GATE ME syllabus 2026

Matrix algebra, systems of linear equations, eigen values and eigen vectors.

• 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.

• 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.

• Analytic functions
• Cauchy-Riemann equations
• Cauchy’s integral theorem and integral formula
• Taylor and Laurent series.

• Definitions of probability, sampling theorems, conditional probability
• mean, median, mode and standard deviation
• random variables, binomial, Poisson and normal distributions.

• Numerical solutions of linear and non-linear algebraic equations
• integration by trapezoidal and Simpson’s rules
• single and multi-step methods for differential equations.

• Free-body diagrams and equilibrium
• friction and its applications including rolling friction, belt-pulley, brakes, clutches, screw jack, wedge, vehicles, etc.
• trusses and frames
• virtual work
• kinematics and dynamics of rigid bodies in plane motion
• impulse and momentum (linear and angular) and energy formulations
• Lagrange’s equation.

• 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
• 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 with universal testing machine
• testing of hardness and impact strength.

• Displacement, velocity and acceleration analysis of plane mechanisms
• dynamic analysis of links
• cams
• gears and gear trains
• flywheels and governors
• balancing of reciprocating and rotating mass
• gyroscope.

• Free and forced vibration of single degree of freedom systems, effect of damping
• vibration isolation
• resonance
• critical speeds of shafts.

• 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.

• Fluid properties
• fluid statics, forces on submerged bodies, stability of float 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
• basics of compressible fluid flow.

• 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.

• 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.

• 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
• steam and gas turbines.

Structure and properties of engineering materials, phase diagrams, heat treatment, stress-strain diagrams for engineering materials.

• 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.

• 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.

• 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 machine (CMM).

• Basic concepts of CAD/CAM and their integration tools
• additive manufacturing.

• Forecasting models, aggregate production planning, scheduling, materials requirement planning
• lean manufacturing.

• Deterministic models
• safety stock inventory control systems.

Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.

Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech.

Words, idioms, and phrases in context.

Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables.

Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series. Mensuration and geometry. Elementary statistics and probability.

Deduction and induction, Analogy, Numerical relations and reasoning.

• Translation, rotation, scale, mirroring, assembling, and grouping
• paper folding, cutting, and patterns in 2 and 3 dimensions.