__
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, 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.

__
Applies 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, including impulse and momentum
(linear and angular) and energy formulations; impact.

**
Strength of Materials: **
Stress and strain, stress-strain relationship and elastic
constants, 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; strain energy
methods; thermal stresses.

**
Theory of Machines: **
Displacement, velocity and acceleration analysis of plane
mechanisms; dynamic analysis of slider-crank mechanism; gear
trains; flywheels.

**
Vibrations: **
Free and forced vibration of single degree of freedom
systems; effect of damping; vibration isolation; resonance,
critical speeds of shafts.

**
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, spur gears, rolling and sliding
contact bearings, brakes and clutches.

__
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; Carnot cycle.
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.

**
Applications: **
Power Engineering:
Steam Tables, Rankine, Brayton cycles with regeneration and
reheat. I.C. Engines: air-standard Otto, Diesel cycles.
Refrigeration and air-conditioning: Vapour refrigeration
cycle, heat pumps, gas refrigeration, Reverse Brayton cycle;
moist air: psychrometric chart, basic psychrometric
processes. Turbomachinery*: *Pelton-wheel, Francis and
Kaplan turbines — impulse and reaction principles, velocity
diagrams.

__
Manufacturing and Industrial Engineering:__

**
Engineering Materials**:
Structure and properties of engineering materials, heat
treatment, stressstrain diagrams for engineering materials.

**
Metal Casting: **
Design of patterns, moulds and cores; solidification and
cooling; riser and gating design, design considerations.

**
Forming: **
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.

**
Joining: **
Physics of welding, brazing and soldering; adhesive bonding;
design considerations in welding.

**
Machining and Machine Tool Operations: **
Mechanics of machining, 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, principles of 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 and probabilistic models; safety stock
inventory control systems.

**
Operations Research: **
Linear programming, simplex and duplex method,
transportation, assignment, network flow models, simple
queuing models, PERT and CPM.