# 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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