The syllabi of the sections of this paper
are as follows:
SECTION A. ENGINEERING MATHEMATICS
(Compulsory)
Linear Algebra : Determinates, algebra of
matrices, rank, inverse, system of linear
equations, symmetric, skew-symmetric and
orthogonal matrices. Hermitian, skew-hermitian
and unitary matrices. eigenvalues and
eigenvectors, diagonalisation of matrices,
Cayley-Hamiltonian, quadratic forms.
Calculus : Functions of single variables,
limit, continuity and differentiability,
Mean value theorems, Intermediate forms and
L'Hospital rule, Maxima and minima, Taylor's
series, Fundamental and mean value-theorems
of integral calculus. Evaluation of definite
and improper integrals, Beta and Gamma
functions, Functions of two variables,
limit, continuity, partial derivatives,
Euler's theorem for homogeneous functions,
total derivatives, maxima and minima,
Lagrange method of multipliers, double and
triple integrals and their applications,
sequence and series, tests for convergence,
power series, Fourier Series, Fourier
integrals.
Complex variable: Analytic functions,
Cauchy's integral theorem and integral
formula without proof. Taylor's and Laurent'
series, Residue theorem (without proof) with
application to the evaluation of real
integarls.
Vector Calculus: Gradient, divergence and
curl, vector identities, directional
derivatives, line, surface and volume
integrals, Stokes, Gauss and Green's
theorems (without proofs) with applications.
Ordinary Differential Equations: First order
equation (linear and nonlinear), higher
order linear differential equations with
constant coefficients, method of variation
of paramaters, Cauchy's and Euler's
equations, initial and boundary value
problems, power series solutions, Legendre
polynomials and Bessel's functions of the
first kind.
Partial Differential Equations: Variables
separable method, solutions of one
dimensional heat, wave and Laplace
equations.
Probability and Statistics: Definitions of
probability and simple theorems, conditional
probability, mean, mode and standard
deviation, random variables, discrete and
continuous distributions, Poisson, normal
and Binomial distribution, correlation and
regression
Numerical Methods: L-U decomposition for
systems of linear equations,Newton-Raphson
method, numerical integration(trapezoidal
and Simpson's rule), numerical methods for
first order differential equation (Euler
method)
SECTION B. COMPUTATIONAL SCIENCE
Numerical Methods: Truncation errors, round
off errors and their propagation;
Interpolation; Lagrange, Newton's forward,
backward and divided difference formulas,
least square curve fitting, solution of
non-linear equations of one variables using
bisection, false position, secant and Newton
Raphson methods; Rate of convergence of
these methods, general iterative methods.
Simple and multiple roots of polynomials.
Solutions of system of linear algebraic
equations using Gauss elimination methods,
Jacobi and Gauss-Seidel iterative methods
and their rate of convergence; ill
conditioned and well conditioned system.
eigen values and eigen vectors using power
methods. Numerical integration using
trapezoidal, Simpson's rule and other
quadrature formulas. Numerical
Differentiation. Solution of boundary value
problems. Solution of initial value problems
of ordinary differential equations using
Euler's method, predictor corrector and
Runge Kutta method.
Programming : Elementary concepts and
terminology of a computer system and system
software, Fortran77 and C programming.
Fortran : Program organization, arithmetic
statements, transfer of control, Do loops,
subscripted variables, functions and
subroutines.
C language : Basic data types and
declarations, flow of control- iterative
statement, conditional statement,
unconditional branching, arrays, functions
and procedures.
SECTION C. ELECTRICAL SCIENCES
Electric Circuits: Ideal voltage and current
sources; RLC circuits, steady state and
transient analysis of DC circuits, network
theorems; alternating currents and voltages,
single-phase AC circuits, resonance;
three-phase circuits.
Magnetic circuits: Mmf and flux, and their
relationship with voltage and current;
transformer, equivalent circuit of a
practical transformer, three-phase
transformer connections.
Electrical machines: Principle of operation,
characteristics, efficiency and regulation
of DC and synchronous machines; equivalent
circuit and performance of three-phase and
single-phase induction motors.
Electronic Circuits: Characteristics of p-n
junction diodes, zener diodes, bipolar
junction transistors (BJT) and junction
field effect transistors (JFET); MOSFET's
structure, characteristics, and operations;
rectifiers, filters, and regulated power
supplies; biasing circuits, different
configurations of transistor amplifiers,
class A, B and C of power amplifiers; linear
applications of operational amplifiers;
oscillators; tuned and phase shift types.
Digital circuits: Number systems, Boolean
algebra; logic gates, combinational
circuits, flip-flops (RS, JK, D and T)
counters.
Measuring instruments: Moving coil, moving
iron, and dynamometer type instruments;
shunts, instrument transformers, cathode ray
oscilloscopes; D/A and A/D converters.
SECTION D. FLUID MECHANICS
Fluid Properties: Relation between stress
and strain rate for Newtonian fluids
Hydrostatics, buoyancy, manometry
Concept of local and convective
accelerations; control volume analysis for
mass, momentum and energy conservation.
