Questions tagged [differentials]
The differentials tag has no usage guidance.
60
questions
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votes
0answers
13 views
Is there any other function similiar to Weierstrass function, that is continuous at every point but non-differentiable at any point on a compact? [migrated]
I’m studying functional series and right now we’re dealing with Weierstrass function. I was wondering if it’s the only known function with this property?
0
votes
1answer
48 views
Problem in table [duplicate]
NDSolve[{t,Evaluate[{ode}\.Sol]},{t,0,10,1}]//TableForm
After executing this with appropriate equations I get solution in the tabular form but when I try to ...
1
vote
1answer
58 views
Partial Differentiation in Mathematica, syntax error? [closed]
I am trying to differentiate some random function using Mathematica at particular nodes, I am though not being able to implement this without being retrieved the following error message:
D: ...
2
votes
1answer
27 views
How to differentiate a composite function which includes unknown functions?
Let $f$ be a $C^2$ function from $\mathbb{R}^3$ to $\mathbb{R}$.
Let $\Phi$ be the function from $(0, \infty) \times [0, \pi] \times [0, 2 \pi]$ to $\mathbb{R}^3$ such that $\Phi(r, \theta, \phi) = (r ...
1
vote
1answer
85 views
0
votes
0answers
57 views
Smooth approximation near a non differentiable point
Let $f:\mathbb{R}_+\rightarrow \mathbb{R}$ be a function differentiable for $x>0$ but non differentiable at $x=0$ (for instance $f=\sqrt{\cdot}$)
and $g$ be a polynomial function.
I know how to ...
0
votes
0answers
29 views
Differential equations system's solutions differ when one of the constant is 0
I am solving the following system of equations with Mathematica.
$u'=-k_{1}ux+k_{2}x^2, x'=k_{1}ux-k_{2}x^2$
and I obtain the solution for x:
$x(t)=\frac{e^{k_{1}C_{1}(t+C_{2})}k_{1}C_{1}}{-1+e^{k_{1}...
2
votes
1answer
52 views
How to differentiate a function that is a function of other functions?
I am trying to differentiate the function epsilon1 with respect to u, but why this does not give me any output?
...
0
votes
2answers
63 views
total differential of a subscripted variable
During use of sub-scripted variables, I came across the following issue
Dt[Subscript[x,0]]
gives
Why is mathematica treating x and not x$_0$ as the ...
4
votes
0answers
75 views
Computing differentials on a manifold
Consider $\phi:SO(3) \to \mathbb{R}^3$, $R \mapsto (R^\top e_3)\times e_3$ where $R$ is a real $3\times 3$ orthogonal matrix and $e_3 = [0\ 0\ 1]^\top$.
Can Mathematica compute the differential of $\...
2
votes
1answer
29 views
Help with evaluation of the differential of a BSplineFunction?
It can be useful to generate a smooth random function over $[-L,L]$ with BSplineFunction:
...
2
votes
2answers
113 views
Vector calculus with index notation
How would you calculate this in Mathematica?
$$\sum_i\partial_i\partial_i G_{jk}$$
$$G_{jk}=\bigg(\frac{\delta_{jk}}{r}+\frac{(x_j-y_j)(x_k-y_k)}{r^3}\bigg)$$
where $r=|\boldsymbol{x}- \boldsymbol{...
2
votes
2answers
49 views
Defining a differential operator that acts on a non-commutative basis
Given a non-commutative basis ${x_0,x_1,x_2}$ I'd like to define a differential operator that acts as so
$$ \Delta_i (\sum_{n=0}^\infty c_n x_i^n) = \sum_{n=1}^\infty c_n x_i^{n-1}, \quad \Delta_i ...
0
votes
0answers
102 views
Transform a field with derivatives
Given a function of Cartesian coordinates $(x, y)$ in $g(x, y) = \frac{d}{dx}f(x, y)-y\frac{d}{dy}f(x, y)$, I want to transform this expression to polar coordinates $(r,\phi)$. I saw a solution using ...
0
votes
0answers
225 views
Commutator of differential operators
Let $P_x = \frac{\hbar}{i}\frac{d}{dx}$, after specifying the commutator relation symbolically $[X, P_x] = i\hbar$, I can ask Mathematica to calculate commutator algebra. My question: is there a way ...
