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.
Questions tagged [calculus]
1188 questions
82
votes
9 answers
How to treat differentials and infinitesimals?
In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such.
In my physics class, it seems like we treat differentials exactly like numbers, and my physics teacher even said that they…
Ovi
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64
votes
4 answers
Rigorous underpinnings of infinitesimals in physics
Just as background, I should say I am a mathematics grad student who is trying to learn some physics. I've been reading "The Theoretical Minimum" by Susskind and Hrabovsky and on page 134, they introduce infinitesimal transformations. Here's the…
Brian Klatt
- 923
51
votes
3 answers
What is the meaning of the third derivative printed on this T-shirt?
Don't be a $\frac{d^3x}{dt^3}$
What does it all mean?
VodkaTampons
38
votes
5 answers
Equivalence between Hamiltonian and Lagrangian Mechanics
I'm reading a proof about Lagrangian => Hamiltonian and one part of it just doesn't make sense to me.
The Lagrangian is written $L(q, \dot q, t)$, and is convex in $\dot q$, and then the Hamiltonian is defined via the Legendre transform
$$H(p,q,t) =…
Mark
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34
votes
7 answers
The usage of chain rule in physics
I often see in physics that, we say that we can multiply infinitesimals to use chain rule. For example,
$$ \frac{dv}{dt} = \frac{dv}{dx} \cdot v(t)$$
But, what bothers me about this is that it raises some serious existence questions for me; when we…
Clemens Bartholdy
- 8,309
28
votes
9 answers
Why use Fourier series instead of Taylor?
In dynamical systems with linear differential equations, we almost always break up the function of independent variable in sines and cosines.
But suppose that my function is smooth and periodic. Then what advantage do I get by using Fourier series…
Atom
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27
votes
21 answers
What happens when a car starts moving? The last moment the car is at rest versus the first moment the car moves
Imagine a car that's at rest and then it starts moving. Consider these two moments:
The last moment the car is at rest.
The first moment the car moves.
The question is: what happens between these 2 moments? It might sound like a silly question and…
fab
- 381
27
votes
14 answers
Explaining how we cannot account for changing acceleration questions without calculus
For context, I am a high school physics teacher.
I am teaching students about the basics of electromagnetic force between two point charges. The equation we use is $F=\frac{kq_1q_2}{r^2}$.
This gives us the instantaneous force and also gives us the…
26
votes
8 answers
Zero velocity, zero acceleration?
In one dimension, the acceleration of a particle can be written as:
$$a = \frac{dv}{dt} = \frac{dv}{dx} \frac{dx}{dt} = v \frac{dv}{dx}$$
Does this equation imply that if:
$$v = 0$$
Then,
$$\Rightarrow a = 0$$
I can think of several situations…
7453rfg
- 403
23
votes
18 answers
Does it make sense to take an infinitesimal volume of shape other than a cube?
The question clearer: Is the infinitesimal cube the absolute smallest infinitesimal volume?
(Sorry if people thought that it meant: "Is it possible and is it done in daily life to use anything other than the Cartesian volume element?" : I know the…
Sidarth
- 1,007
20
votes
3 answers
Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
Mark
- 341
20
votes
5 answers
How to get distance when acceleration is not constant?
I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question.
The equation for distance of an accelerating object with constant acceleration is:
$$d=ut +\frac{1}{2}at^2$$
which…
ben
- 1,547
18
votes
8 answers
Why do we need instantaneous speed?
I am new to this topic and was just wondering about the use of instantaneous speed. I mean, we use to calculate the speed of car let us say at 5 sec. So we take the distance travelled in 4.9 to 5.0 seconds and divide it by time. We get instantaneous…
Srijan
- 735
17
votes
7 answers
What's the difference between average velocity and instantaneous velocity?
Suppose the distance $x$ varies with time as:
$$x = 490t^2.$$
We have to calculate the velocity at $t = 10\ \mathrm s$.
My question is that why can't we just put $t = 10$ in the equation $$x = 490t^2$$ which gives us total distance covered by the…
16
votes
4 answers
Electromagnetic field and continuous and differentiable vector fields
We have notions of derivative for a continuous and differentiable vector fields. The operations like curl,divergence etc. have well defined precise notions for these fields.
We know electrostatic and magneto static fields aren't actually well…
Isomorphic
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