MATLAB for Scientists and Engineers. Differential and Integral Calculus by Pérez López César

Author:Pérez López, César [Pérez López, César]
Language: eng
Format: epub
Publisher: UNKNOWN
Published: 2020-03-23T16:00:00+00:00

We know that the transformation equations are:

.

Obviously, the functions have continuous partial derivatives. Let's see if the determinant of the Jacobian of the transformation is non-zero:

>> J = simplify(jacobian([a*cos(b); a*sin(b)], [a, b]))

J =

[ cos(b), -a*sin(b)]

[ sin(b), a*cos(b)]

>> pretty(simplify(sym(det(J))))

a

We see that the Jacobian of the transformation is non-zero ( a ¹ 0 ). Thus, the inverse function theorem is applicable. The determinant of the Jacobian of the inverse transformation will be 1/a .

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