GATE for Mechanical Engineering comprise questions from engineering mathematics and mechanical engineering. Machine theory, machine design, heat transfer, Fluid mechanics etc are the main topics covered under mechanical engineering syllabus.

Syllabus for Engineering Mathematics

Calculus

• Continuity
• Differentiability
• Directional derivatives
• Divergence and Curl
• Evaluation of definite and improper integrals
• Functions of single variable
• Gauss theorem
• Gradient
• Green’s theorem
• Limits
• Maxima and minima
• Mean value theorems
• Partial derivatives
• Surface and Volume integrals
• Vector identities

Complex variables

• Analytic functions
• Cauchy’s integral theorem
• Taylor and Laurent series

Differential Equations

• Cauchy’s and Euler’s equations
• First order equations (linear and nonlinear)
• Higher order linear differential equations
• Initial and boundary value problems
• Laplace equation
• Laplace transforms
• Solutions of one dimensional heat and wave equations

Probability and Statistics

• Mean
• Binomial distribution
• Conditional probability
• Mode
• Normal distribution
• Poisson distribution
• Probability
• Random variables
• Median
• Sampling
• Standard deviation

Linear Algebra

• Eigen values
• Eigen vectors
• Matrix algebra
• Systems of linear equations

Numerical Methods

• Integration by trapezoidal and Simpson’s rule
• Methods for differential equations
• Numerical solutions of linear and non-linear algebraic equations

Syllabus for Mechanical Engineering

Engineering Mechanics

• Free body diagrams and equilibrium
• Impulse
• Kinematics and dynamics of particles
• Momentum (linear and angular)
• Energy formulations

Strength of Materials

• Bending and shear stresses
• Bending moment diagrams
• Deflection of beams
• Euler’s theory of columns
• Mohr’s circle for plane
• Shear force
• Strain energy methods
• Stress and plane strain
• Stress and strain
• Stress-strain relationship
• Thermal stresses
• Torsion of circular shafts

Theory of Machines

• Displacement
• Dynamic analysis of slider-crank mechanism
• Flywheels
• Gear trains
• Velocity and acceleration analysis of plane mechanisms

Design of Machines

• Design for static and dynamic loading
• Design of machine elements
• Fatigue strength and the S-N diagram

Heat-Transfer

• Electrical analogy
• Heat exchanger performance
• LMTD and NTU methods
• Modes of heat transfer
• Network Analysis
• One dimensional heat conduction
• Radiative heat transfer
• Resistance concept
• Turbulence effect
• Unsteady heat conduction

Fluid Mechanics

• Bernoulli’s equation
• Buoyancy
• Control-volume analysis of mass,
• Elementary turbulent flow
• Fluid acceleration
• Fluid properties
• Fluid statics
• Momentum and energy

Thermodynamics

• Analysis of thermodynamic cycles
• Calculation of work and heat in ideal processes
• Carnot cycle
• First and Second laws of thermodynamics
• Irreversibility and availability
• Properties of pure substances
• Thermodynamic system and processes

Power Engineering:

• I.C. Engines
• Brayton cycles
• Steam Tables

Refrigeration and air-conditioning

• Gas refrigeration
• Reverse Brayton cycle
• Turbomachinery
• Vapour refrigeration cycle

Metal Casting

• Design of patterns, moulds and cores
• Forming
• Joining
• Riser and gating design
• Solidification and cooling

Metrology and Inspection:

• Alignment and testing methods
• Limits
• Linear and angular measurements
• Tolerance analysis

Computer Integrated Manufacturing

• CAD/CAM and their integration tools

Inventory Control

• Deterministic and probabilistic models
• Safety stock inventory control systems

Machining and Machine Tool Operations

• Economics of machining; principles of non-traditional
• Machining processes
• Mechanics of machining
• Single and multi-point cutting tools
• Tool geometry
• Tool life and wear

Operations Research

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

Engineering graduates in mechanical engineering or related subjects can apply for GATE in ME. Exam preparation can be done as per exam syllabus using reference books and e-books.