GATE 2015 Mechanical Engineering Syllabus:
Linear Algebra: Matrix Systems; Systems of linear equations; Eigen values and eigen vectors.
Calculus: Functions of single variable; Limit; continuity and differentiability; Mean Value theorems; Evaluations of definite and improper integrals; Partial derivatives; Total derivatives; Maxima and minima; Gradient; Divergence and Curl; Vector identities; Directional derivatives; Line; Surface and Volume integrals; Stokes; Gauss and Green’s theorems.
Differential Equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems; Laplace transforms; Solutions of one dimensional heat and wave equations and Laplace equation.
Complex Variables: Analytic functions; Cauchy’s integral theorem; Taylor and Laurent series
Probability and Statistics: Definitions of probability and sampling theorems; Conditional probability; Mean; Median; mode and standard deviation; Random variables; Poisson; Normal and Binomial Distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations ; Integration by trapezoidal and Simpson’s rule; single and multistep methods for differential equations.
(b)Applied Mechanics and Design:
Engineering Mechanics: Free body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion; including impulse and momentum(linear and angular) and energy formulation; impact
Strength of Materials: Stress and strain; stress-strain relationship and elastic constants; Mohr’s circle for plane stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler’s theory of columns; strain methods; thermal stresses.
Theory of Machines: Displacement; velocity and acceleration analysis of plane mechanisms; dynamic analysis of slider-crank mechanisms; gear trains; flywheels
Vibrations: Free and forced vibration of single degree of freedom systems; effect of damping; vibration isolation; resonance; critical speed of shafts;
Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machines elements such as bolted; riveted and welded joints; shafts; spur gears; rolling and sliding contact bearing; brakes and clutches
(c)Fluid Mechanics and Thermal Sciences:
Fluid Mechanics: Fluid properties; fluid statics; manometry; buoyancy; control-volume analysis of mass; momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli’s equation; visvous flow of incompressible fluids; boundary layer; elementary turbulent flow; flow through pipes; head losses in pipes; bends etc
Heat Transfer: Modes of heat transfer; one dimensional heat conduction; resistance concept; electrical analogy; unsteady heat conductions; fins; dimensionless parameters in free and forced convective heat transfer; various correlations for heat transfer in flow over flat plates and through pipes; thermal boundary layer; effect of turbulence; radiative heat transfer; black and grey surfaces; shapes factors; network analysis; heat exchanger performance; LMTD and NTU methods
Thermodynamics: Zeroth, First and Second laws of thermodynamics; thermodynamics system and processes; Carnot cycle; irreversibility and availability; behavior of ideal and real gases; properties of pure substances; calculation of work and heat in the ideal processes; analysis of thermodynamics cycle related to energy conversion.
Applications: Power Engineering: Steam Tables; Rankine; Brayton cycles with regeneration and reheat I.C. Engines: air standard Otto; Diesel cycles. Refrigeration and air conditioning: Vapour refrigeration cycle, heat pumps; gas refrigeration; reverse Brayton cycle; moist air: psychrometric chart; basic psychrometric processes. Turbomachinery: Pelton-wheel; Francis and Kaplan turbines – impulse and reactions principles, velocity diagrams.
(d)Manufacturing and Industrial Engineering:
Engineering Materials: Structure and properties of engineering materials; heat treatment; stress-strain diagrams for engineering materials
Metal Casting: Design deformation and yield criteria; fundamental 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;
Joining: Physics of welding; brazing and soldering; adhesive bonding; design considerations in welding
Machining and Machine Tool Operations: Mechanics of machining; single and multipoint cutting tools; tool geometry and materials; tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, principles of 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.
Computer Integrated Manufacturing: Basics concepts of CAD/CAM and their integration tools
Production Planning and Control: Forecasting models; aggregate production planning; scheduling; materials requirement planning
Inventory control: Deterministic and probabilistic models; safety stock inventory control systems
Operations Research: Linear programming; simplex and duplex method; transportation; assignment; network flow models; simple queuing models; PERT and CPM