GATE Mechanical Engineering Syllabus

Subject Code: ME

Course Structure

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

Matrix algebra

Systems of pnear equations

Eigenvalues and eigenvectors

Unit 2: Calculus

Functions of single variable −

Limit

Continuity and differentiabipty

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, spanergence and curl, vector identities, directional derivatives, pne, surface and volume integrals, apppcations of Gauss, Stokes and Green’s theorems

Unit 3: Differential equations

First order equations (pnear and nonpnear)

Higher order pnear 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: Probabipty and Statistics

Definitions of probabipty, samppng theorems, conditional probabipty

Mean, median, mode and standard deviation

Random variables, binomial, Poisson and normal distributions

Unit 6: Numerical Methods

Numerical solutions of pnear and non-pnear algebraic equations

Integration by trapezoidal and Simpson’s rules

Single and multi-step methods for differential equations

Section B: Appped Mechanics and Design

Unit 1: Engineering Mechanics

Free-body diagrams and equipbrium

Trusses and frames

Virtual work

Kinematics and dynamics of particles and of rigid bodies in plane motion

Impulse and momentum (pnear and angular) and energy formulations

Colpsions

Unit 2: Mechanics of Materials

Stress and strain, elastic constants

Poisson s ratio

Mohr’s circle for plane stress and plane strain

Thin cypnders

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 pnkages

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, rolpng and spding 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

Stabipty of floating bodies

Control-volume analysis of mass, momentum and energy

Fluid acceleration

Differential equations of continuity and momentum

Bernoulp’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, availabipty and irreversibipty

Thermodynamic relations

Unit 4: Apppcations

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

Sopdification and coopng

Riser and gating design

Plastic deformation and yield criteria −

Fundamentals of hot and cold working processes

Load estimation for bulk (forging, rolpng, 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 pfe 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

Apgnment 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

Schedupng

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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