Section 1: Engineering Mathematics
Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues, and
eigenvectors.
Calculus: Functions of a single variable, limit, continuity, and
differentiability, mean value theorems, indeterminate forms, evaluation of
definite and improper integrals, double and triple integrals, partial
derivatives, total derivative, Taylor series (in one and two variables), maxima
and minima, Fourier series, gradient, divergence and curl, vector identities,
directional derivatives, line, surface and volume integrals, applications of
Gauss, Stokes, and Green’s Theorems.
Differential equations: First order equations (linear and nonlinear),
higher-order linear differential equations with constant coefficients,
Euler-Cauchy equation, initial and boundary value problems, Laplace transforms,
solutions of heat, wave, and Laplace's equations. Complex variables: Analytic
functions, Cauchy-Riemann equations, Cauchy’s integral theorem, and integral
formula, Taylor, and Laurent series.
Probability and Statistics: Definitions of probability, sampling theorems,
conditional probability, mean, median, mode and standard deviation, random
variables, binomial, Poisson, and Normal Distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations,
integration by trapezoidal and Simpson’s rules, single and multi-step methods
for differential equations.
Section 2: Applied Mechanics and Design
Engineering Mechanics: Free-body diagrams and equilibrium, friction and
its applications including rolling friction, belt-pulley, brakes, clutches,
screw jack, wedge, vehicles, etc., trusses and frames, virtual work,
kinematics, and dynamics of rigid bodies in plane motion, impulse, and momentum
(linear and angular) and energy formulations, Lagrange’s equation.
Mechanics of Materials: Stress and strain, elastic constants, Poisson's
ratio, Mohr’s circle for plane stress and plane strain, thin cylinders, shear
force and bending moment diagrams, bending and shear stresses, the concept of
shear centre, deflection of beams, torsion of circular shafts, Euler’s theory
of columns, energy methods, thermal stresses, strain gauges and rosettes,
testing of materials with the universal testing machine, testing of hardness
and impact strength.
Theory of Machines: Displacement, velocity and acceleration analysis
of plane mechanisms, dynamic analysis of linkages, cams, gears and gear trains,
flywheels, and governors, balancing of reciprocating and rotating masses,
gyroscope.
Vibrations: Free and forced vibration of single degree of freedom systems, the
effect of damping, vibration isolation, resonance, critical speeds of shafts.
Machine Design: Design for static and dynamic loading, failure theories, fatigue
strength and S-N diagram, principles of the design of machine elements such as
bolted, riveted, and welded joints, shafts, gears, rolling, and sliding contact
bearings, brakes, and clutches, springs.
Section 3: Fluid Mechanics and Thermal Sciences
Fluid Mechanics: Fluid properties, fluid statics, forces on submerged bodies, stability
of floating bodies, control-volume analysis of mass, momentum, and energy,
fluid acceleration, differential equations of continuity and momentum,
Bernoulli’s equation, dimensional analysis, viscous flow of incompressible
fluids, boundary layer, elementary turbulent flow, flow through pipes, head
losses in pipes, bends, and fittings, basics of compressible fluid flow.
Heat-Transfer: Modes of heat transfer, one-dimensional heat conduction, resistance
concept, and electrical analogy, heat transfer through fins, unsteady heat
conduction, lumped parameter system, Heisler's charts, thermal boundary layer,
dimensionless parameters in free and forced convective heat transfer, heat
transfer correlations for flow over flat plates and through pipes, the effect
of turbulence, heat exchanger performance, LMTD and NTU methods, radiative heat
transfer, Stefan- Boltzmann law, Wien's displacement law, black and grey
surfaces, view factors, radiation network analysis.
Thermodynamics: Thermodynamic systems and processes, properties of pure substances,
the behavior of ideal and real gases, zeroth and first laws of thermodynamics,
calculation of work and heat in various processes, the second law of
thermodynamics, thermodynamic property charts and tables, availability and
irreversibility, thermodynamic relations.
Applications: Power Engineering: Air and gas compressors, vapour and gas power
cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto,
Diesel, and dual cycles.
Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump
cycles, properties of moist air, psychrometric chart, basic psychrometric
processes.
Turbomachinery: Impulse and reaction principles, velocity diagrams, Pelton-wheel,
Francis and Kaplan turbines, steam, and gas turbines.
Section 4: Materials, Manufacturing, and Industrial
Engineering
Engineering Materials: Structure and properties of engineering
materials, phase diagrams, heat treatment, stress-strain diagrams for
engineering materials.
Casting, Forming, and Joining Processes: Different types of castings, design of patterns,
moulds and cores, solidification and cooling, riser, and gating design. Plastic
deformation and yield criteria, fundamentals of hot and cold working processes,
load estimation for bulk (forging, rolling, extrusion, drawing) and sheet
(shearing, deep drawing, bending) metal forming processes, principles of powder
metallurgy. Principles of welding, brazing, soldering, and adhesive bonding.
Machining and Machine Tool Operations: Mechanics of machining, basic machine tools,
single and multi-point cutting tools, tool geometry and materials, tool life
and wear, the economics of machining, principles of non-traditional machining
processes, principles of work holding, jigs and fixtures, abrasive machining
processes, NC/CNC machines, and CNC programming.
Metrology and Inspection: Limits, fits and tolerances, linear and angular
measurements, comparators, interferometry, form and finish measurement,
alignment and testing methods, tolerance analysis in manufacturing and
assembly, concepts of the coordinate-measuring machine.
Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration
tools, additive manufacturing.
Production Planning and Control: Forecasting models, aggregate production
planning, scheduling, materials requirement planning, lean manufacturing.
Inventory Control: Deterministic models, safety stock inventory control systems.
Operations Research: Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT, and CPM.