Change of Variables

Substitution Theorem

Suppose is a 1-1, Differentiable Transformation that maps the Region in the plane to the region in the plane. Then:

where is the Jacobian Determinant of

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Derivative of Inverse Coordinate Transformation

If is a 1-1 Differentiable Transformation that maps a region in the uv-plane to a region in the xy-plane and , then we have

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