1. Curvilinear Coordinates

2. Cylindrical coordinates

3. Cylindrical Coordinates
From: Boas Fig 4.4

4. Spherical coordinates
𝑟𝑑𝜃
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5. Spherical Coordinates
From: Boas Fig 4.5

6. Grad, div, curl Cartesian coordinate vectors are invariant in space.
For curvilinear coordinates, unit CHANGE depending on position
Formulas for Grad, Div, Curl, Laplacian – see Felder Appendix F
Grad, div, curl

7. E&M: Image sources Infinite conducting plane
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8. Electric Dipole
Image credit: physics.stackexchange.com