GATE Mechanical Engineering Syllabus


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Subject Code: ME

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential Equations
Unit 4 Complex Analysis
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Section B Applied Mechanics and Design
Unit 1 Engineering Mechanics
Unit 2 Mechanics of Materials
Unit 3 Theory of Machines
Unit 4 Vibrations
Unit 5 Machine Design
Section C Fluid Mechanics and Thermal Sciences
Unit 1 Fluid Mechanics
Unit 2 Heat-Transfer
Unit 3 Thermodynamics
Unit 4 Applications
Section D Materials, Manufacturing and Industrial Engineering
Unit 1 Engineering Materials
Unit 2 Casting, Forming and Joining Processes
Unit 3 Machining and Machine Tool Operations
Unit 4 Metrology and Inspection
Unit 5 Computer Integrated Manufacturing
Unit 6 Production Planning and Control
Unit 7 Inventory Control
Unit 8 Operations Research

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Matrix algebra
  • Systems of linear equations
  • Eigenvalues and eigenvectors

Unit 2: 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

Unit 3: 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

Unit 4: Complex variables

  • Analytic functions
  • Cauchy-Riemann equations
  • Cauchy’s integral theorem and integral formula
  • Taylor and Laurent series

Unit 5: Probability and Statistics

  • Definitions of probability, sampling theorems, conditional probability
  • Mean, median, mode and standard deviation
  • Random variables, binomial, Poisson and normal distributions

Unit 6: Numerical Methods

  • Numerical solutions of linear and non-linear algebraic equations
  • Integration by trapezoidal and Simpson’s rules
  • Single and multi-step methods for differential equations

Section B: Applied Mechanics and Design

Unit 1: 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

Unit 2: Mechanics of Materials

  • Stress and strain, elastic constants
  • Poisson's ratio
  • 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

Unit 3: 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

Unit 4: Vibrations

  • Free and forced vibration of single degree of freedom systems, effect of damping

  • Vibration isolation

  • Resonance

  • Critical speeds of shafts

Unit 5: 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

    • Welded joints

  • Shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs

Section C: Fluid Mechanics and Thermal Sciences

Unit 1: 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

Unit 2: Heat-Transfer

  • Modes of heat transfer −

    • One dimensional heat conduction

    • Resistance concept

    • 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

    • Stefan Boltzmann law

    • Wien's displacement law

    • Black and grey surfaces

    • View factors

    • Radiation network analysis

Unit 3: 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

Unit 4: 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

Section D: Materials, Manufacturing and Industrial Engineering

Unit 1: Engineering Materials

  • Structure and properties of engineering materials
  • Phase diagrams
  • Heat treatment
  • Stress-strain diagrams for engineering materials

Unit 2: 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

Unit 3: 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

Unit 4: 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

Unit 5: Computer Integrated Manufacturing

  • Basic concepts of CAD/CAM and their integration tools

Unit 6: Production Planning and Control

  • Forecasting models
  • Aggregate production planning
  • Scheduling
  • Materials requirement planning

Unit 7: Inventory Control

  • Deterministic models
  • Safety stock inventory control systems

Unit 8: Operations Research

  • Linear programming
  • Simplex method
  • Transportation
  • Assignment
  • Network flow models
  • Simple queuing models
  • PERT and CPM

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