GATE MECHANICAL ENGINEERING SYLLABUS 

1)Engineering Mathematics

LINEAR ALGEBRA 

Linear equations, Matrix algebra, eigenvalues and eigenvectors.

DIFFERENTIAL EQUATIONS 

Linear and nonlinear, Euler-Cauchy equation; higher-order linear differential equations with constant coefficients, initial and boundary value problems; solutions of heat, wave and Laplace's equations; Laplace transforms.

CALCULUS 

Evaluation of definite and improper integrals; Functions of single variable, limit, continuity and differentiability, mean value theorem, indeterminate forms; double and triple integrals; total derivative, partial derivatives, maxima and minima, Taylor series (in one and two variables), Fourier series; divergence and curl, gradient, vector identities, line, directional derivatives, surface and volume integrals, and Green’s theorems and applications of Gauss, Stoke.

PROBABILITY AND STATISTICS 

Probability, conditional probability; sampling theorems; median, mean, mode and standard deviation; binomial, random variables, normal and Poisson distributions.

NUMERICAL METHODS 

Integration by trapezoidal and Simpson’s rules; - Numerical solutions of linear and non-linear algebraic equations; single & multi-step for differential 

COMPLEX VARIABLES 

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

2) APPLIED MECHANICS AND DESIGN 

MECHANICS OF MATERIAL 

Elastic constants, Stress and strain, Poisson's ratio, thin cylinders, Mohr’s circle for plane stress and plane strain, shear force and bending moment diagrams, deflection of beams, bending and shear stresses, torsion of circular shafts, energy methods, Euler’s theory of columns, thermal stresses, testing of materials with universal testing machine, strain gauges and rosettes, testing of hardness and impact strength.

ENGINEERING MECHANICS 

Trusses and frames; Free body diagrams and equilibrium, virtual work; impulse and momentum (linear and angular), kinematics and dynamics of particles & of rigid bodies in plane motion and energy formulations, collisions.

MECHANICS OF MATERIAL

 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.

 VIBRATION

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 SN 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 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. 

MATERIAL,MANUFCTURING 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 OPERATION

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-INTEGERATED 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.