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Jacobian transformation [duplicate]

I would like to calculate the Jacobian transformation of the measure $dx dy$ $z = e^{x+iy}, \bar{z}=e^{x-iy}$ which should give $-2i|z|^2$. I am not sure how to do this in Mathematica. Further, I need ...
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How to make traditional output for derivatives

Hello again after some pause. i have a problem how to present partial derivatives in traditional form, not as Mathematica gave it to me in its notation. So I want to present this ...
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Simple ways to evaluate a derivative at a point?

The contrast in behavior between, say, f[x_] = Sin[x^2]; f' vs. u[x_, y_] = Cos[x + y^2]; has always bothered my ...
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Create complicated text formulas in graphics

I want to put somewhat complicated, or at least non-standardly formatted, text on some of my graphics. For example, I'd like to be able to use f^(x) (where the <...
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How to substitute numeric values in a symbolic Jacobian matrix?

I have a multi-variate function from $\mathbb{R}^n\to\mathbb{R}^n$. Choosing any desired initial vector, we can produce the corresponding function value, which is a vector as follows. The main problem ...
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Optimizing an energy functional in mathematica using variational calculus

I have an energy functional which I want to optimize using calculus of variation. It would be nice if someone could please post a working example using mathematica. The procedure is as follows, ...
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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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Computing Jacobian matrix

I am trying to compute the Jacobian matrix J. In my case, f and x are 3-vectors (my vectors are named g and a instead), so J should be a 3X3 matrix. Here's the code I'm using: ...
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Symbolic Jacobian computation

I have an equation for which I would like to compute the Jacobian symbolically. $$f(x)=Ax-diag(x)(Ax+b)$$, where $x\in \mathbb{R}^n$, $A\in \mathbb{R}^{n\times n}$ and $b\in \mathbb{R}^n$. I am new ...
910 views

Factor vector out of a matrix

I am wondering how to factor a,a,...,a out of sim so that I can write sim as the ...
Suppose I have a vector function of $n$ components and it has $n+m$ arguments, $$\vec{f}(x_1,x_2,\dots,x_n, y_1, y_2, \dots, y_{m})$$ where $n, m$ are around 10. I want to create a Jacobian matrix ...