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#### Classical Electrodynamics

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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
3.6.1 Green's Function
3.6.2 Green's Formula and Boundary Value Problems
3.6.3 Interchanging Symmetry of Green's Functions
3.6.4 Examples
3.7 Surface Charge Density, Coulomh's Law and Poisson's Equation
3.7.1 A General Discussion
3.7.2 Examples
3.8 Multipole Expansion
3.8.1 Expansion in Cartesian Coordinates
3.8.2 Expansion in Spherical Coordinates
3.8.3 Energy of a Charge Distribution in External Fields
Problems
Chapter 4 Magnetostaties
4.1 Magnetic Vector Potential
4.1.1 Gauge Conditions
4.1.2 Differential Equation
4.1.3 Boundary Conditions
4.1.4 Energy of Magnetostaic Fields
4.1.5 Examples
4.2 Uniqueness Theorem
4.3 Magnetic Scalar Potential
4.3.1 Differential Equations
4.3.2 Boundary Conditions
4.3.3 Examples
4.4 A Parallel Discussion of Sec
4.4.1 A General Discussion
4.4.2 Examples
4.5 Magnetic Monopole and Singular String
4.5.1 Singular String
4.5.2 Some Details
4.6 Multipole Expansion
4.6.1 Expansion in Cartesian Coordinates
4.6.2 Expansion in Spherical Co0rdinates
4.6.3 Energy of a Current Distribution in External Magnetic Fields
4.7 Aharonov-Bohm Effect
Problems
Chapter 5 Electromagnetic Waves
5.1 Electromagnetic Wave in Free Space
5.1.1 Wave Equations
5.1.2 Planar Waves
5.1.3 Energy and Momentum of EM Waves
5.2 Reflection and Transmission of EM Waves
5.2.1 Law of Reflection and Refraction
5.2.2 Fresnel's Formula
5.2.3 Brewster's Angle
5.2.4 Total Reflection
5.3 EM Waves in Conductors
5.3.1 Perfect and Good Conductors
5.3.2 Wave Equations in Good Conductors
5.3.3 Reflection and Transmission on a Conducting Surface
5.4 Cavity Resonator
5.4.1 Cuboid Resonator
5.4.2 * Microsphere Resonator
5.5 Wave Guide
5.5.1 Rectangular Waveguide
5.5.2 Wave Mode
5.5.3 Cut-off Frequency
5.5.4 Wave Velocities
5.5.5 Physical Picture of TEl0 Mode
Problems