Chapter 1 Mathematical Foundations
1.1 Fields in E3
1.1.1 Symbol Conventions
1.1.2 Coordinate Transformations
1.1.3 Scalar, Vector and Tensor
1.1.4 Pseudo Scalar and Pseudo Vector
1.2 Vector Calculus in E3
1.2.1 Derivatives in E3
1.2.2 Differentiation of Fields
1.2.3 Second Derivatives of Fields
1.2.4 Helmholtz Theorem
Chapter 2 Electromagnetic Phenomenon
2.1 Electrostatics
2.1.1 The Electric Field
2.1.2 Equations of Electrostatic Fields
2.1.3 Electric Scalar Potential
2.2 Magnetostatics
2.2.1 Charge Conservation
2.2.2 Magnetic Field
2.2.3 Equations of Magnetostatic Fields
2.2.4 Magnetic Vector Potential
2.3 Maxwell's Equations
2.3.1 Electrodynamics Before Maxwell
2.3.2 Maxwell's Equations
2.3.3 Magnetic Charges and Symmetry
2.4 Maxwell's Equations in Dielectrics
2.4.1 Polarization
2.4.2 Magnetization
2.4.3 Maxwell's Equations in Matter
2.5 Boundary Conditions
2.5.1 Normal Direction
2.5.2 Tangent Direction
2.6 Energy and Momentum of Electromagnetic Field
2.6.1 Energy Conservation, Poynting's Theorem
2.6.2 Momentum Conservation
2.6.3 Uniqueness Theorem in Electromagnetism
2.6.4 Divergence of Point-Charge Self-Energy
Problems
Chapter 3 Electrostatics
3.1 Electrostatic Field and Scalar Potential
3.2 Electric Potential
3.3 Uniqueness Theorems
3.3.1 Uniqueness Theorem in Dielectrics
3.3.2 Conductors and the Second Uniqueness Theorem
3.4 Separation of Variables
3.4.1 Cartesian Coordinates
3.4.2 Spherical Coordinates
3.4.3 Cylindrical Coordinates
3.5 The Method of Images
3.6 Method of Green's Function
