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AE - AEROSPACE ENGINEERING
ENGINEERING MATHEMATICS
Linear Algebra: Matrix algebra, systems of linear equations, eigen values and
eigen vectors. Calculus: Functions of single variable, limit, continuity and
differentiability, mean value theorems, evaluation of definite and improper
integrals, partial derivatives, total derivative, maxima and minima, gradient,
divergence and curl, vector identities, directional derivatives, line, surface
and volume integrals. Theorems of Stokes, Gauss and Green.
Differential Calculus: First order linear and nonlinear equations, higher order
linear ODEs with constant coefficients, Cauchy and Euler equations, initial and
boundary value problems, Laplace transforms. Partial differential equations and
separation of variables methods.
Numerical methods: Numerical solution of linear and nonlinear algebraic
equations, integration by trapezoidal and Simpson rule, single and multi-step
methods for differential equations.
FLIGHT MECHANICS
Atmosphere: Properties, standard atmosphere. Classification of aircraft.
Airplane (fixed wing aircraft) configuration and various parts.
Airplane performance: Pressure altitude; equivalent, calibrated, indicated air
speeds; Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator.
Drag polar; take off and landing; steady climb & descent,-absolute and
service ceiling; cruise, cruise climb, endurance or loiter; load factor, turning
flight, V-n diagram; Winds: head, tail & cross winds.
Static stability: Angle of attack, sideslip; roll, pitch & yaw controls;
longitudinal stick fixed & free stability, horizontal tail position and
size; directional stability, vertical tail position and size; dihedral
stability. Wing dihedral, sweep & position; hinge moments, stick forces.
Dynamic stability: Euler angles; Equations of motion; aerodynamic forces and
moments, stability & control derivatives; decoupling of longitudinal and
lat-directional dynamics; longitudinal modes; lateral-directional modes.
SPACE DYNAMICS
Central force motion, determination of trajectory and orbital period in simple
cases. Orbit transfer,in-plane and out-of-plane. Elements of rocket motor
performance.
AERODYNAMICS
Basic Fluid Mechanics: Incompressible irrotational flow, Helmholtz and Kelvin
theorem, singularities and superposition, viscous flows, boundary layer on a
flat plate. Airfoils and wings: Classification of airfoils, aerodynamic
characteristics, high lift devices, Kutta Joukowski theorem; lift generation;
thin airfoil theory; wing theory; induced drag; qualitative treatment of low
aspect ratio wings.
Viscous Flows: Flow separation, introduction to turbulence, transition,
structure of a turbulentboundary layer.
Compressible Flows: Dynamics & Thermodynamics of I-D flow, isentropic flow,
normal shock, oblique shock, Prandtl-Meyer flow, flow in nozzles and diffusers,
inviscid flow in a c-d nozzle, flow in diffusers. subsonic and supersonic
airfoils, compressibility effects on lift and drag, critical and drag divergence
Mach number, wave drag.
Wind Tunnel Testing: Measurement and visualisation techniques.
STRUCTURES
Stress and Strain: Equations of equilibrium, constitutive law,
strain-displacement relationship, compatibility equations, plane stress and
strain, Airy's stress function.
Flight Vehicle Structures: Characteristics of aircraft structures and materials,
torsion, bending and flexural shear. Flexural shear flow in thin-walled
sections. Buckling. Failure theories. Loads on aircraft.
Structural Dynamics: Free and forced vibration of discrete systems. Damping and
resonance.
Dynamics of continuous systems.
PROPULSION
Thermodynamics of Aircraft Gas Turbine engines, thrust and thrust augmentation.
Turbomachinery: Axial compressors and turbines, centrifugal pumps and
compressors. Aerothermodynamics of non rotating propulsion components: Intakes,
combustor and nozzle. Thermodynamics of ramjets and scramjets. Elements of
rocket propulsion.
AG - AGRICULTURAL ENGINEERING
ENGINEERING MATHEMATICS:
Linear Algebra: Matrices and Determinants, Systems of linear
equations, Eigen values and eigen vectors.
Calculus: Limit, continuity and differentiability; Partial
Derivatives; Maxima and minima; Sequences and series; Test
for convergence; Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line; surface
and volume integrals; Stokes, Gauss and Green's theorems.
Diferential Equations: Linear and non-linear first order ODEs;
Higher order linear ODEs with constant coefficients; Cauchy's
and Euler's equations; Laplace transforms; PDEs - Laplace,
heat and wave equations.
Probability and Statistics: Mean, median, mode and standard
deviation; Random variables; Poisson, normal and binomial
distributions; Correlation and regression analysis.
Numerical Methods: Solutions of linear and non-linear algebraic
equations; integration of trapezoidal and Simpson's rule;
single and multi-step methods for differential equations.
FARM MACHINERY AND POWER:
Sources of power on the farm-human, animal, mechanical, electrical,
wind, solar and biomass; design and selection of machine elements
- gears, pulleys, chains and sprockets and belts; overload
safety devices used in farm machinery; measurement of force,
torque, speed, displacement and acceleration on machine elements.
Soil tillage; forces acting on a tillage tool; hitch systems
and hitching of tillage implements; functional requirements,
principles of working, construction and operation of manual,
animal and power operated equipment for tillage. sowing, planting,
fertilizer application, inter-cultivation, spraying, mowing,
chaff cutting, harvesting, threshing and transport; testing
of agricultural machinery and equipment; calculation of performance
parameters -field capacity, efficiency, application rate and
losses; cost analysis of implements and tractors.
Thermodynamic principles of I.C. engines; I.C. engine cycles;
engine components; fuels and combustion; lubricants and their
properties; I.C. engine systems - fuel, cooling, lubrication,
ignition, electrical, intake and exhaust; selection, operation,
maintenance and repair of I.C. engines; power efficiencies
and measurement; calculation of power, torque, fuel consumption,
heat load and power losses.
Tractors and power tillers - type, selection, maintenance
and repair; tractor clutches and brakes; power transmission
systems - gear trains, differential, final drives and power
take-off; mechanics of tractor chassis; traction theory; three
point hitches- free link and restrained link operations; mechanical
steering and hydraulic control systems used in tractors; human
engineering and safety in tractor design; tractor tests and
performance.
SOIL AND WATER CONSERVATION ENGINEERING:
Ideal and real fluids, properties of fluids; hydrostatic pressure
and its measurement; hydrostatic forces on plane and curved
surface; continuity equation; Bernoulli's theorem; laminar
and turbulent flow in pipes, Darcy-Weisbach and Hazen-Williams
equations, Moody's diagram; flow through orifices and notches;
flow in open channels.
Engineering properties of soils, fundamental definitions and
relationships; index properties of soils; permeability and
seepage analysis; shear strength, Mohr's circle of stresses;
active and passive earth pressures; stability of slopes.
Hydrological cycle; precipitation measurement, analysis of
precipitation data; abstraction from precipitation; runoff;
hydrograph analysis, unit hydrograph theory and application;
stream flow measurement; flood routing, hydrological reservoir
and channel routing.
Mechanics of soil erosion, factors affecting erosion; soil
loss estimation; biological and engineering measures to control
erosion, terraces and bunds; vegetative waterways; gully control
structures, drop, drop inlet and chute spillways; farm ponds;
earthen dams; principles of watershed management.
Water requirement of crops; consumptive use and evapo-transpiration;
irrigation scheduling; irrigation efficiencies; design of
prismatic and silt loaded channels; methods of irrigation
water application; design and evaluation of irrigation methods;
drainage coefficient; surface and subsurface drainage systems;
leaching requirement and salinity control; irrigation and
drainage water quality; classification of pumps; pump characteristics;
pump selection; types of aquifer; evaluation of aquifer properties;
well hydraulics; ground water recharge.
AGRICULTURAL PROCESSING AND FOOD ENGINEERING:
Steady state heat transfer in conduction, convection and radiation;
transient heat transfer in simple geometry; condensation and
boiling heat transfer; working principles of heat exchangers;
diffusive and convective mass transfer; simultaneous heat
and mass transfer in agricultural processing operations.
Material and energy balances in food processing systems; water
activity, sorption and desorption isotherms; centrifugal separation
of solids, liquids and gases; kinetics of microbial death
- pasteurisation and sterilization of liquid foods; preservation
of food by cooling and freezing; psychrometry - properties
of air-vapour mixture; concentration and dehydration of liquid
foods - evaporators, tray, drum and spray dryers.
Mechanics and energy requirement in size reduction of granular
solids; particle size analysis for comminuted solids; size
separation by screening; fluidisation of granular solids;
cleaning and grading efficiency and effectiveness of grain
cleaners; conditioning and hydrothermal treatments for grains;
dehydration of food grains; processes and machines for processing
of cereals, pulses and oilseeds; design considerations for
grain silos.
AR - ARCHITECTURE AND PLANNING
City planning: Historical development of cities; principles
of city planning; new towns; survey methods, site planning,
planning regulations and building bye-laws.
Housing: Concept of shelter; housing policies and design;
community planning; role of government agencies; finance and
management.
Landscape Design: Principles of landscape design and site
planning; history and landscape styles; landscape elements
and materials; planting design.
Computer Aided Design: Application of computers in architecture
and planning; understanding elements of hardware and software;
computer graphics; programming languages - C and Visual Basic
and usage of packages such as AutoCAD.
Environmental and Building Science: Elements of environmental
science; ecological principles concerning environment; role
of micro-climate in design; climatic control through design
elements; thermal comfort; elements of solar architecture;
principles of lighting and illumination; basic principles
of architectural acoustics; air pollution, noise pollution
and their control.
Visual and Urban Design: Principles of visual composition;
proportion, scale, rhythm, symmetry, harmony, balance, form
and colour; sense of place and space, division of space; focal
point, vista, imageability, visual survey.
History of Architecture: Indian - Indus valley, Vedic, Buddhist,
Indo-Aryan, Dravidian and Mughal periods; European - Egyptian,
Greek, Roman, medieval and renaissance periods.
Development of Contemporary Architecture: Architectural developments
and impacts on society since industrial revolution; influence
of modern art on architecture; works of national and international
architects; post modernism in architecture.
Building Services: Water supply, Sewerage and Drainage systems;
Sanitary fittings and fixtures; principles of electrification
of buildings; elevators, their standards and uses; air-conditioning
systems; fire fighting systems.
Building Construction and Management: Building construction
techniques, methods and details; building systems and prefabrication
of building elements; principles of modular coordination;
estimation, specification, valuation, professional practice;
project management, PERT, CPM.
Materials and Structural Systems: Behavioural characteristics
of all types of building materials e.g. mud, timber, bamboo,
brick, concrete, steel, glass, FRP; principles of strength
of materials; design of structural elements in wood, steel
and RCC; elastic and limit state design; complex structural
systems; principles of pre-stressing.
Planning Theory: Planning process; multilevel planning; comprehensive
planning; central place theory; settlement pattern; land use
and land utilization.
Techniques of Planning: Planning surveys; Preparation of urban
and regional structure plans, development plans, action plans;
site planning principles and design; statistical methods;
application of remote sensing techniques in urban and regional
planning.
Traffic and Transportation Planning: Principles of traffic
engineering and transportation planning; methods of conducting
surveys; design of roads, intersections and parking areas;
hierarchy of roads and levels of services; traffic and transport
management in urban areas; traffic safety and traffic laws;
public transportation planning; modes of transportation.
Services and Amenities: Principles and design of water supply
systems, sewerage systems, solid waste disposal systems, power
supply and communication systems; Health, education, recreation
and demography related standards at various levels of the
settlements.
Development Administration and Management: Planning laws;
development control and zoning regulations; laws relating
to land acquisition; development enforcements, land ceiling;
regional and urban plan preparations; planning and municipal
administration; taxation, revenue resources and fiscal management;
public participation and role of NGO.
CE - CIVIL ENGINEERING
ENGINEERING MATHEMATICS
Linear Algebra: Matrix algebra, Systems of linear equations,
Eigen values and eigenvectors.
Calculus: Functions of single variable, Limit, continuity
and differentiability, Mean value theorems, Evaluation of
definite and improper integrals, Partial derivatives, Total
derivative, Maxima and minima, Gradient, Divergence and Curl,
Vector identities, Directional derivatives, Line, Surface
and Volume integrals, Stokes, Gauss and Green's theorems.
Differential equations: First order equations (linear and
nonlinear), Higher order linear differential equations with
constant coefficients, Cauchy's and Euler's equations, Initial
and boundary value problems, Laplace transforms, Solutions
of one dimensional heat and wave equations and Laplace equation.
Complex variables: Analytic functions, Cauchy's integral theorem,
Taylor and Laurent series.
Probability and Statistics: Definitions of probability and
sampling theorems, Conditional probability, Mean, median,
mode and standard deviation, Random variables, Poisson, Normal
and Binomial distributions.
Numerical Methods: Numerical solutions of linear and non-linear
algebraic equations Integration by trapezoidal and Simpson's
rule, single and multi-step methods for differential equations.
STRUCTURAL ENGINEERING
Mechanics: Bending moments and shear forces in statically
determinate beams; simple stress and strain: relationship;
stress and strain in two dimensions, principal stresses, stress
transformation, Mohr's circle; simple bending theory; flexural
shear stress; thin-walled pressure vessels; uniform torsion.
Structural Analysis: Analysis of statically determinate trusses,
arches and frames; displacements in statically determinate
structures and analysis of statically indeterminate structures
by force/energy methods; analysis by displacement methods
(slope-deflection and moment-distribution methods); influence
lines for determinate and indeterminate structures; basic
concepts of matrix methods of structural analysis.
