Question: Coordinate System Transformation and Gradient Operator- Derive the coordinate transformations for the following systems, providing all necessary steps and details:a- Cartesian (leftrightarrow ) Cylindricalb- Cartesian

Coordinate System Transformation and Gradient Operator- Derive the coordinate transformations for the following systems, providing all necessary steps and details:a- Cartesian $\leftrightarrow $ Cylindricalb- Cartesian $\leftrightarrow $ Spherical- Define a vector: where, and are the last three digits of your Student ID number.- Cartesian $ ightarrow $ Cylindrical Conversion: Convert to cylindrical coordinates at the point .- Cartesian $ ightarrow $ Spherical Conversion: Convert to spherical coordinates at the point .- Derive the gradient operator in:- Cartesian coordinates- Cylindrical coordinates- Spherical coordinates- Given the scalar field, find in cylindrical coordinates.- Given the scalar field, find $ abla \mathrm{f}$ in spherical coordinates.

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