GATE Mechanical Engineering Syllabus

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Subject Code: ME

Course Structure

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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