0
votes
1answer
31 views
Function that takes derivative of another function (with any number of arguments) and evaluates it
I would like to supply a function as an argument to another function which then differentiates the function and evaluates it at a set of points.
Suppose I want to differentiate this function,
...
2
votes
0answers
106 views
Computing quadratic differential trajectories with Mathematica
There was a question about a particular case of this, Quadratic differentials; seemingly it contained too little information, so let me try again. This will be also a second take on my previous ...
1
vote
1answer
76 views
How to define a variable to be a function of all the arguments but one?
I have several variables (coordinates) $x_1, x_2, x_3, x_4, z$ and a lot (21, to be precise) functions $g_i$ which are assumed to depend on $x_1, x_2,x_3, x_4$, but not on $z$. I also have a ...
1
vote
0answers
49 views
Symbolic differentiation on a function of matrices and vectors
Let $I_t$, $I$, $V$, $Z$ be vectors and $R$, $B$, $P$, $A$, $\mathcal{K}$, $\mathcal{P}$ be some matrices such that
$$ \begin{eqnarray}
S&=&-(R I+B^\top V)^\top \mathcal{R}(R I+B^\top V)
...
1
vote
2answers
55 views
Differentiating nested functions, Differentiate unevaluated function
I have two functions
G[x_]:=x^6;
S[x_]:=G[x]+x^12
I would like to operate on S[x] with respect to x in three ways, where we take the differentiation as ...
0
votes
3answers
95 views
Leave Parts of Formula inactive in partial Differentiation
for thermodynamics, I would like to use a thermodynamic derivative
$$
\frac 1 T=\frac{\partial S}{\partial E}\Bigg \vert_V
$$i.e. the derivative of the entropy S with respect to the energy E with ...
1
vote
1answer
276 views
Does Mathematica understand the concept of infinitesimal increment?
Commonly, in textbooks, differential of differential increment vanishes, good example is how Euler-Lagrange equations are derived using the differential (from step 2 to step 3 here, you can see ...
6
votes
2answers
160 views
Chain rule when taking derivatives with UpValues
I have a summation function, for which I have defined derivation via
Custom`sum /: D[Custom`sum[idx_, a_, b_, exprs_], y_] := Custom`sum[idx, a, b D[expr, y]];
...
4
votes
4answers
172 views
Find $\frac{dy}{dx}$ if $x\sqrt{1+y}+y\sqrt{1+x}=0$
Find $\frac{dy}{dx}$ if $x\sqrt{1+y}+y\sqrt{1+x}=0$ for $-1\leq x\leq 1$
$$\frac{dy}{dx}=\frac{-1}{(1+x)^2}\text{ if }x\neq y$$
If it was like $y=\sqrt{1+x}$ i think i know how to do it
...
1
vote
1answer
102 views
How to program Mathematica to do the differential operator calculation
I want to create a surface Laplacian under the spheroidal coordinates,
Now, I already have the surface gradient defined, but I don't know how to find the Laplacian.
Since the surface gradient is too ...
4
votes
2answers
724 views
How to define a differential operator in Mathematica? [duplicate]
I want to define an operator $(\partial_{t}+1)^{2}=\partial_{t}\partial_{t}+2\partial_{t}+1$. Then, I want it to act on $t$. My code looks like this:
...
2
votes
1answer
85 views
Solving algebraic equation system with partial derivatives
I have a list of equations. Some of them are algebraic equations like 2x == y / (y+1), others contains derivatives in them(e.x. ...
1
vote
0answers
51 views
Symbolic summation with variable bounds and variable number of indices
I wish to compute compute terms like Sum[f[t[j[1]],t[j[2]],...],{j[1],m},{j[2],n},...] for arbitrary positive integer n and any ...
0
votes
0answers
47 views
Proving $d(dx)=d^2x$
Is it possible to carry out the following differential in Mathematica?
$$d(dx) = d^2x$$
I tried to write:
Dt[1*Dt[x]]
the result is:
...
1
vote
1answer
57 views
Differentiate an Integral-Assumption needed
I already looked into the smaller problems, but I just don't get the clean first derivative, because Mathematica wants to work with imaginary numbers. How do I best supress this here? I tried it with <...
2
votes
1answer
81 views
How does D work with numerical arguments? [duplicate]
If I define
f[x_?NumericQ] := (Sow[x]; SawtoothWave[x])
D[f[x], x] /. x -> 1.1
(* 5.29432 *)
numeric differentiation fails, despite the function being smooth ...
