Questions tagged [differentials]

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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?
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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 ...
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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: ...
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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 ...
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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 ...
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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}...
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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? ...
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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 ...
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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 $\...
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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: ...
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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{...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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) ...
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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 ...
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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 ...
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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 ...
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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]]; ...
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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 ...
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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 ...
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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: ...
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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. ...
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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 ...
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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: ...
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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 <...
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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 ...
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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. ...
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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(...
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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 ...
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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 ...
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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 $...
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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 ...
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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/...
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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, ...
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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. <...
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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 $y$ ...
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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}}=-\...
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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 ...
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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)
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...