Textbook in PDF format

Contents:

Preface
Integral and Differential Forms of the Maxwell Equations
Relation of the Differential to the Integral Form
Dirac δ Function
Transverse and Longitudinal Components of a Vector Field
Vector and Scalar Potentials
Lorenz Gauge
Coulomb Gauge
Electric and Magnetic Field Energies
Maxwell Stress Tensor
Exercises
Green Function of the Harmonic Oscillator
Poisson and Laplace Equations in Electrostatics
Laplace Equation in Spherical Coordinates
Legendre Functions and Spherical Harmonics
Expansion of the Green Function in Spherical Coordinates
Multipole Expansion of Charge Distributions
Addition Theorem for Spherical Harmonics
Multipole Expansion in Cartesian Coordinates
Multipole Expansion in an External Field
Laplace Equation in Cylindrical Coordinates
Cylindrical Coordinates and Bessel Functions
Orthogonality Properties of Bessel Functions
Expansion of the Green Function in Cylindrical Coordinates
Eigenfunction Expansions for the Green Function
Application to Electrostatics in Spherical Coordinates
Summary: Green Function of Electrostatics
Exercises
Differential Equations of Electrostatics
Boundary-Value Problems: One-Dimensional Analogy
Green’s Theorem: Dirichlet and Neumann Green Functions
Boundary-Value Problems and Laplace Equation
Definition of the Functional Derivative
Variational Principle and Euler–Lagrange Equations
Variations with Constraints
Second Functional Derivative and Hilbert Space
Variational Calculation of the Capacitance of Plates
Variational Calculation for Coaxial Cylinders
Exact Integration of the Capacitance of Coaxial Cylinders
Coordinate Systems and Special Functions
Laplace Equation in a Rectangular Parallelepiped
Laplace Equation in a Two-Dimensional Rectangle
Boundary Conditions on the Finite Part of a Long Strip
Cauchy’s Residue Theorem: A Small Digression
Boundary Conditions on the Infinite Part of a Long Strip
Cylinders and Zeros of Bessel Functions
Dirichlet Green Function for Spherical Shells
Boundary Condition of Dipole Symmetry
Verification Using Series Expansion
Sources and Fields in a Spherical Shell
Induced Charge Distributions on the Boundaries
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Regularization and Renormalization
Potential of a Uniformly Charged Plane
Potential of a Uniformly Charged Long Wire
Charged Structures in and Dimensions
Abraham–Minkowski Controversy
Relativistic Dynamics with Radiative Reaction
Electrodynamics in General Relativity
Exercises
Bibliography
Index