13
votes
2answers
247 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.
...
0
votes
1answer
247 views
How to evaluate and simplify series expansions of long partial derivatives involving trigonometry?
I have 4 maps defined on a plane, i.e. on $\mathbb{R}^{2}$. Let's call them $F,G,H,J$. Let $(s,t) \in \mathbb{R}^{2}$. Define $F(s,t) = (f_{1}(s,t), f_{2}(s,t)).$ Likewise, in components, write
$$ G(...
5
votes
2answers
566 views
How best to write an exponential of differential operators?
I want to evaluate a term like this,
$$\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}$$
and I ...
8
votes
1answer
353 views
Bug? Problem with derivative of interpolating function from FEM
Bug introduced in 10 or earlier and fixed in version 10.4
I am really not sure if this is a bug or I am missing something very trivial.
QUESTION: What I am missing in order to obtain the partial ...
0
votes
0answers
96 views
Problema with Grassmann Derivative: two solutions for the same function
I'm confused as to why mathematica is not giving me the correct answer. I'm using the grassmannOps package and defining $\theta$, $\bar\theta$ as grassmannians and $...
3
votes
2answers
206 views
Defining special function or variable for a derivative in mathematica
I have a question in Mathematica, I would appreciate it if you possibly answered me.
What can I do for defining a special variable for derivative of arbitrary variable.
For example, imagine I have a ...
-4
votes
1answer
450 views
system of differential equations in Mathematica
How can I formulate the addressed system of differential equations in Mathematica for to find a general solution for $f[x_1, x_2, x_3, y_1, y_2, y_3]$.
https://math.stackexchange.com/questions/...
0
votes
3answers
378 views
Computing the first derivative in x, y ,and z
I have the following function:
f:=x^3+yz+z^2x;
I need to compute the first derivative in x, ...
0
votes
0answers
80 views
Series Expansion of Differential Operators [duplicate]
We know about the possibility of series expansion of a function in Mathematica. Same as below, where a function f[a x] is expanded around zero up to 5th order.
<...
9
votes
1answer
433 views
Can we abuse notation and write equations in differential one-form?
Consider a simple equation with a one-form on both sides (mathworld.wolfram is also aware of this):
$$ y\mathrm{d}x = \mathrm{d}y $$
This is a perfectly valid abuse of notation. We can carry the $y$ ...
2
votes
0answers
131 views
How to plot three related differential equations in Mathematica? [closed]
Eq1:
$
\frac{1}{3\phi}=\left[\frac{x}{x+1}\frac{d^{2}}{dx^{2}}+\frac{2x+1}{(x+1)^{2}}\frac{d}{dx}\right]{\phi^{2}}
$
Eq2:
$
\frac{b}{(x+1)^{2}}+\frac{{a}^{\prime}}{x+1}+\frac{b-a}{x(x+1)^{2}}=-\...
2
votes
2answers
958 views
Differentiation of an unknown function
I have to take the partial differentiation of an unknown function.
For example, take the unknown function to be $g(x)$. Then it's derivative w.r.t $x$ is $g'(x)$.
By default, Mathematica ...
2
votes
2answers
6k views
How to take derivative with respect to logarithmic function [closed]
I have a function g as a function of x; i want to take derivative of g with respect to ln x,
i.e. dg/d ln x
where
g= ax^2/(1+ax^2/r^2)
1
vote
1answer
366 views
Derivative of a plot [closed]
I plotted a graph numerically, so I don't have a definition of the plotted function. Now I want to plot the derivative of this graph. Is there any way to do it in Mathematica? I have the following ...
6
votes
1answer
303 views
Better replacement rules to perform this change of variables?
In cosmology, it is common to work with both a normal time variable t and a “conformal” time variable τ, which is defined such ...
1
vote
1answer
431 views
How to compute the composition of linear differential operator [duplicate]
For example, I have to write down the differential operator below as a polynomial in $\partial$
$$(\partial-f_n(x))(\partial-f_{n-1}(x))\cdots(\partial-f_1(x))$$where the product the the composition.
...
0
votes
1answer
85 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 ...
7
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
...
1
vote
1answer
83 views
Specifying independence of a variable in a function
I am dealing with a function of a finite number of variables and among
the operations I wish to do is to differentiate it repeatedly with
respect with any of the variables.
Now this function happens ...