Differential equations of continuity and
momentum (Euler's equation of motion);
concept of fluid rotation, stream function,
potential function; Bernoulli's equation and
its applications.
Qualitative ideas of boundary layers and its
separation; streamlined and bluff bodies;
drag and lift forces.
Fully-developed pipe flow; laminar and
turbulent flows; friction factor; Darcy
Weisbach relation; Moody's friction chart;
losses in pipe fittings; flow measurements
using venturimeter and orifice plates.
Dimensional analysis; similitude and concept
of dynamic similarity; importance of
dimensionless numbers in model studies.
SECTION E. MATERIALS SCIENCE
Atomic structure and bonding in materials:
metals, ceramics and polymers.
Structure of materials: Crystal systems,
unit cells and space lattice; determination
of structures of simple crystals by X-ray
diffraction; Miller indices for planes and
directions. Packing geometry in metallic,
ionic and covalent solids.
Concept of amorphous, single and
polycrystalline structures and their effects
on properties of materials.
Imperfections in crystalline solids and
their role in influencing various
properties.
Fick´s laws of diffusion and applications
of diffusion in sintering, doping of
semiconductors and surface hardening of
metals.
Alloys: solid solution and solubility limit.
Binary phase diagram, intermediate phases
and intermetallic compounds; iron-iron
carbide phase diagram. Phase transformation
in steels. Cold and hot working of metals,
recovery, recrystallization and grain
growth.
Properties and applications of ferrous and
nonferrous alloys.
Structure, properties, processing and
applications of traditional and advanced
ceramics.
Polymers: classification, polymerization,
structure and properties, additives for
polymer products, processing and
application.
Composites: properties and application of
various composites.
Corrosion and environmental degradation of
materials (metals, ceramics and polymers).
Mechanical properties of materials:
Stress-strain diagrams of metallic, ceramic
and polymeric materials, modulus of
elasticity, yield strength, plastic
deformation and toughness, tensile strength
and elongation at break; viscoelasticity,
hardness, impact strength. ductile and
brittle fracture. creep and fatigue
properties of materials.
Heat capacity, thermal conductivity, thermal
expansion of materials.
Concept of energy band diagram for
materials; conductors, semiconductors and
insulators in terms of energy bands.
Electrical conductivity, effect of
temperature on conductivity in materials,
intrinsic and extrinsic semiconductors,
dielectric properties of materials.
Refraction, reflection, absorption and
transmission of electromagnetic radiation in
solids.
Origin of magnetism in metallic and ceramic
materials, paramagnetism, diamagnetism,
antiferromagnetism, ferromagnetism,
ferrimagnetism in materials and magnetic
hysteresis.
Advanced materials: Smart materials
exhibiting ferroelectric, piezoelectric,
optoelectronic, semiconducting behaviour;
lasers and optical fibers; photoconductivity
and superconductivity in materials.
SECTION F. SOLID MECHANICS
Equivalent force systems; free-body
diagrams; equilibrium equations; analysis of
determinate and indeterminate trusses and
frames; friction.
Simple relative motion of particles; force
as function of position, time and speed;
force acting on a body in motion; laws of
motion; law of conservation of energy; law
of conservation of momentum
Stresses and strains; principal stresses and
strains; Mohr's circle; generalized Hooke's
Law; equilibrium equations; compatibility
conditions; yield criteria.
Axial, shear and bending moment diagrams;
axial, shear and bending stresses;
deflection (for symmetric bending); torsion
in circular shafts; thin cylinders; energy
methods (Castigliano's Theorems); Euler
buckling.
SECTION G. THERMODYNAMICS
Basic Concepts: Continuum, macroscopic
approach, thermodynamic system (closed and
open or control volume); thermodynamic
properties and equilibrium; state of a
system, state diagram, path and process;
different modes of work; Zeroth law of
thermodynamics; concept of temperature;
heat.
First Law of Thermodynamics: Energy,
enthalpy, specific heats, first law applied
to systems and control volumes, steady and
unsteady flow analysis.
Second Law of Thermodynamics: Kelvin-Planck
and Clausius statements, reversible and
irreversible processes, Carnot theorems,
thermodynamic temperature scale, Clausius
inequality and concept of entropy, principle
of increase of entropy; availability and
irreversibility.
Properties of Pure Substances: Thermodynamic
properties of pure substances in solid,
liquid and vapour phases, P-V-T behaviour of
simple compressible substances, phase rule,
thermodynamic property tables and charts,
ideal and real gases, equations of state,
compressibility chart.
Thermodynamic Relations: T-ds relations,
Maxwell equations, Joule-Thomson
coefficient, coefficient of volume
expansion, adiabatic and isothermal
compressibilities, Clapeyron equation.
Ideal Gas Mixtures: Dalton's and Amagat's
laws, calculations of properties, air-water
vapour mixtures.
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