Please share the syllabus of GATE Mechanical Engineering Exam.

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.