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Course: Multivariable calculus > Unit 2

Lesson 13: Jacobian
Math
Multivariable calculus
Derivatives of multivariable functions
Jacobian
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Jacobian determinant

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Problem

Let f be a transformation from R2 to R2. Its Jacobian matrix is given below.
J(f)=[cos⁡(θ)−rsin⁡(θ)sin⁡(θ)rcos⁡(θ)]
Find the Jacobian determinant of f.
|J(f)|=
How will f expand or contract space around the point r=12,θ=π2?
Choose 1 answer: