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53 views

Feynman's subscript notation

Consider this vector calculus identity: $$ \mathbf{A} \times \left( \nabla \times \mathbf{B} \right) = \nabla_\mathbf{B} \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A} \cdot \nabla \right) ...
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1answer
116 views

Covariant derivative-Differential

I was trying to prove that the derivative-four vector are covariant. This can be proved only if you consider the time and space derivatives to be $\dfrac{\partial}{\partial ...
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2answers
1k views

Finding an equation for velocity and acceleration

I'm trying to derive an equation for the velocity and acceleration of an object undergoing simple harmonic motion. I have the equation for displacement: $x = A\sin (2 \pi ft)$ If I differentiate the ...
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0answers
35 views

How to derive the schwarzchild metric?

I'm having trouble differentiating the following when making a change of co-ordinates to determine the Schwarzchild metric. $$r'^{2}=r^{2}C(r)$$ Then taking the total derivative of both sides, the ...
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1answer
48 views

Covariant derivative of a vanishing tensor component [closed]

Is the covariant derivative of a vanishing tensor component necessarily zero?
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0answers
55 views

How to do this index notation differentiation?

I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ? $$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} ...
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47 views

Vector Derivative Transport Theorem Application

I have a position vector in frame A, the derivative of which I want to take relative to an observer in frame B. I apply the Vector Derivative Transport Theorem. The obtained velocity vector is left in ...
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0answers
102 views

What is difference between $\frac {dr}{dt}$ and $\frac {\partial r}{\partial t}$? [duplicate]

What is difference in physical meaning of partial time derivative and ordinary derivative of $r$? $$\frac {\partial r}{\partial t}\quad\text{and}\quad \frac {dr}{dt}.$$ I know that ordinary time ...
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0answers
106 views

Why does the cross derivative of the partition function disappear here?

They state that the chemical potential in a canonical ensemble is given by: $$\mu = -kT \frac{\partial{\ln Z(N,V,T)}}{\partial{N}} \tag{1}$$ But if I use the definition of chemical partial (which I ...
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1answer
69 views

Is there any case where one would use, snap, crackle or pop? [duplicate]

As we all know, if you differentiate distance with reference to time, you get speed, and likewise, differentiating speed you get acceleration. However, if you keep differentiating, to the rate of ...
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1answer
221 views

How to find the intrinsic covariant derivative component?

How to find the intrinsic covariant derivative component? In general relativity the elements of the acceleration four-vector are related to the elements of the four-velocity through a covariant ...
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0answers
119 views

Nicholas Kollerstrom article on the history of Calculus

Today, Newton┬┤s birthday, I read an article posted in the arXiv by Nicholas Kollerstrom http://www.arxiv.org/abs/1212.2666 That basically claims that Newton did not invent Calculus. The article does ...
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2answers
145 views

Why and how maximum force is $\frac{dF}{dx}=0$

In an certain question my teacher asked to find the maximum force. She said that the maximum force in electrostatics means $\frac{dF}{dx}=0$. Why is it like that?
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0answers
51 views

Why does $d$ mean? [migrated]

What do the $d$'s mean? I've seen them in other formulas as well.
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3answers
121 views

How to recognize broken candies from whole ones [closed]

Let's say I have a bag full of sugar candy. Some will be whole, some will be dent, some will be broken (in part, or half, etc). Let's say I have a device with an input box where I empty the bag, and ...
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votes
3answers
157 views

Is there any other mathematical tool to measure velocity, instead useing derivative? [closed]

To measure velocity we use derivative $$v=\frac {dr}{dt}.$$ Is the any other mathematical tool to do this?