Mathematics · University
Jacobian of a planar transformation · formula reference
An integral change of variables uses the absolute determinant; this question asks for its signed value.
Formula
An integral change of variables uses the absolute determinant; this question asks for its signed value.
det ∂(u,v)/∂(x,y) = uₓvᵧ − uᵧvₓ
Worked example
Let u = 4x² − y² and v = 5xy. Calculate the signed Jacobian determinant ∂(u,v)/∂(x,y) at (9,5). Round the final result to 4 decimal places if needed.
The derivative matrix is [[72,-10],[25,45]]. Its determinant is 2(5)[4(9)² + (5)²].
3490
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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