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PHYSICAL CHEMISTRY
Structure: Quantum theory: principles and techniques; applications to a
particle in a box, harmonic oscillator, rigid rotor and hydrogen atom;
valence bond and molecular orbital theories, Hückel approximation;
approximate techniques: variation and perturbation; symmetry, point groups;
rotational, vibrational, electronic, NMR, and ESR spectroscopy
Equilibrium: Kinetic theory of gases; First law of thermodynamics, heat,
energy, and work; second law of thermodynamics and entropy; third law and
absolute entropy; free energy; partial molar quantities; ideal and non-ideal
solutions; phase transformation: phase rule and phase diagrams - one, two,
and three component systems; activity, activity coefficient, fugacity, and
fugacity coefficient; chemical equilibrium, response of chemical equilibrium
to temperature and pressure; colligative properties; Debye-Hückel theory;
thermodynamics of electrochemical cells; standard electrode potentials:
applications - corrosion and energy conversion; molecular partition function
(translational, rotational, vibrational, and electronic).
Kinetics: Rates of chemical reactions, temperature dependence of chemical
reactions; elementary, consecutive, and parallel reactions; steady state
approximation; theories of reaction rates - collision and transition state
theory, relaxation kinetics, kinetics of photochemical reactions and free
radical polymerization, homogeneous catalysis, adsorption isotherms and
heterogeneous catalysis.
INORGANIC CHEMISTRY
Main group elements: General characteristics, allotropes, structure and
reactions of simple and industrially important compounds: boranes,
carboranes, silicones, silicates, boron nitride, borazines and phosphazenes.
Hydrides, oxides and oxoacids of pnictogens (N, P), chalcogens (S, Se &
Te) and halogens, xenon compounds, pseudo halogens and interhalogen
compounds. Shapes of molecules and hard- soft acid base concept. Structure
and Bonding (VBT) of B, Al, Si, N, P, S, Cl compounds. Allotropes of carbon:
graphite, diamond, C60. Synthesis and reactivity of inorganic polymers of Si
and P.
Transition Elements: General characteristics of d and f block elements;
coordination chemistry: structure and isomerism, stability, theories of
metal- ligand bonding (CFT and LFT), mechanisms of substitution and electron
transfer reactions of coordination complexes. Electronic spectra and magnetic
properties of transition metal complexes, lanthanides and actinides. Metal
carbonyls, metal- metal bonds and metal atom clusters, metallocenes;
transition metal complexes with bonds to hydrogen, alkyls, alkenes and
arenes; metal carbenes; use of organometallic compounds as catalysts in
organic synthesis. Bioinorganic chemistry of Na, K. Mg, Ca, Fe, Co, Zn, Cu
and Mo.
Solids: Crystal systems and lattices, miller planes, crystal packing,
crystal defects; Bragg’s Law, ionic crystals, band theory, metals and semiconductors,
Different structures of AX, AX2, ABX3 compounds, spinels.
Instrumental methods of analysis: Atomic absorption and emission
spectroscopy including ICP-AES, UV- visible spectrophotometry, NMR, mass,
Mossbauer spectroscopy (Fe and Sn), ESR spectroscopy, chromatography
including GC and HPLC and electro-analytical methods (Coulometry, cyclic
voltammetry, polarography – amperometry, and ion selective electrodes).
ORGANIC CHEMISTRY
Stereochemistry: Chirality of organic molecules with or without chiral
centres. Specification of configuration in compounds having one or more
stereogenic centres. Enantiotopic and diastereotopic atoms, groups and faces.
Stereoselective and stereospecific synthesis. Conformational analysis of
acyclic and cyclic compounds. Geometrical isomerism. Configurational and
conformational effects on reactivity and selectivity/specificity.
Reaction mechanism: Methods of determining reaction mechanisms.
Nucleophilic and electrophilic substitutions and additions to multiple bonds.
Elimination reactions. Reactive intermediates- carbocations, carbanions,
carbenes, nitrenes, arynes, free radicals. Molecular rearrangements involving
electron deficient atoms.
Organic synthesis: Synthesis, reactions, mechanisms and selectivity
involving the following- alkenes, alkynes, arenes, alcohols, phenols,
aldehydes, ketones, carboxylic acids and their derivatives, halides, nitro
compounds and amines. Use of compounds of Mg, Li, Cu, B and Si in organic
synthesis. Concepts in multistep synthesis- retrosynthetic analysis,
disconnections, synthons, synthetic equivalents, reactivity umpolung,
selectivity, protection and deprotection of functional groups.
Pericyclic reactions: Electrocyclic, cycloaddition and sigmatropic
reactions. Orbital correlation, FMO and PMO treatments.
Photochemistry: Basic principles. Photochemistry of alkenes, carbonyl
compounds, and arenes. Photooxidation and photoreduction. Di-p- methane
rearrangement, Barton reaction.
Heterocyclic compounds: Structure, preparation, properties and reactions
of furan, pyrrole, thiophene, pyridine, indole and their derivatives.
Biomolecules: Structure, properties and reactions of mono- and
di-saccharides, physicochemical properties of amino acids, chemical synthesis
of peptides, structural features of proteins, nucleic acids, steroids,
terpenoids, carotenoids, and alkaloids.
