All Questions
19 questions
1
vote
6
answers
539
views
Is integration physical, but differentiation is not? [closed]
There are electrical (e.g. analogue computers), and even mechanical (ball-pen) methods to generate the integral of a given function.
On the other hand, naively differentiating a physically given ...
- 177
0
votes
0
answers
73
views
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 ...
- 21
0
votes
2
answers
234
views
Why is the differential form of Gauss's Law equivalent to the integral form?
I can understand the Differential form of Gauss's Law ∇⋅𝐄= $\frac{ρ}{ɛ_0}$
as saying that the source of electric field vectors or flow disperse(The divergence of the electric field) is equal to the ...
- 1
-2
votes
2
answers
62
views
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
92
views
What does it mean to differentiate a differential quantity with respect to another quantity it is not dependent upon? [closed]
Recently, I came across this equation while solving a few integrations:
d(xy) = xdy + ydx
When I searched for its proof, I found that we assume another differential quantity, say dp, and then ...
- 53
0
votes
1
answer
73
views
Why did my rearrangement with chain rule end up equating velocity to position?
We all know acceleration is the time-derivative of velocity which in turn is the time-derivative of position. Vice versa: position is the integration of velocity and velocity itself is the integration ...
- 401
0
votes
0
answers
50
views
Why area under a curve equals the sum of values of function/quantities taken elementally? [duplicate]
Background:
I was taught basic formulas of differentiation and integration when I started learning physics. However, it wasn't taught through intuitions and concepts. It was like : " Hey these ...
- 325
5
votes
5
answers
656
views
Is $dx$ always positive?
When we refer to change in a quantity, we define it to be (final-initial). If it is positive it indicates an increase from the initial value and negative indicates a decrease.
But when we take this to ...
- 71
0
votes
1
answer
435
views
Find the distance travelled between $t=0$ and $t=5$ [closed]
The position vector of a particle is given as $\vec r = \frac43 t^{3/2}\hat i - \frac{1}{2} t^2\hat j + 2 \hat k$, $t$ is in seconds. Find the distance travelled between $t = 0$ and $t = 5$ seconds.
...
- 231
-3
votes
2
answers
308
views
If we divide the second equation of motion by time $t$, why don't we get the first equation of motion where has $1/2$ come from? [duplicate]
The first equation of motion is $v = u + at$.
The second equation of motion is $s = ut + \frac{at^2}{2}$.
If we divide the second equation of motion by time $t$, why don't we get the first equation of ...
1
vote
1
answer
141
views
What is the difference between zero and an infinitesimal number?
In a standard Atwood machine physics problem, the string going over the pulley is considered massless. So does that imply mass = 0 or mass = dm? General question: what is the difference between 0 and ...
- 87
2
votes
4
answers
979
views
Question about infinitesimals
In physics for example in electrostatics we consider infinitesimal quantities like $dq$ which means a very small charge which we integrate over the entire body. Now the meaning of $dy$ or $dx$ means a ...
- 317
0
votes
3
answers
2k
views
How to derive kinematics equations using calculus? [closed]
I read derivation of kinematics equations using calculus:
$$a=\frac{\text dv}{\text dt}$$
$$\implies \text dv=a\text dt$$
$$\implies \int_{v_0}^v\text dv=\int_0^t a\text dt$$
$$\implies v-v_0=at$$
$$\...
- 259
0
votes
0
answers
94
views
Get rid of the derivatives and relativistic mass in Feynman lectures
i have a problem with get rid of the derivatives in Feynman lectures (chapter 15, Equivalence of mass and energy). The problem:
we have $\frac {d(mc^2)}{dt} = v\cdot \frac {d(mv)}{dt}$, then we ...
4
votes
2
answers
861
views
Integration of tangential acceleration with respect to time
Here, by tangential acceleration, I mean the component of acceleration along the velocity vector.
What do you get when you integrate tangential acceleration with respect to time? What does the '$v$' ...
- 1,106
1
vote
4
answers
4k
views
Area under and slope of the motion graphs
I wanted to ask in general what area under the graph means. Also which physical quantity is highlighted by area under distance vs time graph.
I'm confused that area is a 2 dimensional concept and it ...
- 1,157
4
votes
2
answers
18k
views
Why and when do we differentiate or integrate equations in physics? [closed]
I'm an engineering student and none of my professors ever explained why do we use derivations and/or integrations in physics. So I have this task, it goes like:
The object is moving in a positive ...
- 41
2
votes
3
answers
390
views
Physical motivation for differentiation under the integral
I am thinking about the mathematical process of "differentiating underneath the integral", i.e. applying the theorem $$\partial_s \int_{-\infty}^\infty f(x,s)\,dx=\int_{-\infty}^\infty \partial_s f(x,...
- 153
14
votes
4
answers
22k
views
How do you do an integral involving the derivative of a delta function?
I got an integral in solving Schrodinger equation with delta function potential. It looks like
$$\int \frac{y(x)}{x} \frac{\mathrm{d}\delta(x-x_0)}{\mathrm{d}x}$$
I'm trying to solve this by ...
- 325