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# 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

• 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;

• 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

• 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

• 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

• StefanBoltzmann law

• Wien's displacement law

• black and grey surfaces

• view factors

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.