Pre-Quantum Electrodynamics
Diagnostics: Compendium - Mathematicsd.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

Created: 2024-02-27 Tue 10:31