THE ARK OF MATHEMATICS PART 4: MULTIVARIABLE CALCULUS INTEGRALS by Chad Clawitter

Author:Chad Clawitter [Clawitter, Chad]
Language: eng
Format: azw3, pdf
Published: 2019-03-27T16:00:00+00:00

We want to do a change of variables from our rectangular coordinates, x, y, to our new parameters, u, v. We need to represent our rectangular coordinates as a function of our new parameters, x(u,v), y(u,v).

The area of each small patch can be approximated as the magnitude of the cross product of the two vectors spanning the parallelogram. The area of the patch is calculated as the magnitude of the cross product of the vectors that resulted from subtracting the position vectors at the three endpoints of the parallelogram. The matrix formed out the partial derivatives is called the Jacobian Matrix. The determinant of this matrix is called the Jacobian Determinant.

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