$-...
- 337
1
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2
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118
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Lagrangian total time derivative - continues second-order differential
In the lagrangian, adding total time derivative doesn't change equation of motion.
$$L' = L + \frac{d}{dt}f(q,t).$$
After playing with it, I realize that this is only true if the $f(q,t)$ function has ...
- 525
1
vote
1
answer
141
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What does it mean to differentiate a scalar with respect to a vector?
I am reading the special relativity lecture notes that I got from a professor of mine. It says that the Lagrangian is
$$L = \frac{1}{2}m|\dot{\boldsymbol{x}}|^2 - V(\boldsymbol{x}) \tag{1}$$
The notes ...
- 1,212
1
vote
2
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63
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Expressing infinitesimal physical quantities
In physics class, my teacher demonstrated that in polar coordinates, an infinitesimal area involving radial length dr and infinitesimal angle dθ is equal to rdr dθ, since the area is roughly a square ...
- 303
3
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3
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323
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What is wrong with this analogy finding equality between two formulae of average velocity?
I have seen several questions on this confusion. Most are related with the issue of using variable acceleration. So here is an example where I am using a constant acceleration, but it still seems to ...
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