Fleisch Daniel. A Student's Guide to Maxwell's Equations

Cambridge: Cambridge University Press, 2008. — 142 p. — ISBN: 978-0-511-39308-2.Maxwell’s Equations are four of the most influential equations in science: Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell’s Equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics.Gauss's law for electric fields.
The integral form of Gauss's law.
The electric field.
The dot product.
The unit normal vector.
The component of E normal to a surface.
The surface integral.
The flux of a vector field.
The electric flux through a closed surface.
The enclosed charge.
The permittivity of free space.
Applying Gauss’s law (integral form).
The differential form of Gauss's law.
Nabla – the del operator.
Del dot – the divergence.
The divergence of the electric field.
Applying Gauss's law (differential form).
Gauss's law for magnetic fields.
The integral form of Gauss's law.
The magnetic field.
The magnetic flux through a closed surface.
Applying Gauss's law (integral form).
The differential form of Gauss's law.
The divergence of the magnetic field.
Applying Gauss's law (differential form).
Faraday's law.
The integral form of Faraday's law.
The induced electric field.
The line integral.
The path integral of a vector field.
The electric field circulation.
The rate of change of flux.
Lenz's law.
Applying Faraday's law (integral form).
The differential form of Faraday's law.
Del cross – the curl.
The curl of the electric field.
Applying Faraday's law (differential form).
The Ampere–Maxwell law.
The integral form of the Ampere–Maxwell law.
The magnetic field circulation.
The permeability of free space.
The enclosed electric current.
The rate of change of flux.
Applying the Ampere–Maxwell law (integral form).
The differential form of the Ampere–Maxwell law.
The curl of the magnetic field.
The electric current density.
The displacement current density.
Applying the Ampere–Maxwell law (differential form).
From Maxwell's Equations to the wave equation.
The divergence theorem.
Stokes' theorem.
The gradient.
Some useful identities.
The wave equation.
Appendix: Maxwell's Equations in matter.
Further reading.