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Questions tagged [differentials]

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9
votes
1answer
422 views

Can we abuse notation and write equations in differential one-form?

Consider a simple equation with a one-form on both sides (mathworld.wolfram is also aware of this): $$ y\mathrm{d}x = \mathrm{d}y $$ This is a perfectly valid abuse of notation. We can carry the $y$ ...
13
votes
2answers
239 views

Differentiation and series expansion of dot product - inconsistent results

Bug introduced in 9.0 or earlier and persisting through 11.3 or later Bug resolved in 12.0 As of 12.0, we have an unevaluated result - inconsistent with the differentiation result, but not invalid. ...
5
votes
2answers
542 views

How best to write an exponential of differential operators?

I want to evaluate a term like this, $$\left.\exp\left({1\over 2}\sum_{i,j=1}^{n}(A^{-1})_{ij}{\partial \over \partial x_i}{\partial \over \partial x_j}\right) f(\vec{x})\right|_{\vec{x}=0}$$ and I ...
-4
votes
1answer
432 views

system of differential equations in Mathematica

How can I formulate the addressed system of differential equations in Mathematica for to find a general solution for $f[x_1, x_2, x_3, y_1, y_2, y_3]$. https://math.stackexchange.com/questions/...
6
votes
1answer
1k views

Taking the derivative of a function with indexed variables

I have a number of functions that depend on a variable x. I am using a second, integer variable to index these functions, i.e. something like ...
5
votes
1answer
125 views

Apparently contradictory output from Series and D

I defined a function as: g[b_] := Integrate[f[n]Exp[-b DA (n.u)^2], n] Obviously D[g[b], b] /. b -> 0 gives ...
3
votes
1answer
662 views

Extract coefficients of differential form in package RGTC

I am using the Package RGTC to do some calculations in Supergravity. It allows to define differential forms after specifying a co-frame. I am working in with the 10d coordinates $\{t,x,y,z,r,\phi_1,\...
2
votes
2answers
916 views

Differentiation of an unknown function

I have to take the partial differentiation of an unknown function. For example, take the unknown function to be $g(x)$. Then it's derivative w.r.t $x$ is $g'(x)$. By default, Mathematica ...
0
votes
1answer
84 views

Differentiating two tables x and y?

I have two tables x and y with x={673,674,675,...} and y={0,1,2,...} and delta=dx/dy. I would like to know how delta can be calculated knowing that delta is the derivative of x divided by the ...