SECTION A. ENGINEERING MATHEMATICS (Compulsory)
Linear Algebra: Algebra of matrices, inverse, rank, system of linear
equations, symmetric, skewsymmetric and orthogonal matrices. Hermitian,
skew-Hermitian and unitary matrices. eigenvalues and eigenvectors,
diagonalisation of matrices, Cayley-Hamilton Theorem.
Calculus: Functions of single variable, limit, continuity and
differentiability, Mean value theorems, Indeterminate 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, Half range sine and cosine series.
Complex variable: Analytic functions, Cauchy-Riemann equations, Application
in solving potential problems, Line integral, Cauchy's integral theorem and
integral formula (without proof), Taylor's and Laurent' series, Residue theorem
(without proof) and its applications.
Vector Calculus: Gradient, divergence and curl, vector identities,
directional derivatives, line, surface and volume integrals, Stokes, Gauss and
Green's theorems (without proofs) applications.
Ordinary Differential Equations: First order equation (linear and nonlinear),
Second order linear differential equations with variable coefficients, Variation
of parameters method, higher order linear differential equations with constant
coefficients, Cauchy- Euler's equations, power series solutions, Legendre
polynomials and Bessel's functions of the first kind and their properties.
Partial Differential Equations: Separation of variables method, Laplace
equation, solutions of one dimensional heat and wave equations.
Probability and Statistics: Definitions of probability and simple theorems,
conditional probability, Bayes Theorem, random variables, discrete and
continuous distributions, Binomial, Poisson, and normal distributions,
correlation and linear regression.
Numerical Methods: Solution of a system of linear equations by L-U
decomposition, Gauss- Jordan and Gauss-Seidel Methods, Newton’s interpolation
formulae, Solution of a polynomial and a transcendental equation by
Newton-Raphson method, numerical integration by trapezoidal rule, Simpson’s
rule and Gaussian quadrature, numerical solutions of first order differential
equation by Euler’s method and 4th order Runge-Kutta 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; Solutions of non linear equations of one
variable 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 quadtrature 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.
Computer System Concepts: Representation of fixed- and floating-point
numbers; Elementary concepts and terminology of basic building blocks of a
computer system and system software.
Fortran: Fortran-90 for Numerical Computation: Basic data types including
complex numbers; Arrays; Assignment statements; Structured Programming
Constructs: Loops, Conditional execution, iteration and recursion; Functions and
subroutines; Structured programming practices.
C language: Basic data types including pointers; Assignments statements;
Control statements; Dynamic memory allocation; Functions and procedures;
Parameter passing mechanisms; Structured programming practices.
SECTION C. ELECTRICAL SCIENCES
Electric Circuits: Ideal voltage and current sources; RLC circuits, steady
state and transient analysis of DC circuits, network theorems; single phase AC
circuits, resonance and three phase circuits.
Magnetic Circuits: MMF and flux, and their relationship with voltage and
current; principle of operation of transformer, equivalent circuit of a
practical transformer, efficiency and regulation of transformer.
Electric Machines: Principle of operation, characteristics and performance
equations of DC machines; principle of operation, equivalent circuit of
three-phase Induction machin
Electronic Circuits: Characteristics of p-n junction diode, Zener diode,
bi-polar junction transistor (BJT) and junction field effect transistor (JFET);
structure of MOSFET, its characteristics and operation; rectifiers, filters, and
regulated power supply, transistor biasing circuits, operational amplifiers,
linear applications of operational amplifier, oscillators (tuned and phase shift
Digital circuits: Number systems, Boolean algebra, logic gates, combinational
and sequential circuits, Flip-Flops (RS, JK, D and T), Counters.
Measuring Instruments: Cathode Ray oscilloscope, D/A and A/D converters.
SECTION D. FLUID MECHANICS
Fluid Properties: Relation between stress and strain rate for Newtonian
Hydrostatics: Buoyancy, manometry, forces on submerged bodies.
