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GATE Online Preparation - 2019

We fill the gap between Aspiration & Reality of GATE

GATE 2019 Syllabus for Mechanical Engineering

Engineering Mathematics


Linear Algebra
  • Matrix algebra

  • Systems of linear equations

  • Eigen values and Eigen vectors

Ordinary Differential Equation ( ODE )
  • First order ( linear and non – linear ) equations

  • higher order linear equations with constant coefficients

  • Euler – Cauchy equations

  • Laplace transform and its application in solving linear ODEs

  • Initial and boundary value problems.

Partial Differential Equation ( PDE ) : Fourier series
  • separation of variables

  • solutions of onedimensional diffusion equation

  • first and second order one – dimensional wave equation and two-dimensional Laplace equation.

Calculus
  • Functions of single variable

  • Limit, continuity and differentiability

  • Mean value theorems

  • local maxima and minima

  • Taylor and Maclaurin series

  • Evaluation of definite and indefinite integrals

  • application of definite integral to obtain area and volume

  • Partial derivatives

  • Total derivative

  • Gradient

  • Divergence and Curl, Vector identities

  • Directional derivatives

  • Line, Surface and Volume integrals

  • Stokes

  • Gauss and Green's theorems.

Probability and Statistics
  • Definitions of probability and sampling theorems

  • Conditional probability

  • Discrete Random variables

  • Poisson and Binomial distributions

  • Continuous random variables

  • normal and exponential distributions

  • Descriptive statistics – Mean, median, mode and standard deviation

  • Hypothesis testing

Numerical Methods
  • Accuracy and precision

  • error analysis

  • Numerical solutions of linear and non – linear algebraic equations

  • Least square approximation

  • Newton's and Lagrange polynomials

  • numerical differentiation

  • Integration by trapezoidal and Simpson's rule

  • single and multi – step methods for first order differential equations

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

  • impulse and momentum ( linear and angular ) and energy formulations, collisions.

Mechanics of Materials
  • Stress and strain, elastic constants

  • Poisson's rati

  • 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

  • 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.

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.

Fluid Mechanics and Thermal Sciences


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.

Thermodynamics
  • Thermodynamic systems and processes

  • properties of pure substances

  • Behaviour 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.

Manufacturing and Industrial Engineering


Engineering Materials
  • Structure and properties of engineering materials

  • phase diagrams

  • heat treatment

  • stress-strain diagrams for engineering materials.

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.

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

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.

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