### Diagnostics: Compendium - Mathematics
d.m

Things you should be completely at ease with:

- vectors and their algebra
- the representation of vectors in Cartesian, spherical and cylindrical coordinate systems (including the required basic trigonometry)
- differentiation and integration of scalar and vector fields (including manipulations such as changes of variables and integration by parts)

Fundamentals: Things you should be able to do (ideally: from scratch, on a blank sheet of paper):

- write the gradient of a function \(f({\bf r})\) in Cartesian coordinates
- write the divergence of a vector field \({\bf F} ({\bf r})\) in Cartesian coordinates
- write the curl of a vector field \({\bf F} ({\bf r})\) in Cartesian coordinates
- write the Laplacian of a function \(f({\bf r})\) in Cartesian coordinates
- write the Laplacian of a vector field \({\bf F} ({\bf r})\) in Cartesian coordinates
- write the transformation law from Cartesian to spherical coordinates
- write the Jacobian for the transformation from Cartesian to spherical coordinates
- write the transformation law from Cartesian to cylindrical coordinates
- write the Jacobian for the transformation from Cartesian to cylindrical coordinates
- Gauss' theorem (also know as the divergence theorem)
- write Stokes' theorem
- use the Dirac delta function in one, two and three dimensions

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Author: Jean-Sébastien Caux

Created: 2022-03-24 Thu 08:42