GATE 2025 Syllabus for Mechanical Engineering

ME Mechanical Engineering
Section 1: Engineering Mathematics
Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors.

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; 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.

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; 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.

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, 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; basics of compressible fluid flow.

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. 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 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, 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 machine
(CMM).

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.