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This complementary text to "MaX-1: A Visual Electromagnetics Platform for PCs" also serves as a stand-alone text offering an introduction to modern computational electromagnetics methods based on numeric, semi-analytic and analytic Maxwell solvers. Coverage spans all theories and tools that are important for computational electromagnetics, including chapters on mathematics, numerical methods, Maxwell theory, etc. Deliberately intended not to be another electromagnetics text, the author explains how to invent and develop numerical techniques, also how existing techniques can be analyzed, compared, improved, and adapted to special applications. The book discusses specialities in the modelling of various applications, including statics, scattering, gratings, antenna, antenna arrays, guided waves on arbitrary structures, resonators, mode coupling, waveguide discontinuities, both frequency and time domain solutions; boundary methods as well as domain methods will be considered The text focuses on two main methods: finite differences (a domain method) and MMP (a boundary method). It covers all theory and tools important to modern computational electromagnetics and teaches users to invent and develop numerical techniques. It also demonstrates how existing techniques can be analyzed, compared, improved and adapted to special conditions, and describes special, advanced techniques that can be applied to any method for improving its performance.