**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.

**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:** 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.

**Engineering Materials:** Structure and properties
of engineering materials, heat treatment, stress-strain 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;

**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.