Concrete Structures: Basic working stress and limit states
design concepts; analysis of ultimate load capacity and design
of members subject to flexure, shear, compression and torsion
(beams, columns and isolated footings); basic elements of
prestressed concrete: analysis of beam sections at transfer
and service loads.
Steel Structures: Analysis and design of tension and compression
members, beams and beam-columns, column bases; connections
- simple and eccentric, beam-column connections, plate girders
and trusses; plastic analysis of beams and frames.
GEOTECHNICAL ENGINEERING
Soil Mechanics: Origin of soils; soil classification; three-phase
system, fundamental definitions, relationship and inter-relationships;
permeability and seepage; effective stress principle: consolidation,
compaction; shear strength.
Foundation Engineering: Sub-surface investigation - scope,
drilling bore holes, sampling, penetrometer tests, plate load
test; earth pressure theories, effect of water table, layered
soils; stability of slopes - infinite slopes, finite slopes;
foundation types - foundation design requirements; shallow
foundations; bearing capacity, effect of shape, water table
and other factors, stress distribution, settlement analysis
in sands and clays; deep foundations - pile types, dynamic
and static formulae, load capacity of piles in sands and clays.
WATER RESOURCES ENGINEERING
Fluid Mechanics and Hydraulics: Hydrostatics, applications
of Bernoulli equation, laminar and turbulent flow in pipes,
pipe networks; concept of boundary layer and its growth; uniform
flow, critical flow and gradually varied flow in channels,
specific energy concept, hydraulic jump; forces on immersed
bodies; flow measurement in channels; tanks and pipes; dimensional
analysis and hydraulic modeling. Applications of momentum
equation, potential flow, kinematics of flow; velocity triangles
and specific speed of pumps and turbines.
Hydrology: Hydrologic cycle; rainfall; evaporation infiltration,
unit hydrographs, flood estimation, reservoir design, reservoir
and channel routing, well hydraulics.
Irrigation: Duty, delta, estimation of evapo-transpiration;
crop water requirements; design of lined and unlined canals;
waterways; head works, gravity dams and Ogee spillways. Designs
of weirs on permeable foundation, irrigation methods.
ENVIRONMENTAL ENGINEERING
Water requirements; quality and standards, basic unit processes
and operations for water treatment, distribution of water.
Sewage and sewerage treatment: quantity and characteristic
of waste water sewerage; primary and secondary treatment of
waste water; sludge disposal; effluent discharge standards.
TRANSPORTATION ENGINEERING
Highway planning; geometric design of highways; testing and
specifications of paving materials; design of flexible and
rigid pavements.
CH - CHEMICAL ENGINEERING
ENGINEERING MATHEMATICS
Linear Algebra: Matrix algebra, Systems of linear equations,
Eigen values and eigenvectors.
Calculus: Functions of single variable, Limit, continuity
and differentiability, Mean value theorems, Evaluation of
definite and improper integrals, Partial derivatives, Total
derivative, Maxima and minima, Gradient, Divergence and Curl,
Vector identities, Directional derivatives, Line, Surface
and Volume integrals, Stokes, Gauss and Green's theorems.
Differential equations: First order equations (linear and
nonlinear), Higher order linear differential equations with
constant coefficients, Cauchy's and Euler's equations, Initial
and boundary value problems, Laplace transforms, Solutions
of one dimensional heat and wave equations and Laplace equation.
Complex variables: Analytic functions, Cauchy's integral theorem,
Taylor and Laurent series.
Probability and Statistics: Definitions of probability and
sampling theorems, Conditional probability, Mean, median,
mode and standard deviation, Random variables, Poisson, Normal
and Binomial distributions.
Numerical Methods: Numerical solutions of linear and non-linear
algebraic equations Integration by trapezoidal and Simpson's
rule, single and multi-step methods for differential equations.
CHEMICAL ENGINEERING
Process Calculations and Thermodynamics: Laws of conservation
of mass and energy; use of tie components; recycle, bypass
and purge calculations; degree of freedom analysis.
First and Second laws of thermodynamics and their applications;
equations of state and thermodynamic properties of real systems;
phase equilibria; fugacity, excess properties and correlations
of activity coefficients; chemical reaction equilibria.
Fluid Mechanics and Mechanical Operations: Fluid statics,
Newtonian and non-Newtonian fluids, Bernoulli equation, Macroscopic
friction factors, energy balance, dimensional analysis, shell
balances, flow through pipeline systems, flow meters, pumps
and compressors, packed and fluidized beds, elementary boundary
layer theory, size reduction and size separation; free and
hindered settling; centrifuge and cyclones; thickening and
classification, filtration, mixing and agitation; conveying
of solids.
Heat Transfer: Conduction, convection and radiation, heat
transfer coefficients, steady and unsteady heat conduction,
boiling, condensation and evaporation; types of heat exchangers
and evaporators and their design.
Mass Transfer: Fick's law, molecular diffusion in fluids,
mass transfer coefficients, film, penetration and surface
renewal theories; momentum, heat and mass transfer analogies;
stagewise and continuous contacting and stage efficiencies;
HTU & NTU concepts design and operation of equipment for
distillation, absorption, leaching, liquid-liquid extraction,
crystallization, drying, humidification, dehumidification
and adsorption.
Chemical Reaction Engineering: Theories of reaction rates;
kinetics of homogeneous reactions, interpretation of kinetic
data, single and multiple reactions in ideal reactors, non-ideal
reactors; residence time; non-isothermal reactors; kinetics
of heterogeneous catalytic reactions; diffusion effects in
catalysis.
Instrumentation and Process Control: Measurement of process
variables; sensors, transducers and their dynamics, dynamics
of simple systems, dynamics such as CSTRs, transfer functions
and responses of simple systems, process reaction curve, controller
modes (P, PI, and PID); control valves; analysis of closed
loop systems including stability, frequency response (including
Bode plots) and controller tuning, cascade, feed forward control.
Plant Design and Economics: Design and sizing of chemical
engineering equipment such as compressors, heat exchangers,
multistage contactors; principles of process economics and
cost estimation including total annualized cost, cost indexes,
rate of return, payback period, discounted cash flow, optimization
in Design.
Chemical Technology: Inorganic chemical industries; sulfuric
acid, NaOH, fertilizers (Ammonia, Urea, SSP and TSP); natural
products industries (Pulp and Paper, Sugar, Oil, and Fats);
petroleum refining and petrochemicals; polymerization industries;
polyethylene, polypropylene, PVC and polyester synthetic fibers.
CS - COMPUTER SCIENCE AND ENGINEERING
ENGINEERING MATHEMATICS
Mathematical Logic: Propositional Logic; First Order Logic.
Probability: Conditional Probability; Mean, Median, Mode and
Standard Deviation; Random Variables; Distributions; uniform,
normal, exponential, Poisson, Binomial.
