### Syllabus

Electrostatics: Continuous Charge Distribution, Delta Function, Field and Potential, Poisson and Laplace's equations, Boundary Conditions and Uniqueness theorems, Electrostatic potential energy, Capacitance, Conductors.
Boundary Value Problems: Solution of Laplace and Poisson equations in 2 & 3 dimensions. Method of images, separation of variables in Cartesian, Cylindrical and Spherical coordinate systems, Multipole expansion, Green's function approach.
Dielectrics: Polarization, bound charges, susceptibility, energy and force, boundary conditions, boundary value problems.
Magnetostatics: Biot-Savert's Law, Ampere's law, vector potential, magnetic field, moments, force, torque and energy of localized current distributions. Boundary conditions, boundary value problems.
Electrodynamics: Electromotive force, Ohm's law, Faraday's law, self and mutual inductance, energy in magnetic fields, Maxwell's equations, Gauge transformations, potential formulation, energy and momentum conservation, Poynting theorem.
Electromagnetic Waves: Wave equation, Propagation of electromagnetic waves in non conducting medium, reflection, transmission, Snell's law, Brewster's angle, critical angle, Dispersion in non-conducting medium.

### Detailed Layout

N Topic Lectures
1 Coulomb's Law and Examples; Continuous charge distributions; Electric Field; Gauss Law
2 Scalar Potential; Poisson and Laplace Equations; Integral Equation for electric potential; Boundary conditions and Uniqueness theorem; Formal Solution by Green's Function method.
3 Electrostatic Energy; Continuous Charge distributions; Conductors and Capacitance
4 Method of Images; Green's Functions for a spherical boundary surface
5 Method of separation of variables; Function Spaces and bases; Two Dimensional Problems in rectangular and cylindrical geometries;
6 Green's Functions in two dimensions
7 Laplace equation in 3D; Spherical coordinates; Spherical Harmonics;
8 Green's Functions in Spherical coordinates
9 Multipole Expansion; Quadrupole moment tensors
10 Dielectrics; Electric Displacement; Linear Dielectrics; Boundary Value Problems; Energy;
11 Steady Currents; Biot-Savart Law; Magnetic Field; Ampere's Law
12 Vector Potential; Multipole Expansion; Magnetic Dipoles;
13 Magnetic Fields in Matter; Boundary Value Problems
14 Faraday's Law; Inductance - Self and Mutual; Energy in Magnetic Fields
15 Maxwell's Equations; Macroscopic version; Potentials; Gauge transformations;
16 Conservation Laws; Energy Conservation and Poynting Theorem; Momentum conservation; Angular Momentum
17 Electromagnetic Waves: Wave equation, Propagation of electromagnetic waves in non conducting medium, reflection, transmission, Snell's law, Brewster's angle, critical angle, Dispersion in non-conducting medium.