Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect and perfect differentials, Taylor expansion. Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem. First order equations and linear second order differential equations with constant coefficients. Matrices and determinants, Algebra of complex numbers.

Elements Complex analysis, Limit and continuity, Cauchy's Riemann equations, Complex integrations, Cauchy's theorem for simply and multiply connected regions, Cauchy's integral formula, Taylor and Laurent series, Poles and singularities, Cauchy's residue theorem and its application to evaluation of definite integrals.

Electricity and Magnetism: Coulomb’s Law, Gauss’s law, Energy of a charge distribution, Laplace’s and Poisson’s equations, Conductors, Method of images, Field and Potential due to dipole. Polarization in a dielectric, vectors D, P and E, linear dielectrics, force on dielectrics. Line, surface and volume currents and current densities, electrical conductivity and Ohm’s law, equation of continuity, energy dissipation. Motion of charged particles in electric and magnetic fields. Biot-Savart and Ampere’s law, divergence and curl of B and the differential form of Ampere’s law, vector potential, Magnetic dipoles, magnetization in materials, H, B and M, Dia-, para- and ferro-magnetism. Electromagnetic induction, motional e.m.f and Faraday’s law, inductance and energy in magnetic field, the displacement current, Maxwell’s equations, Ising Model, Anti Ferromagnetism , Two Sub Lattice Model, Ferrimagnetism, Ferrites.

Quantum states of an electron in an atom. Electron spin. Spectrum of helium and alkali atom. Relativistic corrections for energy levels of hydrogen atom, hyperfine structure and isotopic shift, width of spectrum lines, LS & JJ couplings. Zeeman, Paschen-Bach & Stark effects. Electron spin resonance. Nuclear magnetic resonance, chemical shift. Frank-Condon principle. Electronic, rotational, vibrational and Raman spectra of diatomic molecules, selection rules. Lasers: spontaneous and stimulated emission, Einstein A & B coefficients. Optical pumping, population inversion, rate equation. Modes of resonators and coherence length.

Bravais lattices. Reciprocal lattice. Diffraction and the structure factor. Bonding of solids. Elastic properties, phonons, lattice specific heat. Free electron theory and electronic specific heat. Response and relaxation phenomena. Drude model of electrical and thermal conductivity. Hall effect and thermoelectric power. Electron motion in a periodic potential, band theory of solids: metals, insulators and semiconductors. Superconductivity: type-I and type-II superconductors. Josephson junctions. Superfluidity. Defects and dislocations. Ordered phases of matter: translational and orientational order, kinds of liquid crystalline order. Quasi crystals. Magnetic materials: diamagnetism, paramagnetism and ferromagnetism.

Basic nuclear properties: size, shape and charge distribution, spin and parity. Binding energy, semiempirical mass formula, liquid drop model. Nature of the nuclear force, form of nucleon-nucleon potential, charge-independence and charge-symmetry of nuclear forces. Deuteron problem. Evidence of shell structure, single-particle shell model, its validity and limitations. Rotational spectra. Elementary ideas of alpha, beta and gamma decays and their selection rules. Fission and fusion. Nuclear reactions, reaction mechanism, compound nuclei and direct reactions. Classification of fundamental forces. Elementary particles and their quantum numbers (charge, spin, parity, isospin, strangeness, etc.). Gellmann-Nishijima formula. Quark model, baryons and mesons. C, P, and T invariance. Application of symmetry arguments to particle reactions. Parity non-conservation in weak interaction. Relativistic kinematics.

Introduction to Nano Physics: Definition, Length scale, Importance of Nano-scale and technology, History of Nanotechnology, Benefits and challenges in molecular manufacturing. Molecular assembler concept, Understanding advanced capabilities. Vision and objective of Nano-technology, Nanotechnology in different field, Automobile, Electronics, Nano- biotechnology, Materials, Medicine.