Presents extensive treatment of the time-dependent equations

Includes the foundations of the analysis of the numerical schemes and computational methods

Uses only the "classical" formulation of electromagnetism (i.e. gradient, divergence and curl operators) avoiding the "intrinsic" formulations based on differential geometry

Foreword.- Physical framework and models.- Electromagnetic fields and Maxwell's equations.- Stationary equations.- Coupling with other models.- Approximate models.- Elements of mathematical classifications.- Boundary conditions and radiation conditions.- Energy matters.- Bibliographical notes.- Basic applied functional analysis.- Function spaces for scalar fields.- Vector fields: standard function spaces.- Practical function spaces in the (t, x) variable.- Complements of applied functional analysis.- Vector fields: tangential trace revisited.- Scalar and vector potentials: the analyst's and topologist's points of view.- Extraction of scalar potentials and consequences.- Extraction of vector potentials.- Extraction of vector potentials - Vanishing normal trace.- Extraction of vector potentials - Complements.- Helmholtz decompositions.- Abstract mathematical framework.- Basic Results.- Static problems.- Time-dependent problems.- Time-dependent problems: improved regularity results.- Time-harmonic problems.- Summing up.- Analyses of exact problems: first-order models.- Energy matters: uniqueness of the fields.- Well-posedness.- Analyses of approximate models.- Electrostatic problem.- Magnetostatic problem.- Further comments around static problems.- Other approximate models.- Analyses of exact problems: second-order models.- First-order to second-order equations.- Well-posedness of the second-order Maxwell equations.- Second-order to first-order equations.- Other variational formulations.- Compact imbeddings.- Improved regularity for augmented and mixed augmented formulations.- Analyses of time-harmonic problems.- Compact imbeddings: complements.- Free vibrations in a domain encased in a cavity.- Sustained vibrations.- Interface problem between a dielectric and a Lorentz material.- Comments.- Dimensionally reduced models: derivation and analyses.- Two-and-a-half dimensional (2 1/2 2D) models.- Two-dimensional (2D) models.- Some results of functional analysis.- Existence and uniqueness results (2D problems).- Analyses of coupled models.- The Vlasov-Maxwell and Vlasov-Poisson systems.- Magnetohydrodynamics.- References.- Index of function spaces.- Basic Spaces.- Electromagnetic spaces.- Dimension reduction and weighted spaces.- Spaces measuring time regularity.- List of Figures.- Index.