Eulerian and Lagrangian description of fluid motion, concept of local and
convective accelerations, steady and unsteady flows, control volume analysis for
mass, momentum and energy.
Differential equations of mass and momentum (Euler equation), Bernoulli’s
equation and its applications.
Concept of fluid rotation, vorticity, stream function and potential function.
Potential flow: elementary flow fields and principle of superposition,
potential flow past a circular cylinder.
Dimensional analysis: Concept of geometric, kinematic and dynamic similarity,
importance of non-dimensional numbers.
Fully-developed pipe flow, laminar and turbulent flows, friction factor,
Darcy-Weisbach relation. Qualitative ideas of boundary layer and separation,
streamlined and bluff bodies, drag and lift forces.
Basic ideas of flow measurement using venturimeter, pitot-static tube and
SECTION E. MATERIALS SCIENCEM
Structure: Atomic structure and bonding in materials. Crystal structure of
materials, crystal systems, unit cells and space lattices, determination of
structures of simple crystals by x-ray diffraction, miller indices of planes and
directions, packing geometry in metallic, ionic and covalent solids. Concept of
amorphous, single and polycrystalline structures and their effect on properties
of materials. Crystal growth techniques. Imperfections in crystalline solids and
their role in influencing various properties.
Diffusion: Fick’s laws and application of diffusion in sintering, doping of
semiconductors and surface hardening of metals.
Metals and Alloys: Solid solutions, solubility limit, phase rule, binary
phase diagrams, intermediate phases, intermetallic compounds, iron-iron carbide
phase diagram, heat treatment of steels, cold, hot working of metals, recovery,
recrystallization and grain growth. Microstrcture, properties and applications
of ferrous and non-ferrous alloys.
Ceramics: Structure, properties, processing and applications of traditional
and advanced ceramics.
Polymers: Classification, polymerization, structure and properties, additives
for polymer products, processing and applications.
Composites: Properties and applications of various composites.
Advanced Materials and Tools: Smart materials, exhibiting ferroelectric,
piezoelectric, optoelectric, semiconducting behavior, lasers and optical fibers,
photoconductivity and superconductivity, nanomaterials – synthesis, properties
and applications, biomaterials, superalloys, shape memory alloys. Materials
characterization techniques such as, scanning electron microscopy, transmission
electron microscopy, atomic force microscopy, scanning tunneling microscopy,
atomic absorption spectroscopy, differential scanning calorimetry.
Mechanical Properties: stress-strain diagrams of metallic, ceramic and
polymeric materials, modulus of elasticity, yield strength, tensile strength,
toughness, elongation, plastic deformation, viscoelasticity, hardness, impact
strength, creep, fatigue, ductile and brittle fracture.
Thermal Properties: Heat capacity, thermal conductivity, thermal expansion of
Electronic Properties: Concept of energy band diagram for materials -
conductors, semiconductors and insulators, electrical conductivity – effect of
temperature on conductility, intrinsic and extrinsic semiconductors, dielectric
Optical Properties: Reflection, refraction, absorption and transmission of
electromagnetic radiation in solids.
Magnetic Properties: Origin of magnetism in metallic and ceramic materials,
paramagnetism, diamagnetism, antiferro magnetism, ferromagnetism,
ferrimagnetism, magnetic hysterisis.
Environmental Degradation: Corrosion and oxidation of materials, prevention.
SECTION F. SOLID MECHANICS
Equivalent force systems; free-body diagrams; equilibrium equations; analysis
of determinate 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
Stresses and strains; principal stresses and strains; Mohr's circle;
generalized Hooke's Law; thermal strain; theories of failure.
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.
Free vibration of single degree of freedom systems.
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 vapor 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. Thermodynamic cycles: Carnot vapor power
cycle, Ideal Rankine cycle, Rankine Reheat cycle, Air standard Otto cycle, Air
standard Diesel cycle, Air-standard Brayton cycle, Vapor-compression
Ideal Gas Mixtures: Dalton’s and Amagat’s laws, calculations of
properties, air-water vapor mixtures and simple thermodynamic processes