Concept of sequentially following up the steps of a algorithm.Notion of program, programmability and programming languages, Structure of programs, Object codes, compilers.
Complex Variables: Curves and Regions in the Complex Plane, Complex Functions, Limits, Derivative, Analytic Function, Cauchy-Riemann Equations, Laplaces Equation, Rational, Exponential, Trigonometric, Hyperbolic Functions, Linear Fractional Transformations, Conformal Mapping, Complex Line Integral, Cauchys Integral Theorem, Cauchys Integral Formula, Derivatives of Analytic Function, Power Series, Taylor Series, Laurent Series, Methods of obtaining Power Series, Analyticity at Infinity, Zeroes, Singularities, Residues, Residue Theorem, Evaluation of Real Integrals.
Probability and Statistics: Random Variables, Discrete and Continuous Distribution, Mean and Variance of a Distribution, Moments, Moment Generating Functions, Skewness, Kurtosis, Binomial, Poisson, Normal Distributions, Testing of Statistical Hypothesis, F-Test, T-test, Wave particle duality, de Broglie waves, evidences for the wave nature of matter the experiment of Davisson and Germer, electron diffraction, physical interpretation of the wave function and its properties, the wave packet, the uncertainty principle. The Schrodinger wave equation (1-dimensional), Eigen values and Eigen functions, expectation values, simple Eigen value problems solutions of the Schrodingers equations for the free particle, the infinite well, the finite well, tunneling effect, simple harmonic oscillator (qualitative), zero point energy. The statistical distributors: Maxwell Boltzmann, Bose-Einstein and Fermi-Dirac statistics, their comparisons, Fermions and Bosons Applications: Molecular speed and energies in an ideal gas, The Black body spectrum, the failure of classical to give the correct explanations the applications of Bose-Einstein statistics to the Black body radiation spectrum, Fermi-Dirac distribution, free electron theory, electronic specific heats, Fermi energy and average energy its significance. Origin of energy bands in solids, motion of electrons in a periodic potential the Kronig Penny model, Brillouin zones, effective mass, metals, semi-conductors and insulators and their energy band structures, Extrinsic and Intrinsic semiconductors, doping-fermi energy for doped and undoped semiconductors, the p-n junction (energy band diagrams with fermi energy), the unbiased diode, forward and reverse biased diodes tunnel diodes, zener diode, photo diode its characteristics, LED, Introduction to transistors. Elementary Probability theory, Random Variables: discrete and continuous, distribution and density functions, Expectation, Moments, Moment Generating function, Skewness, Kurtosis, Binomial, Poisson and Normal distribution, Method of least square for linear and parabolic curves, Correlation of a bivariate distribution, Linear regression, properties of regression coefficient, Sampling distribution of mean and variance, Testing of Statistical hypothesis, F-test, T-test and chi square test.17 hrs.
Different definitions of molecular eights viz., Mw, Mn, Mv and then determinations, Industrial applications of polymers, Addition, condensation and Ionic polymerizations, solutions of polymers, good solvents, & bad solvent, solubility parameter, solutions viscosity and determination of intrinsic viscosity.
Definition and types of corrosion, Laws of Oxide film growth (Linear, parabolic and logarithmic), different theories of corrosion, Atmospheric corrosion, Stress corrosion, water-line, pitting and soil corrosion.
(Fresnel and Fraunhofer types of diffraction) Fraunhofer diffraction: Single slit, double slit, circular aperture and N-slit, diffraction wavelength determination, resolving power and dispersive power, Fresnel Diffraction: Zone plate, circular aperture, opaque circular disc, narrow slit. Introduction, coherence, Einstein A and B coefficients, population inversion, basic principle and operation of a laser, type of lasers, He-Ne laser, Ruby laser semiconductor laser, holography theory and applications. Introduction to optical fibre, types of optical fibres and their characteristics, (Attenuation and dispersion step index and graded index fibres, principle of fibre optic communicationtotal internal reflection, numerical aperture, fibre optical communication network (qualitative) its advantages. Absolute and Inertial frames of reference, Galenlian transformations, Michelson-Morley experiment, the postulates of the special theory of relativity, Lorentz transformations, time dilation, length contraction, velocity addition, mass energy equivalence 5 hrs.