Gate Syllabus
Gate Syllabus
Gate Syllabus
Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
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.
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.
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FLUID MECHANICS AND THERMAL SCIENCE
Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy, 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
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, StefanBoltzmann law, Wien’s displacement law, black and grey surfaces, view
factors, radiation network analysis.
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.
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,
design of jigs and fixtures.
Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements;
comparators; gauge design; interferometry; form and finish measurement; alignment and
testing methods; tolerance analysis in manufacturing and assembly.