GATE 2013- Syllabus for Mechanical Engineering (ME)
- 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
- Evaluation of definite and improper integrals
- Partial derivatives
- Total derivative
- 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 multi-step methods for differential equations.
- Linear Algebra:
- 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 formulations 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 energy methods
- thermal stresses.
- Theory of Machines:
- Displacement
- velocity and acceleration analysis of plane mechanisms
- dynamic analysis of slider-crank mechanism
- gear trains
- flywheels.
- Vibrations:
- Free and forced vibration of single degree of freedom systems
- effect of damping
- vibration isolation
- resonance
- critical speeds of shafts.
- 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
- spur gears
- rolling and sliding contact bearings
- brakes and clutches.
- Engineering Mechanics:
- 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
- viscous 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 conduction
- 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
- shape factors
- network analysis
- heat exchanger performance
- LMTD and NTU methods.
- Thermodynamics:
- Zeroth, First and Second laws of thermodynamics
- thermodynamic system and processes
- Carnot cycle. irreversibility and availability
- behaviour of ideal and real gases
- properties of pure substances
- calculation of work and heat in ideal processes
- analysis of thermodynamic cycles related to energy conversion.
- Applications of Thermo dynamics:
- 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: Peltonwheel, Francis and Kaplan turbines - impulse and reaction principles, velocity diagrams.
- Fluid Mechanics:
- Manufacturing and Industrial Engineering
- Engineering Materials
- Structure and properties of engineering materials
- heat treatment
- stress-strain diagrams for engineering materials.
- Metal Casting:
- Design of patterns
- moulds and cores
- solidification and cooling
- riser and gating design
- design considerations.
- Forming:
- 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.
- Joining:
- Physics of welding,brazing and soldering
- adhesive bonding
- design considerations in welding.
- Machining and Machine Tool Operations:
- Mechanics of machining
- 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
- 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:
- Basic 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.
- Engineering Materials
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