Set Theory & Algebra: Sets; Relations; Functions; Groups;
Partial Orders; Lattice; Boolean Algebra.
Combinatorics: Permutations; Combinations; Counting; Summation;
generating functions; recurrence relations; asymptotics.
Graph Theory: Connectivity; spanning trees; Cut vertices &
edges; covering; matching; independent sets; Colouring; Planarity;
Isomorphism.
Linear Algebra: Algebra of matrices, determinants, systems
of linear equations, Eigen values and Eigen vectors.
Numerical Methods: LU decomposition for systems of linear
equations; numerical solutions of non linear algebraic equations
by Secant, Bisection and Newton-Raphson Methods; Numerical
integration by trapezoidal and Simpson's rules.
Calculus: Limit, Continuity & differentiability, Mean
value Theorems, Theorems of integral calculus, evaluation
of definite & improper integrals, Partial derivatives,
Total derivatives, maxima & minima.
THEORY OF COMPUTATION
Formal Languages and Automata Theory: Regular languages and
finite automata, Context free languages and Push-down automata,
Recursively enumerable sets and Turing machines, Un-decidability;
Analysis of Algorithms and Computational Complexity: Asymptotic
analysis (best, worst, average case) of time and space, Upper
and lower bounds on the complexity of specific problems, NP-completeness.
COMPUTER HARDWARE
Digital Logic: Logic functions, Minimization, Design and synthesis
of Combinational and Sequential circuits; Number representation
and Computer Arithmetic (fixed and floating point);
Computer Organization: Machine instructions and addressing
modes, ALU and Data-path, hardwired and micro-programmed control,
Memory interface, I/O interface (Interrupt and DMA mode),
Serial communication interface, Instruction pipelining, Cache,
main and secondary storage.
SOFTWARE SYSTEMS
Data structures: Notion of abstract data types, Stack, Queue,
List, Set, String, Tree, Binary search tree, Heap, Graph;
Programming Methodology: C programming, Program control (iteration,
recursion, Functions), Scope, Binding, Parameter passing,
Elementary concepts of Object oriented, Functional and Logic
Programming;
Algorithms for problem solving: Tree and graph traversals,
Connected components, Spanning trees, Shortest paths; Hashing,
Sorting, Searching; Design techniques (Greedy, Dynamic Programming,
Divide-and-conquer);
Compiler Design: Lexical analysis, Parsing, Syntax directed
translation, Runtime environment, Code generation, Linking
(static and dynamic); Operating Systems: Classical concepts
(concurrency, synchronization, deadlock), Processes, threads
and Inter-process communication, CPU scheduling, Memory management,
File systems, I/O systems, Protection and security.
Databases: Relational model (ER-model, relational algebra,
tuple calculus), Database design (integrity constraints, normal
forms), Query languages (SQL), File structures (sequential
files, indexing, B+ trees), Transactions and concurrency control;
Computer Networks: ISO/OSI stack, sliding window protocol,
LAN Technologies (Ethernet, Token ring), TCP/UDP, IP, Basic
concepts of switches, gateways, and routers.
CH - CHEMISTRY
PHYSICAL CHEMISTRY
Structure: Quantum theory - principles and techniques; applications
to particle in a box, harmonic oscillator, rigid rotor and
hydrogen atom; valence bond and molecular orbital theories
and Huckel approximation, approximate techniques: variation
and perturbation; symmetry, point groups; rotational, vibrational,
electronic, NMR and ESR spectroscopy.
Equilibrium: 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; kinetic
theory of gases; 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, theories of reaction
rates, collision and transition state theory; temperature
dependence of chemical reactions; elementary reactions, consecutive
elementary reactions; steady state approximation, kinetics
of photochemical reactions and free radical polymerization,
homogenous and heterogeneous catalysis.
INORGANIC CHEMISTRY
Non-Transition Elements: General characteristics, structure
and reactions of simple and industrially important compounds,
boranes, carboranes, silicates, silicones, diamond and graphite;
hydrides, oxides and oxoacids of N, P, S and halogens; boron
nitride, borazines and phosphazenes; xenon compounds. Shapes
of molecules, hard-soft acid base concept.
Transition Elements: General characteristics of d and f block
elements; coordination chemistry: structure and isomerism,
stability, theories of metal-ligand bonding (CFT and LFT),
electronic spectra and magnetic properties of transition metal
complexes and lanthanides; 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; mechanisms of substitution and electron
transfer reactions of coordination complexes. Role of metals
with special reference to Na, K, Mg, Ca, Fe, Co, Zn, and Mo
in biological systems.
Solids: Crystal systems and lattices, Miller planes, crystal
packing, crystal defects; Bragg's Law; ionic crystals, band
theory, metals and semiconductors. Spinels.
Instrumental methods of analysis: atomic absorption, UV-visible
spectrometry, chromatographic and electro-analytical methods.
ORGANIC CHEMISTRY
Synthesis, reactions and mechanisms involving the following:
Alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones,
carboxylic acids and their derivatives; halides, nitro compounds
and amines; stereochemical and conformational effects on reactivity
and specificity; reactions with diborane and peracids. Michael
reaction, Robinson annulation, reactivity umpolung, acyl anion
equivalents; molecular rearrangements involving electron deficient
atoms.
Photochemistry: Basic principles, photochemistry of olefins,
carbonyl compounds, arenes, photo oxidation and reduction.
Pericyclic reactions: Cycloadditions, electrocyclic reactions,
sigmatropic reactions; Woodward-Hoffmann rules.
Heterocycles: Structural properties and reactions of furan,
pyrrole, thiophene, pyridine, indole.
Biomolecules: Structure, properties and reactions of mono-
and di-saccharides, physico-chemical properties of amino acids,
structural features of proteins and nucleic acids.
Spectroscopy: Principles and applications of IR, UV-visible,
NMR and mass spectrometry in the determination of structures
of organic compounds.
EC - ELECTRONICS AND COMMUNICATION ENGINEERING
ENGINEERING MATHEMATICS
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 & 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, 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, LASERs. Device technology: integrated
circuits fabrication process, oxidation, diffusion, ion implantation,
photolithography, n-tub, p-tub and twin-tub CMOS process.
Analog Circuits: Equivalent circuits (large and small-signal)
of diodes, BJTs, JFETs, and MOSFETs. Simple diode circuits,
clipping, clamping, rectifier. Biasing and bias stability
of transistor and FET amplifiers. Amplifiers: single-and multi-stage,
differential, operational, feedback and power. Analysis of
amplifiers; 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. Power supplies.
Digital circuits: Boolean algebra, minimization of Boolean
functions; logic gates digital IC families (DTL, TTL, ECL,
MOS, CMOS). Combinational circuits: arithmetic circuits, code
converters, multiplexers and decoders. 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, z-transform.
