Ref 1 Although many books on electromagnetism briefly cover cavity resonators I have yet to see one which is easy to follow and yet covers them really comprehensively. Worth mentioning are:-
1a H.R.L Lamont, Wave Guides, A Methuen’s Monograph on Physical Subjects, Methuen & Co. Ltd., London. First Published June 1942. A small book with just one chapter on cavity resonators but does give field equations and some field plots for rectangular, cylindrical and spherical cavities.
1b G. Goubau, Electromagnetic Waveguides and Cavities, Pergamon Press, 1961. Derives the equations for rectangular, cylindrical and spherical cavities but not easy to follow due to use of non standard symbols in equations. No field plots given.
Ref 2 2a The Finite Difference Time Domain Method for Electromagnetics by Karl S. Kunz and Raymond J. Luebbers, CRC Press, 1993. This is the simplest book covering the basics of the technique and giving detailed cell calculation programs. Unfortunately it uses a method for calculating separately the field scattered off objects and the incident field and this is an unnecessary complication as just computing the total field is simpler.
2b Computational Electrodynamics The Finite-Difference Time-Domain Method by Allan Taflove, Artech House, Inc.,1995. Covers many of the different FDTD techniques but misses some of the detail for beginners such as how to handle fields at boundaries and build objects out of grid squares which Kunz does better.
2c Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media, Kane S. Yee. IEEE Transactions on Antennas and Propagation, Volume Ap-14, number 3, May 1966. The original paper described the FDTD technique in 2 dimensional space only but is probably the simplest introduction to the topic. Gives an example of a 2 dimensional calculation.
Ref 3 The Feynman Lectures on Physics, Richard P. Feynman, Robert B Leighton and Mathew Sands, Addison-Wesley Publishing Company, 1977. In three volumes and the complete set is well worth reading as they cover a wide range of topics in an exceptionally clear and unambiguous manner. If only all physics books could be written like this!
3a Electromagnetism is mainly in volume 2.
3b The motion of a free charge in a plane electromagnetic wave is briefly discussed in volume 1, page 34-10.
Ref 4 The velocity Verlet algorithm is described briefly at http://www.fisica.uniud.it/~ercolessi/md/md/node21.html. and http://ciks.cbt.nist.gov/~garbocz/dpd1/node3.html. These sites contain information on various computer computational algorithms.
Ref 5 The Classical Theory of Fields by L.D. Landau and E.M. Lifshitz. First published by Pergamon Presas Ltd 1951. This is a classic but fairly advanced text and is part of the authors Course of Theoretical Physics, which comprises ten volumes. It is currently in print by Butterworth-Heine, 1998. The equation referred to is given on page 49 of this reprint as an answer to a problem.
Ref 6 Pictures of Dynamic Electric Fields by Roger Y. Tsien. American Journal of Physics, Volume 40, January 1972, Pages 46 to 56.Gives excellent field line plots of charges moving in various ways at relativistic speeds.
of Electrodynamics by Melvin Schwartz. Originally published by McGraw-Hill Book Company,
Ref 8 Electromagnetic Theory by Julius Adams Stratton. McGraw-Hill Book Company, Inc New Yorkand London, 1941. Although this is another classic work I have not used it a lot. It does have the advantage (to me at least!) of being in MKS units and page 476 has the equation for obtaining the magnetic field from the electric field for a moving point charge.