New answers tagged coordinate-transformation
7
ClearAll[f]
f[x0_, y0_] := D[{Sqrt[x^2 + y^2], ArcTan[x, y]}, {{x, y}}] /. {x -> x0, y -> y0}
f[0.3, 0.5] // MatrixForm
I would caution you against using MatrixForm in the definition, as that would leave you with results that cannot be easily used in further computation.
1
You can write something like
f[{r_, θ_}] :=
Module[{M = D[{Sqrt[x^2 + y^2], ArcTan[x, y]}, {{x, y}}]},
Block[{x = r Cos[θ], y = r Sin[θ]}, M]]
I wouldn't be surprised if this has a slightly simpler formulation. The symbolic result agrees with what I expect:
Assuming[r > 0, Simplify[f[{r, θ}]]]
(* {{Cos[θ], Sin[θ]}, {-(Sin[θ]/r), Cos[θ]/r}} *)
...
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