Differentiating vector function [Mathematica]

In summary, the speaker is asking for help with differentiating a vector function in Mathematica. They mention that the function is tricky to differentiate by hand and provide the function itself as well as a known correct derivative from a paper they are basing their work on. They want to know how to show this equality in Mathematica and question the lack of gamma dependence in the derivation.
  • #1
Phudge
1
0
Hi.
So I have this vector function which I need to differentiate, it is however very tricky to do by hand, so I'm doing it in Mathematica.
[tex]\hat{u}=\left\langle\bar{u}+\bar{r}\frac{(1+\gamma)}{r(r+\bar{u}\cdot \bar{r})}\right\rangle[/tex]
(The brackets denote normalisation)

I want to do this differentiation for the different components of r but first I want to show:

[tex]\frac{\partial\hat{u}}{\partial\gamma}=(\bar{r}-\bar{u}(\bar{u}\cdot\bar{r})\frac{1}{r(r+\bar{u}\cdot\bar{r})}[/tex]
which I know to be correct from the paper I am basing my work on.
So my question to you guys is, how would I show that equality in Mathematica?
 
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  • #2
How come that there is no gamma dependence in you derivation?
 

Related to Differentiating vector function [Mathematica]

1. What is a vector function?

A vector function is a mathematical function that maps a set of inputs to a corresponding set of outputs, where both the inputs and outputs are vectors. In other words, it takes in a vector as its input and produces a vector as its output.

2. How do I differentiate a vector function using Mathematica?

To differentiate a vector function in Mathematica, you can use the function D followed by the vector function and the variable you want to differentiate with respect to. For example, if the vector function is f[x_, y_] := {x^2, y^3}, then D[f[x, y], x] will give the derivative with respect to x.

3. Can I differentiate a vector function with multiple variables?

Yes, you can differentiate a vector function with multiple variables in Mathematica. You just need to specify which variable you want to differentiate with respect to using the D function. For example, D[f[x, y], x] will differentiate f with respect to x, while D[f[x, y], y] will differentiate f with respect to y.

4. How do I plot the derivative of a vector function in Mathematica?

To plot the derivative of a vector function in Mathematica, you can use the VectorPlot function. This function takes in the vector function and its derivative as arguments and will produce a plot of the vector field corresponding to the derivative.

5. Is it possible to differentiate a vector function numerically in Mathematica?

Yes, it is possible to differentiate a vector function numerically in Mathematica using the NDSolve function. This function can take in a vector function and numerically compute its derivative over a specified range of values. Additionally, you can use the ListVectorPlot function to visualize the resulting numerical derivative.

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