Sampling theorems. Linear Time-Invariant (LTI) Systems: definitions
and properties; casuality, stability, impulse response, convolution,
poles and zeros frequency response, group delay, phase delay.
Signal transmission through LTI systems. Random signals and
noise: probability, random variables, probability density
function, autocorrelation, power spectral density.
Controls 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: 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. Digital
communication systems: pulse code modulation (PCM), differential
pulse code modulation (DPCM), delta modulation (DM); digital
modulation schemes-amplitude, phase and frequency shift keying
schemes (ASK, PSK, FSK), matched filter receivers, bandwith
consideration and probability of error calculations for these
schemes.
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; pulse excitation. Waveguides:
modes in rectangular waveguides; boundary conditions; cut-off
frequencies; dispersion relations. Antennas: Dipole antennas;
antenna arrays; radiation pattern; reciprocity theorem, antenna
gain.
EE - ELECTRICAL ENGINEERING
ENGINEERING MATHEMATICS
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.
ELECTRICAL ENGINEERING
Electrical Circuits and Fields: Network graph, KCL, KVL, node/
cut set, mesh/ tie set analysis, transient response of d.c.
and a.c. networks; sinusoidal steady-state analysis; resonance
in electrical circuits; concepts of ideal voltage and current
sources, network theorems, driving point, immittance and transfer
functions of two port networks, elementary concepts of filters;
three phase circuits; Fourier series and its application;
Gauss theorem, electric field intensity and potential due
to point, line, plane and spherical charge distribution, dielectrics,
capacitance calculations for simple configurations; Ampere's
and Biot-Savart's law, inductance calculations for simple
configurations.
Electrical Machines: Single phase transformer - equivalent
circuit, phasor diagram, tests, regulation and efficiency;
three phase transformers - connections, parallel operation;
auto transformer and three-winding transformer; principles
of energy conversion, windings of rotating machines: D. C.
generators and motors - characteristics, starting and speed
control, armature reaction and commutation; three phase induction
motors-performance characteristics, starting and speed control;
single-phase induction motors; synchronous generators-performance,
regulation, parallel operation; synchronous motors - starting,
characteristics, applications, synchronous condensers; fractional
horse power motors; permanent magnet and stepper motors.
Power Systems: Electric power generation - thermal, hydro,
nuclear; transmission line parameters; steady-state performance
of overhead transmission lines and cables and surge propagation;
distribution systems, insulators, bundle conductors, corona
and radio interference effects; per-unit quantities; bus admittance
and impedance matrices; load flow; voltage control and power
factor correction; economic operation; symmetrical components,
analysis of symmetrical and unsymmetrical faults; principles
of over current, differential and distance protections; concept
of solid state relays and digital protection; circuit breakers;
concept of system stability-swing curves and equal area criterion;
basic concepts of HVDC transmission.
Control Systems: Principles of feedback; transfer function;
block diagrams: steady-state errors; stability-Routh and Nyquist
criteria; Bode plots; compensation; root loci; elementary
state variable formulation; state transition matrix and response
for Linear Time Invariant systems.
Electrical and Electronic Measurements: Bridges and potentiometers,
PMMC, moving iron, dynamometer and induction type instruments;
measurement of voltage, current, power, energy and power factor;
instrument transformers; digital voltmeters and multimeters;
phase, time and frequency measurement; Q-meter, oscilloscopes,
potentiometric recorders, error analysis.
Analog and Digital Electronics: Characteristics of diodes,
BJT, FET, SCR; amplifiers-biasing, equivalent circuit and
frequency response; oscillators and feedback amplifiers, operational
amplifiers- characteristics and applications; simple active
filters; VCOs and timers; combinational and sequential logic
circuits, multiplexer, Schmitt trigger, multivibrators, sample
and hold circuits, A/D and D/A converters; microprocessors
and their applications.
Power Electronics and Electric Drives: Semiconductor power
devices-diodes, transistors, thyristors, triacs, GTOs, MOSFETs
and IGBTs - static characteristics and principles of operation;
triggering circuits; phase control rectifiers; bridge converters-fully
controlled and half controlled; principles of choppers and
inverters, basic concepts of adjustable speed dc and ac drives.
GG - GEOLOGY AND GEOPHYSICS
PART - I
Earth and planetary system; size, shape, internal structure
and composition of the earth; atmosphere and greenhouse effect;
isostasy; elements of seismology; continents and continental
processes; physical oceanography; palaeomagnetism, continental
drift plate tectonics, geothermal energy.
Weathering; soil formation; action of river, wind and glacier;
oceans and oceanic features; earthquakes, volcanoes, orogeny
and mountain building; elements of structural geology; crystallography;
classification, composition and properties of minerals and
rocks; engineering properties of rocks and soils, role of
geology in the construction of engineering structures.
Processes of ore formation, occurrence and distribution of
ores on land and on ocean floor; coal and petroleum resources
in India; ground water geology including well hydraulics,
geological time scale and geochronology; stratigraphic principles
and stratigraphy of India; basics concepts of gravity, magnetic
and electrical prospecting for ores and ground water.
PART - IIA: GEOLOGY
Crystal symmetry, forms, twinning; crystal chemistry; optical
mineralogy, classification of minerals, diagnostic properties
of rock minerals.
Mineralogy, structure, texture and classification of igneous,
sedimentary and metamorphic rock, their origin and evolution;
application of thermodynamics; structure and petrology of
sedimentary rocks; sedimentary processes and environments,
sedimentary facies, basin studies; basement cover relationship;
Primary and secondary structures; geometry and genesis of
folds, faults, joints, unconformities, cleavage, schistosity
and lineation; methods of projection. Tectonites and their
significance; shear zone; superposed folding.
Morphology, classification and geological significance of
important invertebrates, vertebrates, microfossils and palaeoflora;
stratigraphic principles and Indian stratigraphy; geomorphic
processes and agents; development and evolution of landforms;
slope and drainage; processes on deep oceanic and near-shore
regions; quantitative and applied geomorphology; air photo
interpretation and remote sensing; chemical and optical properties
of ore minerals; formation and localization of ore deposits;
prospecting and exploration of economic minerals; coal and
petroleum geology; origin and distribution of mineral and
fuel deposits in India; ore dressing and mineral economics.
Cosmic abundance; meteorites; geochemical evolution of the
earth; geochemical cycles; distribution of major, minor and
trace elements; isotope geochemistry; geochemistry of waters
including solution equilibria and water rock interaction.
Engineering properties of rocks and soils; rocks as construction
material; geology of dams, tunnels and excavation sites; natural
hazards; the fly ash problem; ground water geology and exploration;
water quality; impact of human activity; Remote sensing techniques
for the interpretation of landforms and resource management.
