GATE Mechanical Engineering (ME) syllabus:
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.
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