GATE Mechanical Engineering Syllabus and Exam Pattern

GATE Mechanical Engineering (ME) tests the core subjects of a mechanical engineering degree. This page lists the full syllabus; every other lesson in this track covers one part of it, with key concepts, formulas, a worked example and GATE-style questions.

Exam pattern

Syllabus

Section 1: Engineering Mathematics (see the Engineering Mathematics track)

• Linear algebra: matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
• Calculus: functions of one variable, limits, continuity, differentiability, mean value theorems, indeterminate forms, evaluation of definite and improper integrals, double and triple integrals, partial derivatives, total derivative, Taylor series, maxima and minima, gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, theorems of Stokes, Gauss and Green.
• Differential equations: first order equations (linear and non-linear), higher order linear equations with constant coefficients, Euler-Cauchy equation, initial and boundary value problems, Laplace transforms, solutions of the heat, wave and Laplace equations.
• Complex variables: analytic functions, Cauchy-Riemann equations, Cauchy's integral theorem and integral formula, Taylor and Laurent series.
• Probability and statistics: sampling theorems, conditional probability, mean, median, mode, 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, friction, trusses and frames, virtual work, kinematics and dynamics of rigid bodies in plane motion, impulse and momentum, energy methods, Lagrange's equation.
• Mechanics of materials: stress and strain, elastic constants, Poisson's ratio, Mohr's circle for plane stress and strain, thin cylinders, shear force and bending moment diagrams, bending and shear stresses, concept of shear centre, deflection of beams, torsion of circular shafts, Euler's theory of columns, energy methods, thermal stresses, strain gauges and rosettes, testing of materials (tensile, compression, hardness, impact).
• 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 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, 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 convection, heat transfer correlations, radiative heat transfer, black and grey surfaces, shape factors, network analysis, heat exchanger performance, LMTD and NTU methods.
• Thermodynamics: thermodynamic systems and processes, properties of pure substances, behaviour of ideal and real gases, zeroth and first laws, calculation of work and heat in various processes, second law, 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), IC 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, steam and gas 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, load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming, 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, jigs and fixtures, abrasive machining processes, NC/CNC machines and CNC programming.
• Metrology and inspection: limits, fits and tolerances, linear and angular measurements, comparators, interferometry, form and finish measurement, alignment and testing methods, tolerance analysis in manufacturing and assembly, concepts of coordinate measuring machines.
• Computer integrated manufacturing: basic concepts of CAD/CAM and their integration tools, additive manufacturing.
• Production planning and control: forecasting models, aggregate production planning, scheduling, materials requirement planning, lean manufacturing.
• 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.

How to use this track

Work through the lessons in order, then the Engineering Mathematics and General Aptitude tracks. Thermal sciences and applied mechanics together usually carry the largest share of the paper.