PART - II B: GEOPHYSICS
The earth as a planet; different motions of the earth; gravity
filed of the earth and its shape; geochronology; isostasy,
seismology and interior of the earth; variation of density,
velocity, pressure, temperature, electrical and magnetic properties
inside the earth; earthquakes-causes and measurements; zonation
and seismic hazards; geomagnetic field, palaeomagnetism; oceanic
and continental lithosphere; plate tectonics; heat flow; upper
and lower atmospheric phenomena.
Theories of scalar and vector potential fields; Laplace, Maxwell
and Helmholtz equations for solution of different types of
boundary value problems for Cartesian, cylindrical and spherical
polar coordinates; Green's theorem; Image theory; integral
equations and conformal transformations in potential theory;
Eikonal equation and ray theory.
'G' and 'g' units of measurement, density of rocks, gravimeters,
preparation, analysis and interpretation of gravity maps;
derivative maps, analytical continuation; gravity anomaly
type curves; calculation of mass.
Earth's magnetic field, units of measurement, magnetic susceptibility
of rocks, magnetometers, corrections, preparation of magnetic
maps, magnetic anomaly type curve, analytical continuation,
interpretation and application; magnetic well logging.
Conduction of electricity through rocks, electrical conductivities
of metals, metallic, non-metallic and rock forming minerals,
D.C. resistivity units and methods of measurement, electrode
configuration for sounding and profiling, application of filter
theory, interpretation of resistivity field data, application;
self potential origin, classification, field measurement,
interpretation of induced polarization time frequency, phase
domain; IP units and methods of measurement, interpretation
and application; ground-water exploration.
Origin of electromagnetic field elliptic polarization, methods
of measurement for different source-receiver configuration
components in EM measurements, interpretation and applications;
earth's natural electromagnetic field, tellurics, magneto-tellurics;
geomagnetic depth sounding principles, methods of measurement,
processing of data and interpretation.
Seismic methods of prospecting: Reflection, refraction and
CDP surveys; land and marine seismic sources, generation and
propagation of elastic waves, velocity increasing with depth,
geophones, hydrophones, recording instruments (DFS), digital
formats, field layouts, seismic noises and noise profile analysis,
optimum geophone grouping, noise cancellation by shot and
geophone arrays, 2D and 3D seismic data acquisition and processing,
CDP stacking charts, binning, filtering, dip-moveout, static
and dynamic corrections, deconvolution, migration, signal
processing, Fourier and Hilbert transforms, attribute analysis,
bright and dim spots, seismic stratigraphy, high resolution
seismics, VSP.
Principles and techniques of geophysical well-logging, SP,
resistivity, induction, micro gamma ray, neutron, density,
sonic, temperature, dip meter, caliper, nuclear magnetic,
cement bond logging. Quantitative evaluation of formations
from well logs; well hydraulics and application of geophysical
methods for groundwater study; application of bore hole geophysics
in ground water, mineral and oil exploration. Remote sensing
techniques and application of remote sensing methods in geophysics.
IN - INSTRUMENTATION ENGINEERING
ENGINEERING MATHEMATICS
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.
INSTRUMENTATION ENGINEERING
Measurement Basics and Metrology: Static and dynamic characteristics
of measurement systems. Standards and calibration. Error and
uncertainty analysis, statistical analysis of data, and curve
fitting. Linear and angular measurements; Measurement of straightness,
flatness, roundness and roughness.
Transducers, Mechanical Measurements and Industrial Instrumentation:
Transducers - elastic, resistive, inductive, capacitive, thermo-electric,
piezoelectric, photoelectric, electro-mechanical, electro-chemical,
and ultrasonic. Measurement of displacement, velocity (linear
and rotational), acceleration, shock, vibration, force, torque,
power, strain, stress, pressure, flow, temperature, humidity,
viscosity, and density. energy storing elements, suspension
systems and dampers.
Analog Electronics: Characteristics of diodes, BJTs, JFETs
and MOSFETs; Diode circuits; Amplifiers: single and multi-stage,
feedback; Frequency response; Operational amplifiers - design,
characteristic, linear and non-linear applications: difference
amplifiers; instrumentation amplifiers; precision rectifiers,
I-to-V converters, active filters, oscillators, comparators,
signal generators, wave shaping circuits.
Digital Electronics: Combinational logic circuits, minimization
of Boolean functions; IC families (TTL, MOS, CMOS), arithmetic
circuits, multiplexer and decoders. Sequential circuits: flip-flops,
counters, shift registers. Schmitt trigger, timers, and multivibrators.
Analog switches, multiplexers, S/H circuits. Analog-to-digital
and digital-to-analog converters. Basics of computer organization
and architecture. 8-bit microprocessor (8085), applications,
memory, I/O interfacing, and microcontrollers.
Signals and Systems: Vectors and matrices; Fourier series;
Fourier transforms; Ordinary differential equations. Impulse
and frequency responses of first and second order systems.
Laplace transform and transfer function, convolution and correlation.
Amplitude and frequency modulations and demodulations. Discrete
time systems, difference equations, impulse and frequency
responses; Z-transforms and transfer functions; IIR and FIR
filters.
Electrical and Electronic Measurements: Measurement of R,
L and C; bridges and potentiometers. Measurement of voltage,
current, power, power factor, and energy; Instrument transformers;
Q meter, waveform analyzers. Digital volt-meters and multi-meters.
Time, phase and frequency measurements; Oscilloscope. Noise
and interference in instrumentation.
Control Systems & Process Control: Principles of feedback;
transfer function, signal flow graphs. Stability criteria,
Bode plots, root-loci, Routh and Nyquist criteria. Compensation
techniques; State space analysis. System components: mechanical,
hydraulic, pneumatic, electrical and electronic; Servos and
synchros; Stepper motors. On-off, cascade, P, PI, PID and
feed-forward controls. Controller tuning and general frequency
response.
Analytical, Optical and Biomedical Instrumentation: Principles
of spectrometry, UV, visible, IR mass spectrometry, X-ray
methods; nuclear radiation measurements, gas, solid and semi
conductor lasers and their characteristics, interferometers,
basics of fibre optics, transducers in biomedical applications,
cardiovascular system measurements, instrumentation for clinical
laboratory.
IT - INFORMATION TECHNOLOGY
ENGINEERING MATHEMATICS
Mathematical Logic: Propositional Logic; First Order Logic.
Probability: Conditional Probability; Mean, Median, Mode and
Standard Deviation; Random Variables; Distributions; uniform,
normal, exponential, Poisson, Binomial.
Set Theory & Algebra: Sets; Relations; Functions; Groups;
Partial Orders; Lattice; Boolean Algebra.
Combinatorics: Permutations; Combinations; Counting; Summation;
generating functions; recurrence relations; asymptotics.
Graph Theory: Connectivity; spanning trees; Cut vertices &
edges; covering; matching; independent sets; Colouring; Planarity;
Isomorphism.
Linear Algebra: Algebra of matrices, determinants, systems
of linear equations, Eigen values and Eigen vectors.
