1. Mathematical preliminaries

1. Vector analysis
2. Coordinate systems    
3. Integrals
4. Integral theorems

2. Introduction to Electrostatics

1. Coulomb's law
2. Electric field
3. Gauss's law
4. Differential form of Gauss's law
5. Another equation of electrostatics and the scalar potential
6. Surface distributions of charges and dipoles and discontinuities in the electric field and potential
7. Poisson and Laplace equations
8. Green's Theorem
9. Uniqueness of the solution with Dirichlet or Neumann boundary conditions
10. Formal solution of electrostatic boundary-value problem with Green Function
11. Electrostatic potential energy and energy density, capacitance
    

3. Boundary-Value Problems in Electrostatics: I

1. Method of images
2. Point charge in the presence of a grounded conducting sphere
3. Point charge in the presence of a charged, insulated, conducting sphere
4. Point charge near a conducting sphere at fixed potential
5. Conducting sphere in a uniform electric field by method of images
6. Green function for the plane, general solution for the potential
7. Green function for the sphere, general solution for the potential
8. Conducting sphere with hemispheres at difference potentials
9. Orthogonal functions and expansions
10. Separation of variables, Laplace equation in rectangular coordinates
11. A two-dimensional potential problem, summation of a Fourier series

 

4. Boundary-Value Problems in Electrostatics: II
   
   1. Laplace equation in spherical coordinates
   2. Legendre equation and Legendre polynomials
   3. Boundary-value problems with azimuthal symmetry
   4. Associated Legendre functions and the spherical harmonics Ylm (q , f )
   5. Addition theorem for spherical harmonics
   6. Expansion of Green functions in spherical coordinates
   7. Solution of potential problems with the spherical Green function expansion
   8. Multipoles, Electrostatics of Macroscopic Media, Dielectrics
   9. Multipole expansion
   10. Multipole expansion of the energy of a charge distribution in an external field
   11. Elementary treatment of electrostatics with ponderable media
   12. Boundary-value problems with dielectrics
   13. Electrostatic energy in dielectric media

    

5. Magnetostatics 
   
   1. Introduction and definitions
   2. Biot and Savart law
   3. Differential equations of magnetostatics and Ampere’s law
   4. Vector potential
   5. Vector potential and magnetic induction for a long, straight current- carrying wire
   6. Magnetic fields of a localized current distribution, magnetic moment
   7. Force and torque on and energy of a localized current distribution in an external magnetic induction
   8. Macroscopic equations, boundary conditions on B and H
   9. Methods of solving boundary-value problems in magnetostics
   10. Uniformly magnetized sphere
   11. Faraday’s law of induction
   12. Energy in the magnetic field

    

6. Maxwell Equations and Plane Wave Propagation 
   
   1. Maxwell Equations
   2. Derivation of the Equations of Macroscopic EM
   3. Conservation Laws
   4. Plane EM waves
   5. Propagation in noncondcutiing media
   6. Propagation in condcutiing media
   7. Dispersion relation
   8. Kramers Kronig relations