# GATE Mechanical Engineering Syllabus

## 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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