Pre-Quantum Electrodynamics

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