**GATE Mechanical Engineering 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.

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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, behavior 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.

*Turbo machinery*: 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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