GATE 2027 Mechanical Engineering (ME) Syllabus OUT: Download PDF, Important Topics

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 contour
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 ordinary differential equations

Engineering Mechanics

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

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.

Mechanics of Materials

Stress and strain, elastic constants and their relationships; stress and strain
components transformations in 2D; Mohr’s circle for plane stress and plane strain; thin-walled pressure vessels; 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; Mechanical properties of materials, toughness, hardness, impact strength

Vibrations

Free and forced vibration of linear systems with single and two degrees of freedom, damping
estimation and effects; vibration isolation, transmissibility ratio; resonance; critical speeds of shafts; Control system, PID controller, transfer function.

Machine Design

Design for static and dynamic loading; failure theories; fatigue strength and the S-N
diagram; principles and design of machine elements such as bolted, riveted and welded joints; shafts, gears, belt drives, rolling and sliding contact bearings, brakes and clutches, springs

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; concept of velocity potential; 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; One dimensional high speed compressible fluid flow; flow through converging and converging-diverging nozzles.

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, thermal boundary layer, dimensionless parameters in free and forced convective heat transfer, heat transfer correlations for flow
over flat plates and through pipes; boiling and condensation; 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, first and second laws of thermodynamics, calculation of work, heat, energy changes and entropy changes in various processes; application of first and second laws for analysis of closed and open systems; thermodynamic property charts and tables, availability and irreversibility; thermodynamic relations

Applications

Power Engineering: vapour and gas power cycles, concepts of regeneration and reheat; I.C. Engines: Air-standard Otto, Diesel and dual cycles; Basics of Combustion: Air- Fuel Ratio, Equivalence, Ratio; 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, Air and gas compressors, pumps and pump characteristics.

Engineering Materials

 Crystal structure of common metals, phase diagrams, heat treatment; Properties and
applications of engineering materials - metals and alloys, polymers, composites and ceramics; Engineering and true stress-strain diagrams.

Casting, forming, and Joining Processes

Different types of casting processes; Patterns, moulds and core;
Solidification and cooling, riser and gating design, casting defects; Plastic deformation and yield criteria; Hot working and cold working; Principles of bulk forming and sheet forming processes and estimation of load in these processes; Fundamentals of powder metallurgy and its applications; Principles of welding, brazing, soldering; Solid-state welding processes, adhesive bonding; Non-destructive testing methods

Machining and Machine Tool Operations

 Basic machining operations and machine tools; Single-point and
multipoint cutting tools; Geometry of single-point turning tools - ASA and ORS systems; Mechanics of machining; Cutting tool materials, tool life and tool wear; Economics of machining; Abrasive machining processes; Principles and applications of non-traditional machining processes; Principles of work holding, jigs and fixtures.

Additive Manufacturing

Principles of different types of additive manufacturing processes for engineering
materials; Additively manufactured products – advantages, limitations, and applications

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; Principle of coordinate- measuring machine (CMM).

Computer-Integrated Manufacturing

Basic concepts of CAD/CAM and their integration tools; NC/CNC machines and CNC programming; Pneumatic, electro-pneumatic, and hydraulic actuators for automation; Programmable logic controllers.

Producing Planning and Control

Work study, Productivity, Forecasting models, Aggregate production
planning, Scheduling, Materials requirement planning, Six sigma, Lean manufacturing, Inventory Control – deterministic models, safety stock, inventory control systems, Quality and reliability concepts for product lifecycle analysis.

Operations Research

Linear programming, Simplex method, Transportation, Assignment, Network flow
models, Simple queuing models, PERT and CPM.