# Questions tagged [differentials]

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• 335
1 vote
57 views

### solving differential equation with matrices

I have to solve two coupled differential equations: ...
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
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
143 views

### How can i solve and plot this non linear ODEs usin NDSOLVE?

I am trying to solve the following non-linear ODEs ...
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
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 ...
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
37 views

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? ...
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
91 views

• 946
119 views

• 445
1 vote
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 ...
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 ...
1 vote
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
245 views

### Chain rule when taking derivatives with UpValues

I have a summation function, for which I have defined derivation via Customsum /: D[Customsum[idx_, a_, b_, exprs_], y_] := Custom`sum[idx, a, b D[expr, y]]; ...
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
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
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: ...
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
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
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: ...
1 vote
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
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
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
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(...