Week 1: Mathematical preliminaries: Vector analysis, Scalar and vector fields, Vector identities using Levi-Civita symbols, Orthogonal coordinate systems and transformation.
Week 2: Line, surface, volume integration, Differential calculus, Concept of gradient, divergence and curl and its representation in different coordinate system.
Week 3: Statement and proof of vector theorems (Gauss’s and Stokes theorem), Curvilinear coordinate system, delta function, Helmholtz’s theorem (statement only), Tutorial-1
Week 4: Electrostatic in vacuum: quantization of charge, volume charge density and classical point charge, Continuity equation, Different aspects of Coulomb’s law, Gauss’s Law and its application (Numeric Problems).
Week 5: Concept of potential, Poisson and Laplace equation, Green’s function, Electrostatic energy.
Week 6: Multipole expansion, dipole and quadrupole (Problems), Electric field in matter: Conductor, Dielectric, Electric polarization, Boundary condition, Tutorial-2
Week 7: Uniqueness theorem, Electrostatic boundary value problem (Problems by solving Poisson and Laplace equation), Image method
Week 8: Magnetostatic: Biot-Savart law, Applications (Problems), Divergence and curl of B, Ampere’s Law
Week 9: Vector potential A, Concept of gauge, Multipole expansion, Magnetic dipole, Magnetization , Bound current, Tutorial-3
Week 10: Electromagnetic induction, Faraday’s Law (Problems), Mutual inductance.
Week 11: Electrodynamics: Concept of wave equation, Maxwell’s equation in medium, Solution of the Maxwell’s wave equation, Pointing vector.
Week 12: A complete over view of Maxwell’s equation, Scalar and vector potential, Coulomb and Lorentz gauge, Gauge invariance, Tutorial-4
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