Questions tagged [differentials]
The differentials tag has no usage guidance.
76
questions
2
votes
2
answers
56
views
Product of different differential operators
I need to define a multivariable differential equation of the type
$$
\mathcal{D}=\Theta_1^2-z_1(-\Theta_1+\Theta_2+\Theta_3+\Theta_4)(1+\Theta_1+\Theta_2+\Theta_3+\Theta_4)\\
\;\;\;\;\;\;\;\;\;\;\;\;\...
- 21
1
vote
1
answer
61
views
How to perform the first and second derivatives of Nth polynomials?
Suppose
$P(x,y)=\displaystyle\sum^{N}_{i+j=0}\alpha_{ij}x^{i}y^{i} \equiv \alpha_{00}+\alpha_{10}x+\alpha_{01}y+a_{11}xy+\ldots+a_{0N}y^{N}$
is a multivariable polynomial of $N$th degree. I want to ...
5
votes
3
answers
129
views
What's the Mathematica command for $\frac{\partial^a}{\partial n^a}\binom{n}{k}$?
What's the Mathematica command for
$$f(a,n,k)=\frac{\partial^a}{\partial n^a}\binom{n}{k}$$
I tried
f[a_,n_,k_]:=D[Binomial[n,k], {n,a}]
but didn't work. To make ...
- 435
0
votes
1
answer
47
views
How to evaluate these derivatives
I'm trying to evaluate the following functions S1,S2 and their derivatives:
As you can see the S1 and it's derivatives it's working but for the S2 and it's derivatives I'm getting the error displayed ...
- 103
0
votes
1
answer
109
views
Second order differential operator in Mathematica
I am trying to write the code for the following expression in Mathematica:
$$\partial_{x} e^{-g x}=-g e^{-g x}+e^{-g x} \partial_{x}\,.$$
I was able to do so with the help of the following links with ...
- 3
0
votes
1
answer
74
views
Mathematica: Partial derivative with respect to tensors
Anyone know how to do the partial derivative of a tensor in d dimensions on Mathematica ?
I want to implement something which will calculate directly like that :
1
vote
1
answer
67
views
How can I make sure if the given curve is monotonic with respect to $x$ and $y$?
I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1<x< 2$ and $0<y<\pi$. I use ContourPlot to ses those values of $(x,y)$ for which $g(...
- 463
-1
votes
1
answer
99
views
Van der Pol's equation [closed]
Consider the van der Pol equation below:
(x′′)+c(x^2−1)(x′)+(x)=0 , which governs
the flow of current in a vacuum tube with three internal elements. It can be written as
the system
x′= y , y′= -x-c(x^...
0
votes
0
answers
58
views
Exclude a term in a differential equation
How can I exclude this term (The red box) from derivation to make it consider it as a constant (Just a constant to be multiplied ), I am getting the differentiation for the whole equation but I want a ...
- 37
0
votes
0
answers
66
views
Derivative with respect to function of any argument
I have the expression
L = v1[k1] * M[k1, k2] * v2[k2].
v1, M, and ...
- 21
0
votes
0
answers
50
views
Table with two indices does not work properly
I am a beginner in computational mathematics so apologies in advance for my probably poor code writing skills. I am using the package << matrixEDC.m to do some exterior algebra computations.
...
0
votes
1
answer
213
views
Partial derivatives of this function
I have a function $y(x)$ which is the solution of the initial value problem -
$y = \frac{1-y}{A} - \frac{y.|r(x)+m(x)|^2}{B}$ with an initial condition $y_0=1$.
I solved for $y(x)$ using the following ...
- 109
1
vote
2
answers
133
views
How to make a change of variable $y=x^2$ in the differential operator $\frac{d^2}{d y^2}$?
I have this differential operator
$$\frac{d^2}{d y^2}\qquad (1)$$
I want to make a change of variable $y=x^2$ in $(1)$ so that I get this differential operator
$$ \frac{1}{4 x^2} \frac{d^2 }{d x^...
- 335
1
vote
1
answer
57
views
solving differential equation with matrices
I have to solve two coupled differential equations:
...
0
votes
1
answer
94
views
Transformation of Differential Operators
I would like to gain some knowledge about how to transform differential operators to different coordinate systems using Mathematica. I know that the Laplacian ...
- 831
2
votes
2
answers
168
views
How to solve these two differential equations
I have two differential equations and I try to use function DSolve to solve them together.
