D. J. Griffths, Introduction to Electrodynamics, 4th Edition

1.: Vector Analysis
1.1.: Vector Algebra
1.1.1.: Vector Operations
1.1.2.: Vector Algebra: Component Form
1.1.3.: Triple Products
1.1.4.: Position, Displacement, and Separation Vectors
1.1.5.: How Vectors Transform
1.2.: Differential Calculus
1.2.1.: “Ordinary” Derivatives
1.2.2.: Gradient
1.2.3.: The Del Operator
1.2.4.: The Divergence
1.2.5.: The Curl
1.2.6.: Product Rules
1.2.7.: Second Derivatives
1.3.: Integral Calculus
1.3.1.: Line, Surface, and Volume Integrals
1.3.2.: The Fundamental Theorem of Calculus
1.3.3.: The Fundamental Theorem for Gradients
1.3.4.: The Fundamental Theorem for Divergences
1.3.5.: The Fundamental Theorem for Curls
1.3.6.: Integration by Parts
1.4.: Curvilinear Coordinates
1.4.1.: Spherical Coordinates
1.4.2.: Cylindrical Coordinates
1.5.: The Dirac Delta Function
1.5.1.: The Divergence of r/r2
1.5.2.: The One-Dimensional Dirac Delta Function
1.5.3.: The Three-Dimensional Delta Function
1.6.: The Theory of Vector Fields
1.6.1.: The Helmholtz Theorem
1.6.2.: Potentials
2.: Electrostatics
2.1.: The Electric Field
2.1.1.: Introduction
2.1.2.: Coulomb’s Law
2.1.3.: The Electric Field
2.1.4.: Continuous Charge Distributions
2.2.: Divergence and Curl of Electrostatic Fields
2.2.1.: Field Lines, Flux, and Gauss’s Law
2.2.2.: The Divergence of E
2.2.3.: Applications of Gauss’s Law
2.2.4.: The Curl of E
2.3.: Electric Potential
2.3.1.: Introduction to Potential
2.3.2.: Comments on Potential
2.3.3.: Poisson’s Equation and Laplace’s Equation
2.3.4.: The Potential of a Localized Charge Distribution
2.3.5.: Boundary Conditions
2.4.: Work and Energy in Electrostatics
2.4.1.: The Work It Takes to Move a Charge
2.4.2.: The Energy of a Point Charge Distribution
2.4.3.: The Energy of a Continuous Charge Distribution
2.4.4.: Comments on Electrostatic Energy
2.5.: Conductors
2.5.1.: Basic Properties
2.5.2.: Induced Charges
2.5.3.: Surface Charge and the Force on a Conductor
2.5.4.: Capacitors
3.: Potentials
3.1.: Laplace’s Equation
3.1.1.: Introduction
3.1.2.: Laplace’s Equation in One Dimension
3.1.3.: Laplace’s Equation in Two Dimensions
3.1.4.: Laplace’s Equation in Three Dimensions
3.1.5.: Boundary Conditions and Uniqueness Theorems
3.1.6.: Conductors and the Second Uniqueness Theorem
3.2.: The Method of Images
3.2.1.: The Classic Image Problem
3.2.2.: Induced Surface Charge
3.2.3.: Force and Energy
3.2.4.: Other Image Problems
3.3.: Separation of Variables
3.3.1.: Cartesian Coordinates
3.3.2.: Spherical Coordinates
3.4.: Multipole Expansion
3.4.1.: Approximate Potentials at Large Distances
3.4.2.: The Monopole and Dipole Terms
3.4.3.: Origin of Coordinates in Multipole Expansions
3.4.4.: The Electric Field of a Dipole
4.: Electric Fields in Matter
4.1.: Polarization
4.1.1.: Dielectrics
4.1.2.: Induced Dipoles
4.1.3.: Alignment of Polar Molecules
4.1.4.: Polarization
4.2.: The Field of a Polarized Object
4.2.1.: Bound Charges
4.2.2.: Physical Interpretation of Bound Charges
4.2.3.: The Field Inside a Dielectric
4.3.: The Electric Displacement
4.3.1.: Gauss’s Law in the Presence of Dielectrics
4.3.2.: A Deceptive Parallel
4.3.3.: Boundary Conditions
4.4.: Linear Dielectrics
4.4.1.: Susceptibility, Permittivity, Dielectric Constant
4.4.2.: Boundary Value Problems with Linear Dielectrics
4.4.3.: Energy in Dielectric Systems
4.4.4.: Forces on Dielectrics
5.: Magnetostatics
5.1.: The Lorentz Force Law
5.1.1.: Magnetic Fields
5.1.2.: Magnetic Forces
5.1.3.: Currents
5.2.: The Biot-Savart Law
5.2.1.: Steady Currents
5.2.2.: The Magnetic Field of a Steady Current
5.3.: The Divergence and Curl of B
5.3.1.: Straight-Line Currents
5.3.2.: The Divergence and Curl of B
5.3.3.: Ampère’s Law
5.3.4.: Comparison of Magnetostatics and Electrostatics
5.4.: Magnetic Vector Potential
5.4.1.: The Vector Potential
5.4.2.: Boundary Conditions
5.4.3.: Multipole Expansion of the Vector Potential
6.: Magnetic Fields in Matter
6.1.: Magnetization
6.1.1.: Diamagnets, Paramagnets, Ferromagnets
6.1.2.: Torques and Forces on Magnetic Dipoles
6.1.3.: Effect of a Magnetic Field on Atomic Orbits
6.1.4.: Magnetization
6.2.: The Field of a Magnetized Object
6.2.1.: Bound Currents
6.2.2.: Physical Interpretation of Bound Currents
6.2.3.: The Magnetic Field Inside Matter
6.3.: The Auxiliary Field H
6.3.1.: Ampere’s Law in Magnetized Materials
6.3.2.: A Deceptive Parallel
6.3.3.: Boundary Conditions
6.4.: Linear and Nonlinear Media
6.4.1.: Magnetic Susceptibility and Permeability
6.4.2.: Ferromagnetism
7.: Electrodynamics
7.1.: Electromotive Force
7.1.1.: Ohm’s Law
7.1.2.: Electromotive Force
7.1.3.: Motional emf
7.2.: Electromagnetic Induction
7.2.1.: Faraday’s Law
7.2.2.: The Induced Electric Field
7.2.3.: Inductance
7.2.4.: Energy in Magnetic Fields
7.3.: Maxwell’s Equations
7.3.1.: Electrodynamics Before Maxwell
7.3.2.: How Maxwell Fixed Ampere’s Law
7.3.3.: Maxwell’s Equations
7.3.4.: Magnetic Charge
7.3.5.: Maxwell’s Equations in Matter
7.3.6.: Boundary Conditions
8.: Conservation Laws
8.1.: Charge and Energy
8.1.1.: The Continuity Equation
8.1.2.: Poynting’s Theorem
8.2.: Momentum
8.2.1.: Newton’s Third Law in Electrodynamics
8.2.2.: Maxwell’s Stress Tensor
8.2.3.: Conservation of Momentum
8.2.4.: Angular Momentum
8.3.: Magnetic Forces Do No Work