June 6, 2007
Electricity and Magnetism:
Review of calculus-gradient, curl, divergence and Laplacian. Spherical polar
and cylindrical coordinates, volume, surface and length elements, Stokes and
divergence theorems. Principle of superposition for determining electric
field due to a continuous charge distribution (Examples of calculation of
electric field due to uniformly charged planes, disk, cylinder and sphere).
Gauss's law in integral and differential form. examples from planar,
cylindrical and spherical symmetry.
Work done in assembling a charge distribution, electric potential,
potential, energy of electrostatic field. Poisson's and Laplace's equation,
simple examples of solutions. Properties of conductors. Polarization and
bound charges, expression for D, illustrative examples of capacitors
containing dielectrics. Revisiting magnetostatics, Lorentz force law
(cylindrical motion in a electric and magnetic field), Ampere's and
Biot-Savart's law.
Divergence and curl of B. Vector potential ~A and concept of gauge,
Calculation of A for a finite straight conductor, infinite wire and for a
uniform magnetic field. Magnetism in matter M, volume and surface current,
Field H, Ampere's law for H, Faraday's law in integral and differential
form, Motional emf, self and mutual inductance. Displacement current.
Gathering of all the four Maxwell's equations. Electromagnetic waves, wave
equation, e.m. waves in vacuum, Energy and momentum of e.m.w., Poynting
vector, radiation pressure. Polarization of e.m.w., elliptic polarization.
Reflection from a plane surface (normal incidence only), reflection from a
metal surface, skin depth, Standing electromagnetic waves, resonating
cavity. Waveguides with rectangular metallic boundaries, TE, TM modes,
impossibility of supporting TEM modes in a hollow cavity Electric dipole
radiation, Larmor's formula. Qualitative ideas on radiation pattern,
Relativistic invariance of Maxwell's equation.

Modern physics: Review of quantum concepts : particle nature of light,
photoelectric effect, Compton effect, matter waves, wave packets, phase and
group velocity, Davisson Germer experiment, Heisenberg uncertainty
principle. Schrödinger equation : probabilistic interpretation of wave
function, one dimensional problems �~@~S particle in a box, harmonic
oscillator, potential barrier and tunneling. Hydrogen atom, electrons in a
magnetic field, Landau levels. Elements of statistical physics : density of
states, Fermi energy, Bose condensation. Solid state physics : Free electron
model of metals, classical and quantum Hall effect, superconductivity,
London equation, coherence and penetration depth, flux quantization,
applications of superconductivity, SQUIDS. Nuclear physics : binding energy,
nuclear reactions, elements of nuclear reactors, fission and fusion,
fundamental forces, elementary particles, quarks and leptons.

CH 101: Chemistry-I (2-1-0-6)
Schrodinger equation: interpretation of wave function; hydrogen atom; atomic
and molecular orbital structure; bonding and energy levels in molecules and
solids. Intermolecular forces. Chemical potential; fugacities activities and
equilibrium constants; Relation between G and emf; Standard potentials;
Chemical Kinetics: steady state approximation; Collision theory.
Trends in the periodic table; metallurgy; basic principles and applications;
purification of elements and metals; transition metal ions and complexes;
coordination chemistry, magnetochemistry, role of metal ions in biological
processes; some relevant uses of transition elements; catalysis;
semiconducting and super conducting materials; zeolites; VSEPR; spinel.
Conformations of alkanes and cycloalkanes; configurations, molecular
chirality, geometrical isomerism. Linear and cyclic conjugation, benzene,
aromaticity, properties of conjugated systems. Reactivity, reaction types,
reaction mechanisms; nucleophilic substitution reaction, electrophilic and
free radical addition reactions, electrophilic aromatic substitutions,
nucleophilic addition; principles of nucleophilic addition to carbonyl
groups; Molecular systems of technological and biological importance.

MA 205: Complex Analysis (3-1-0-4)
Definition and properties of analytic functions, Cauchy-Riemann equations,
harmonic functions.
Power series and their properties. Elementary functions.
Cauchy theorem and its applications. Taylor's series and Laurent expansions.
Residues and the Cauchy residue formula.
Evaluation of improper integrals. Conformal mappings. Inversion of Laplace
transforms.

MA 207: Differential Equations-II  (3-1-0-4)
Review of power series and series solutions of ODE's. Legendre's equation
and Legendre polynomials.
Regular and irregular singular points, method of Frobenius.
Bessel's equation and Bessel's functions. Sturm-Liouville problems.
Fourier Series. D'Alembert solution to the Wave equation.
Classification of linear second order PDE in two variables.
Vibration of a circular membrane. Heat equation in the half space.