Numerical Methods: LU decomposition for systems of linear
equations; numerical solutions of non linear algebraic equations
by Secant, Bisection and Newton-Raphson Methods; Numerical
integration by trapezoidal and Simpson's rules.
Calculus: Limit, Continuity & differentiability, Mean
value Theorems, Theorems of integral calculus, evaluation
of definite & improper integrals, Partial derivatives,
Total derivatives, maxima & minima.
FORMAL LANGUAGES AND AUTOMATA
Regular Languages: finite automata, regular expressions, regular
grammar.
Context free languages: push down automata, context free grammars
COMPUTER HARDWARE
Digital Logic: Logic functions, minimization, design and synthesis
of combinatorial and sequential circuits, number representation
and computer arithmetic (fixed and floating point)
Computer organization: Machine instructions and addressing
modes, ALU and data path, hardwired and microprogrammed control,
memory interface, I/O interface (interrupt and DMA mode),
serial communication interface, instruction pipelining, cache,
main and secondary storage
SOFTWARE SYSTEMS
Data structures and Algorithms: the notion of abstract data
types, stack, queue, list, set, string, tree, binary search
tree, heap, graph, tree and graph traversals, connected components,
spanning trees, shortest paths, hashing, sorting, searching,
design techniques (greedy, dynamic, divide and conquer), asymptotic
analysis (best, worst, average cases) of time and space, upper
and lower bounds, intractability
Programming Methodology: C programming, program control (iteration,
recursion, functions), scope, binding, parameter passing,
elementary concepts of object oriented programming
Operating Systems (in the context of Unix): classical concepts
(concurrency, synchronization, deadlock), processes, threads
and interprocess communication, CPU scheduling, memory management,
file systems, I/O systems, protection and security
Information Systems and Software Engineering: information
gathering, requirement and feasibility analysis, data flow
diagrams, process specifications, input/output design, process
life cycle, planning and managing the project, design, coding,
testing, implementation, maintenance.
Databases: relational model, database design, integrity constraints,
normal forms, query languages (SQL), file structures (sequential,
indexed), b-trees, transaction and concurrency control
Data Communication: data encoding and transmission, data link
control, multiplexing, packet switching, LAN architecture,
LAN systems (Ethernet, token ring), Network devices: switches,
gateways, routers
Networks: ISO/OSI stack, sliding window protocols, routing
protocols, TCP/UDP, application layer protocols & systems
(http, smtp, dns, ftp), network security
Web technologies: three tier web based architecture; JSP,
ASP, J2EE, .NET systems; html, XML
MA - MATHEMATICS
Linear Algebra: Finite dimensional vector spaces. Linear transformations
and their matrix representations, rank; systems of linear
equations, eigenvalues and eigenvectors, minimal polynomial,
Cayley-Hamilton theorem, diagonalisation, Hermitian, Skew-Hermitian
and unitary matrices. Finite dimensional inner product spaces,
self-adjoint and Normal linear operators, spectral theorem,
Quadratic forms.
Complex Analysis: Analytic functions, conformal mappings,
bilinear transformations, complex integration: Cauchy's integral
theorem and formula, Liouville's theorem, maximum modulus
principle, Taylor and Laurent's series, residue theorem and
applications for evaluating real integrals.
Real Analysis: Sequences and series of functions, uniform
convergence, power series, Fourier series, functions of several
variables, maxima, minima, multiple integrals, line, surface
and volume integrals, theorems of Green, Stokes and Gauss;
metric spaces, completeness, Weierstrass approximation theorem,
compactness. Lebesgue measure, measurable functions; Lebesgue
integral, Fatou's lemma, dominated convergence theorem.
Ordinary Differential Equations: First order ordinary differential
equations, existence and uniqueness theorems, systems of linear
first order ordinary differential equations, linear ordinary
differential equations of higher order with constant coefficients;
linear second order ordinary differential equations with variable
coefficients, method of Laplace transforms for solving ordinary
differential equations, series solutions; Legendre and Bessel
functions and their orthogonality, Sturm Liouville system,
Greeen's functions.
Algebra: Normal subgroups and homomorphisms theorems, automorphisms.
Group actions, sylow's theorems and their applications groups
of order less than or equal to 20, Finite p-groups. Euclidean
domains, Principal ideal domains and unique factorizations
domains. Prime ideals and maximal ideals in commutative rings.
Functional Analysis: Banach spaces, Hahn-Banach theorems,
open mapping and closed graph theorems, principle of uniform
boundedness; Hilbert spaces, orthonormal sets, Riesz representation
theorem, self-adjoint, unitary and normal linear operators
on Hilbert Spaces.
Numerical Analysis: Numerical solution of algebraic and transcendental
equations; bisection, secant method, Newton-Raphson method,
fixed point iteration, interpolation: existence and error
of polynomial interpolation, Lagrange, Newton, Hermite(osculatory)interpolations;
numerical differentiation and integration, Trapezoidal and
Simpson rules; Gaussian quadrature; (Gauss-Legendre and Gauss-Chebyshev),
method of undetermined parameters, least square and orthonormal
polynomial approximation; numerical solution of systems of
linear equations: direct and iterative methods, (Jacobi Gauss-Seidel
and SOR) with convergence; matrix eigenvalue problems: Jacobi
and Given's methods, numerical solution of ordinary differential
equations: initial value problems, Taylor series method, Runge-Kutta
methods, predictor-corrector methods; convergence and stability.
Partial Differential Equations: Linear and quasilinear first
order partial differential equations, method of characteristics;
second order linear equations in two variables and their classification;
Cauchy, Dirichlet and Neumann problems, Green's functions;
solutions of Laplace, wave and diffusion equations in two
variables Fourier series and transform methods of solutions
of the above equations and applications to physical problems.
Mechanics: Forces in three dimensions, Poinsot central axis,
virtual work, Lagrange's equations for holonomic systems,
theory of small oscillations, Hamiltonian equations;
Topology: Basic concepts of topology, product topology, connectedness,
compactness, countability and separation axioms, Urysohn's
Lemma, Tietze extension theorem, metrization theorems, Tychonoff
theorem on compactness of product spaces.
Probability and Statistics: Probability space, conditional
probability, Bayes' theorem, independence, Random variables,
joint and conditional distributions, standard probability
distributions and their properties, expectation, conditional
expectation, moments. Weak and strong law of large numbers,
central limit theorem. Sampling distributions, UMVU estimators,
sufficiency and consistency, maximum likelihood estimators.
Testing of hypotheses, Neyman-Pearson tests, monotone likelihood
ratio, likelihood ratio tests, standard parametric tests based
on normal, X2 ,t, F-distributions. Linear regression and test
for linearity of regression. Interval estimation.