...
- 121
0
votes
1
answer
143
views
How can i solve and plot this non linear ODEs usin NDSOLVE?
I am trying to solve the following non-linear ODEs
...
3
votes
2
answers
220
views
How calculate integral of differential form [duplicate]
I've this differential form:
w = (e^y + z*e^x)dx + ((x + 1) e^y + e^z)dy + ((y + 2) e^z + e^x)dz
It is sure exact, so I'm trying to find a primitive of w.
...
- 121
0
votes
1
answer
58
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 ...
- 11
2
votes
1
answer
161
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: ...
- 87
2
votes
1
answer
37
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 ...
- 371
1
vote
1
answer
93
views
0
votes
0
answers
77
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 ...
- 442
0
votes
0
answers
35
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:
$x(t)=\frac{e^{k_{1}C_{1}(t+C_{2})}k_{1}C_{1}}{-1+e^{k_{1}...
2
votes
1
answer
56
views
How to differentiate a function that is a function of other functions?
I am trying to differentiate the function epsilon1 with respect to u, but why this does not give me any output?
...
- 25
0
votes
2
answers
126
views
total differential of a subscripted variable
During use of sub-scripted variables, I came across the following issue
Dt[Subscript[x,0]]
gives
Why is mathematica treating x and not x$_0$ as the ...
- 902
4
votes
0
answers
91
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 $\...
- 13.6k
2
votes
1
answer
41
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:
...
- 1,197
2
votes
2
answers
209
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{...
- 946
3
votes
2
answers
119
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
$$ \Delta_i (\sum_{n=0}^\infty c_n x_i^n) = \sum_{n=1}^\infty c_n x_i^{n-1}, \quad \Delta_i ...
- 203
0
votes
0
answers
183
views
Transform a field with derivatives
Given a function of Cartesian coordinates $(x, y)$ in $g(x, y) = \frac{d}{dx}f(x, y)-y\frac{d}{dy}f(x, y)$, I want to transform this expression to polar coordinates $(r,\phi)$. I saw a solution using ...
- 368
0
votes
0
answers
517
views
Commutator of differential operators
Let $P_x = \frac{\hbar}{i}\frac{d}{dx}$, after specifying the commutator relation symbolically $[X, P_x] = i\hbar$, I can ask Mathematica to calculate commutator algebra. My question: is there a way ...
- 368
0
votes
1
answer
37
views
Function that takes derivative of another function (with any number of arguments) and evaluates it
I would like to supply a function as an argument to another function which then differentiates the function and evaluates it at a set of points.
Suppose I want to differentiate this function,
...
- 3,077
2
votes
0
answers
191
views
Computing quadratic differential trajectories with Mathematica
There was a question about a particular case of this, Quadratic differentials; seemingly it contained too little information, so let me try again. This will be also a second take on my previous ...
- 2,037
1
vote
1
answer
100
views
How to define a variable to be a function of all the arguments but one?
I have several variables (coordinates) $x_1, x_2, x_3, x_4, z$ and a lot (21, to be precise) functions $g_i$ which are assumed to depend on $x_1, x_2,x_3, x_4$, but not on $z$. I also have a ...
- 283
1
vote
0
answers
53
views
Symbolic differentiation on a function of matrices and vectors
Let $I_t$, $I$, $V$, $Z$ be vectors and $R$, $B$, $P$, $A$, $\mathcal{K}$, $\mathcal{P}$ be some matrices such that
$$ \begin{eqnarray}
S&=&-(R I+B^\top V)^\top \mathcal{R}(R I+B^\top V)
...
- 445
1
vote
2
answers
144
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 ...
- 241
0
votes
3
answers
112
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 ...
- 241
1
vote
1
answer
496
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 ...
- 113
6
votes
2
answers
245
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]];
...
- 91
5
votes
4
answers
219
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
...
- 311
1
vote
1
answer
192
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 ...
- 323
4
votes
2
answers
1k
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:
...
- 53
2
votes
1
answer
123
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. ...
- 123
1
vote
0
answers
66
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 ...
- 21
0
votes
0
answers
58
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:
...
- 929
1
vote
1
answer
61
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 <...
- 313
2
votes
1
answer
97
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 ...
- 14.7k
13
votes
2
answers
310
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.
...
- 14.7k
0
votes
1
answer
305
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(...
- 211