Fluid Dynamics : Consistency Equations (Navier-Stokes, Euler), LinearHyperbolic Systems, Convective and Diffusive analysis for systems in 1-D and 2-D, Finite Difference Operations - Point, Matrix, Pade's formula, Stability and
Consistency of Flow by Fourier stability analysis, Vortex, Turbulence of Flow,
Differential Geometry in Physics: Vectors and Curves, Differential Forms - 1
forms, Tensors, Exterior derivatives, Hodge-* Operator, Connections - Frames,
Curvilinear coordinates, Covariant Derivatives, Theory Of Surfaces - Flux,
Manifolds, Fundamental Theorems
Electromagnetic : Integral and Differential Calculus of Vector Fields,
Electromagnetic Theory - Maxwell, Vector Potentials, Principle of Least Action,
Solutions to Maxwell's equations of Free Space and Currents Charges,
Waveguides - Transmission Lines, Cut Off, Cavity Resonators, Alternating
Currents, Lorentz Transformations for fields, EM Mass, Internal Crystal
Geometry, AC Circuits, Reactance, Susceptance
Semiconductors: Junction Diodes, Transistors, Characteristics, Light based
devices, Amplifiers, Oscillators.
Quantum Theory: Introduction and History of the Quantum Theory, Wave-
Particle Duality, Probability Amplitudes, Spin One and Spin Half Mechanics,
Time-Dependence of Amplitude, Hamiltonian Matrices, Schrödinger Equation in
Quantum and Classical Contexts, Hyperfine Splitting in H-Atom, Heisenberg's
Uncertainty Principle
Relativity: Introduction to theory of Relativity, Special Relativity, Relativistic
Effects on Radiation, Relativistic Effects on Matter - Time Dilation etc.,
Geometry of Space time, Dynamics in 4-D, Unifying Electromagnetism and
relativity
Mechanics: Translational and Rotational Kinematics, 2D and 3D Mechanics,
Forces, Energy, Transients, Resonance, Oscillations, Wave mechanics,
Gravitational Field, Elasticity, Molecular Forces and Solid Materials
Optics: Introduction to Geometrical ray optics, Hygens principle, Freunhofer/Fresnel diffraction, Interference, YDSE, Single slit, Multiple slits, Polarisation, Wave-Particle duality of light