Linear Programming: Linear programming problem and its formulation,
convex sets their properties, graphical method, basic feasible
solution, simplex method, big-M and two phase methods, infeasible
and unbounded LPP's, alternate optima. Dual problem and duality
theorems, dual simplex method and its application in post
optimality analysis, interpretation of dual variables. Balanced
and unbalanced transportation problems, unimodular property
and u-v method for solving transportation problems. Hungarian
method for solving assignment problems.
Calculus of Variations and Integral Equations: Variational
problems with fixed boundaries; sufficient conditions for
extremum, Linear integral equations of Fredholm and Volterra
type, their iterative solutions. Fredholm alternative.
ME - MECHANICAL ENGINEERING
ENGINEERING MATHEMATICS
Linear Algebra: Matrix algebra, Systems of linear equations,
Eigen values and eigenvectors.
Calculus: Functions of single variable, Limit, continuity
and differentiability, Mean value theorems, Evaluation of
definite and improper integrals, Partial derivatives, Total
derivative, Maxima and minima, Gradient, Divergence and Curl,
Vector identities, Directional derivatives, Line, Surface
and Volume integrals, Stokes, Gauss and Green's theorems.
Differential equations: First order equations (linear and
nonlinear), Higher order linear differential equations with
constant coefficients, Cauchy's and Euler's equations, Initial
and boundary value problems, Laplace transforms, Solutions
of one dimensional heat and wave equations and Laplace equation.
Complex variables: Analytic functions, Cauchy's integral theorem,
Taylor and Laurent series.
Probability and Statistics: Definitions of probability and
sampling theorems, Conditional probability, Mean, median,
mode and standard deviation, Random variables, Poisson, Normal
and Binomial distributions.
Numerical Methods: Numerical solutions of linear and non-linear
algebraic equations Integration by trapezoidal and Simpson's
rule, single and multi-step methods for differential equations.
APPLIED MECHANICS AND DESIGN
Engineering Mechanics: Equivalent force systems, free-body
concepts, equations of equilibrium, trusses and frames, virtual
work and minimum potential energy. Kinematics and dynamics
of particles and rigid bodies, impulse and momentum (linear
and angular), energy methods, central force motion.
Strength of Materials: Stress and strain, stress-strain relationship
and elastic constants, Mohr's circle for plane stress and
plane strain, shear force and bending moment diagrams, bending
and shear stresses, deflection of beams, torsion of circular
shafts, thin and thick cylinders, Euler's theory of columns,
strain energy methods, thermal stresses.
Theory of Machines: Displacement, velocity and acceleration,
analysis of plane mechanisms, dynamic analysis of slider-crank
mechanism, planar cams and followers, gear tooth profiles,
kinematics of gears, governors and flywheels, balancing of
reciprocating and rotating masses.
Vibrations: Free and forced vibration of single degree freedom
systems, effect of damping, vibration isolation, resonance,
critical speed of rotors.
Design of Machine Elements: Design for static and dynamic
loading, failure theories, fatigue strength; design of bolted,
riveted and welded joints; design of shafts and keys; design
of spur gears, rolling and sliding contact bearings; brakes
and clutches; belt, rope and chain drives.
FLUID MECHANICS AND THERMAL SCIENCES
Fluid Mechanics: Fluid properties, fluid statics, manometry,
buoyancy; control-volume analysis of mass, momentum and energy;
fluid acceleration; differential equations of continuity and
momentum; Bernoulli's equation; viscous flow of incompressible
fluids; boundary layer; elementary turbulent flow; flow through
pipes, head losses in pipes, bends etc.
Heat-Transfer: Modes of heat transfer; one dimensional heat
conduction, resistance concept, electrical analogy, unsteady
heat conduction, fins; dimensionless parameters in free and
forced convective heat transfer, various correlations for
heat transfer in flow over flat plates and through pipes;
thermal boundary layer; effect of turbulence; radiative heat
transfer, black and grey surfaces, shape factors, network
analysis; heat exchanger performance, LMTD and NTU methods.
Thermodynamics: Zeroth, First and Second laws of thermodynamics;
thermodynamic system and processes; irreversibility and availability;
behaviour of ideal and real gases, properties of pure substances,
calculation of work and heat in ideal processes; analysis
of thermodynamic cycles related to energy conversion; Carnot,
Rankine, Otto, Diesel, Brayton and vapour compression cycles.
Power Plant Engineering: Steam generators; steam power cycles;
steam turbines; impulse and reaction principles, velocity
diagrams, pressure and velocity compounding; reheating and
reheat factor; condensers and feed heaters.
I.C. Engines: Requirements and suitability of fuels in IC
engines, fuel ratings, fuel-air mixture requirements; normal
combustion in SI and CI engines; engine performance calculations.
Refrigeration and air-conditioning: Refrigerant compressors,
expansion devices, condensers and evaporators; properties
of moist air, psychrometric chart, basic psychometric processes.
Turbomachinery: Components of gas turbines; compression processes,
centrifugal and axial flow compressors; axial flow turbines,
elementary theory; hydraulic turbines; Euler-turbine equation;
specific speed, Pelton-wheel, Francis and Kaplan turbines;
centrifugal pumps.
MANUFACTURING AND INDUSTRIAL ENGINEERING
Engineering Materials: Structure and properties of engineering
materials and their applications, heat treatment.
Metal Casting: Casting processes (expendable and non-expendable)
-pattern, moulds and cores, heating and pouring, solidification
and cooling, gating design, design considerations, defects.
Forming Processes: Stress-strain diagrams for ductile and
brittle material, Plastic deformation and yield criteria,
fundamentals of hot and cold working processes, Bulk metal
forming processes (forging, rolling, extrusion, drawing),
sheet metal working processes (punching, blanking, bending,
deep drawing, coining, spinning, load estimation using homogeneous
deformation methods, defects). processing of powder metals-
atomization, compaction, sintering, secondary and finishing
operations. forming and shaping of plastics- extrusion, injection
moulding.
Joining Processes: Physics of welding, fusion and non-fusion
welding processes, brazing and soldering, adhesive bonding,
design considerations in welding, weld quality defects.
Machining and Machine Tool Operations: Mechanics of machining,
single and multi-point cutting tools, tool geometry and materials,
tool life and wear, cutting fluids, machinability, economics
of machining, non-traditional machining processes.
Metrology and Inspection: Limits, fits and tolerances, linear
and angular measurements, comparators, gauge design, interferometry,
form and finish measurement, measurement of screw threads,
alignment and testing methods.
Tool Engineering: Principles of work holding, design of jigs
and fixtures.
Computer Integrated Manufacturing: Basic concepts of CAD,
CAM and their integration tools.
Manufacturing Analysis: Part-print analysis, tolerance analysis
in manufacturing and assembly, time and cost analysis.
Work-Study: Method study, work measurement, time study, work
sampling, job evaluation, merit rating.
Production Planning and Control: Forecasting models, aggregate
production planning, master scheduling, materials requirements
planning.
Inventory Control: Deterministic and probabilistic models,
safety stock inventory control systems.
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