Spectroscopy: Principles and applications of
UV-visible, IR, NMR and Mass spectrometry in the determination of structures
of organic molecules.
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Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values
and eigen vectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation
of definite and improper integrals, Partial Derivatives, Maxima and minima,
Multiple integrals, Fourier series. Vector identities, Directional
derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s
theorems.
Differential equations: First order equation (linear and nonlinear),
Higher order linear differential equations with constant coefficients, Method
of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary
value problems, Partial Differential Equations and variable separable method.
Complex variables: Analytic functions, Cauchy’s integral theorem and
integral formula, Taylor’s and Laurent’ series, Residue theorem, solution
integrals.
Probability and Statistics: Sampling theorems, Conditional probability,
Mean, median, mode and standard deviation, Random variables, Discrete and
continuous distributions, Poisson, Normal
and Binomial distribution, Correlation and regression analysis.
Numerical Methods: Solutions of non-linear algebraic equations, single and
multi-step methods for differential equations.
Transform Theory: Fourier transform, Laplace
transform, Z-transform.
ELECTRONICS AND COMMUNICATION ENGINEERING
Networks: Network graphs: matrices associated with graphs; incidence,
fundamental cut set and fundamental circuit matrices. Solution methods: nodal
and mesh analysis. Network theorems: superposition, Thevenin and Norton’s
maximum power transfer, Wye-Delta transformation. Steady state sinusoidal
analysis using phasors. Linear constant coefficient differential equations;
time domain analysis of simple RLC circuits, Solution of network equations
using Laplace transform: frequency domain
analysis of RLC circuits. 2-port network parameters: driving point and
transfer functions. State equations for networks.
Electronic Devices: Energy bands in silicon, intrinsic and extrinsic
silicon. Carrier transport in silicon: diffusion current, drift current,
mobility, and resistivity. Generation and recombination of carriers. p-n
junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET,
LED, p-I-n and avalanche photo diode, Basics of LASERs. Device technology:
integrated circuits fabrication process, oxidation, diffusion, ion
implantation, photolithography, n-tub, p-tub and twin-tub CMOS process.
Analog Circuits: Small Signal Equivalent circuits of diodes, BJTs, MOSFETs
and analog CMOS. Simple diode circuits, clipping, clamping, rectifier.
Biasing and bias stability of transistor and FET amplifiers. Amplifiers:
single-and multi-stage, differential and operational, feedback, and power.
Frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal
oscillators; criterion for oscillation; single-transistor and op-amp
configurations. Function generators and wave-shaping circuits, 555 Timers.
Power supplies.
Digital circuits: Boolean algebra, minimization of Boolean functions;
logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinatorial
circuits: arithmetic circuits, code converters, multiplexers, decoders, PROMs
and PLAs. Sequential circuits: latches and flip-flops, counters and
shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor
memories. Microprocessor(8085): architecture, programming, memory and I/O interfacing.
Signals and Systems: Definitions and properties of Laplace
transform, continuous-time and discrete-time Fourier series, continuous-time
and discrete-time Fourier Transform, DFT and FFT, z-transform. Sampling
theorem. Linear Time-Invariant (LTI) Systems: definitions and properties;
causality, stability, impulse response, convolution, poles and zeros,
parallel and cascade structure, frequency response, group delay, phase delay.
Signal transmission through LTI systems.
Control Systems: Basic control system components; block diagrammatic
description, reduction of block diagrams. Open loop and closed loop
(feedback) systems and stability analysis of these systems. Signal flow
graphs and their use in determining transfer functions of systems; transient
and steady state analysis of LTI control systems and frequency response.
Tools and techniques for LTI control system analysis: root loci,
Routh-Hurwitz criterion, Bode and Nyquist plots. Control system compensators:
elements of lead and lag compensation, elements of
Proportional-Integral-Derivative (PID) control. State variable representation
and solution of state equation of LTI control systems.
Communications: Random signals and noise: probability, random variables,
probability density function, autocorrelation, power spectral density. Analog
communication systems: amplitude and angle modulation and demodulation
systems, spectral analysis of these operations, superheterodyne receivers;
elements of hardware, realizations of analog communication systems;
signal-to-noise ratio (SNR) calculations for amplitude modulation (AM) and
frequency modulation (FM) for low noise conditions. Fundamentals of
information theory and channel capacity theorem. Digital communication
systems: pulse code modulation (PCM), differential pulse code modulation
(DPCM), digital modulation schemes: amplitude, phase and frequency shift
keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth
consideration and probability of error calculations for these schemes. Basics
of TDMA, FDMA and CDMA and GSM.
Electromagnetics: Elements of vector
calculus: divergence and curl; Gauss’ and Stokes’ theorems, Maxwell’s
equations: differential and integral forms. Wave equation, Poynting vector.
Plane waves: propagation through various media; reflection and refraction;
phase and group velocity; skin depth. Transmission lines: characteristic
impedance; impedance transformation; Smith chart; impedance matching; S
parameters, pulse excitation. Waveguides: modes in rectangular waveguides;
boundary conditions; cut-off frequencies; dispersion relations. Basics of
propagation in dielectric waveguide and optical fibers. Basics of Antennas:
Dipole antennas; radiation pattern; antenna gain.
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