Section 1: Engineering Mathematics

Linear   Algebra:   Matrix   algebra,   systems   of  linear   equations,   eigenvalues  and eigenvectors.

Calculus:  Functions  of  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;  trusses  and  frames; virtual  work;  kinematics  and  dynamics  of  particles  and  of  rigid  bodies  in  plane motion;  impulse  and  momentum  (linear  and  angular)  and  energy  formulations, collisions.

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;  deflection  of  beams;  torsion  of circular  shafts;  Euler’s  theory  of  columns;  energy  methods;  thermal  stresses;  strain gauges and rosettes; testing of materials with 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, effect of damping; vibration isolation; resonance; critical speeds of shafts.

Machine  Design:  Design  for  static  and  dynamic  loading;  failure  theories;  fatigue strength and the 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,  manometry,  buoyancy,  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.

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, 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,   behaviour   of   ideal   and   real   gases;   zeroth   and   first   laws   of thermodynamics, calculation of work and heat in various processes; 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.

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; economics of machining; principles of non-traditional machining processes; principles of work holding, design of jigs and fixtures.

Metrology   and   Inspection:   Limits,   fits    and    tolerances;   linear   and   angular measurements;   comparators;   gauge   design;   interferometry;   form   and   finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly.

Computer   Integrated   Manufacturing:   Basic   concepts   of   CAD/CAM   and   their integration tools.

Production   Planning   and   Control:   Forecasting   models,   aggregate   production planning, scheduling, materials requirement planning.

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.