Chapter 1 Vector Analysis
1.1 Vector Function and Vector Operations
1.1.1 Vector Function
1.1.2 Limits and Continuity of Vector Function
1.1.3 Derivatives and Differentiation of Vector Function
1.1.4 Integration of Vector Function
1.2 Cartesian Curvilinear System
1.2.1 Concept of Orthogonal Curvilinear Coordinate System
1.2.2 Unit Vector
1.2.3 Infinitesimal Line, Surface, and Volume Elements
1.3 Gradient, Divergence, and Curl
1.3.1 Scalar Field and Vector Field
1.3.2 Directional Derivative and Gradient of Scalar Field
1.3.3 Flux and Divergence of Vector Field
1.3.4 Rotation and Curl of Vector Field
1.4 Several Important Vector Fields
1.4.1 Potential Field
1.4.2 Tubular Field
1.4.3 Harmonic Field
1.5 * δFunction, Green's Theorem, and Helmholtz Theorem
1.5.1 δFunction
1.5.2 Green's Theorem
1.5.3 Properties of Harmonic Function
1.5.4 Helmhohz's Theorem
Chapter 2 Electrostatics
2.1 Charge and Charge Density
2.2 Coulomb's Law
2.3 Electric Field and Electric Field Intensity
2.4 Electric Field Line and Electric Flux
2.4.1 Electric Force Line
2.4.2 Electric Flux
2.5 Gauss's Law
2.5.1 Beam Solid Angle
2.5.2 Integral Form of Gauss's Law
2.5.3 Differential Form of Gauss's Law
2.6 Electrostatic Field Loop Theorem
2.7 Electric Potential and Potential Difference
2.8 Poisson's and Laplace's Equation of Electric Potential
2.9 Electric Dipole
2.10 Electrostatic Field in Dielectrics
2.10.1 Polarization of Dielectrics
2.10.2 Fundamental Laws of Dielectrics in Electrostatic Field
2.10.3 Boundary Conditions on Dielectric Interface
2.11 Conductors in Electrostatic Field
2.11.1 Electrostatic Equilibrium and Boundary Condition of Conductor
2.11.2 Electrostatic Field Analysis and Calculation in Conductors
2.11.3 Electrostatic Shielding
2.12 Energy and Force of Electric Field
2.12.1 Energy of Electric Field
2.12.2 Electrostatic Force