#### GATE Syllabus for Mechanical Engineering (ME)

#### ENGINEERING MATHEMATICS

**Linear Algebra**: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.

**Calculus**: Functions of single variable, Limit,
continuity and differentiability, Mean value theorems, Evaluation of
definite and improper integrals, Partial derivatives, Total derivative,
Maxima and minima, Gradient, Divergence and Curl, Vector identities,
Directional derivatives, Line, Surface and Volume integrals, Stokes,
Gauss and Green’s theorems.

**Differential equations**: First order equations
(linear and nonlinear), Higher order linear differential equations with
constant coefficients, Cauchy’s and Euler’s equations, Initial and
boundary value problems, Laplace transforms, Solutions of one
dimensional heat and wave equations and Laplace equation.

**Complex variables**: Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series.

**Probability and Statistics**: Definitions of
probability and sampling theorems, Conditional probability, Mean,
median, mode and standard deviation, Random variables, Poisson,Normal
and Binomial distributions.

**Numerical Methods**: Numerical solutions of linear and
non-linear algebraic equations Integration by trapezoidal and
Simpson’s rule, single and multi-step methods for differential
equations.

#### APPLIED MECHANICS AND DESIGN

**Engineering Mechanics:** Free body diagrams and
equilibrium; trusses and frames; virtual work; kinematics and dynamics
of particles and of rigid bodies in plane motion, including impulse and
momentum (linear and angular) and energy formulations; impact.

**Strength of Materials:** Stress and strain,
stress-strain relationship and elastic constants, 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; strain energy
methods; thermal stresses.

**Theory of Machines:** Displacement, velocity and
acceleration analysis of plane mechanisms; dynamic analysis of
slider-crank mechanism; gear trains; flywheels.

**Vibrations:** Free and forced vibration of single
degree of freedom systems; effect of damping; vibration isolation;
resonance, critical speeds of shafts.

**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 and welded
joints, shafts, spur gears, rolling and sliding contact bearings, brakes
and clutches.

#### FLUID MECHANICS AND THERMAL SCIENCES

**Fluid Mechanics:** Fluid properties; fluid statics,
manometry, buoyancy; control-volume analysis of mass, momentum and
energy; fluid acceleration; differential equations of continuity and
momentum; Bernoulli’s equation; viscous flow of incompressible fluids;
boundary layer; elementary turbulent flow; flow through pipes, head
losses in pipes, bends etc.

**Heat-Transfer:** Modes of heat transfer; one
dimensional heat conduction, resistance concept, electrical analogy,
unsteady heat conduction, fins; dimensionless parameters in free and
forced convective heat transfer, various correlations for heat transfer
in flow over flat plates and through pipes; thermal boundary layer;
effect of turbulence; radiative heat transfer, black and grey surfaces,
shape factors, network analysis; heat exchanger performance, LMTD and
NTU methods.

**Thermodynamics:**Zeroth, First and Second laws of
thermodynamics; thermodynamic system and processes; Carnot
cycle.irreversibility and availability; behaviour of ideal and real
gases, properties of pure substances, calculation of work and heat in
ideal processes; analysis of thermodynamic cycles related to energy
conversion.

**Applications:***Power Engineering*: Steam Tables, Rankine, Brayton cycles with regeneration and reheat. *I.C. Engines*: air-standard Otto, Diesel cycles. *Refrigeration and air-conditioning*:
Vapour refrigeration cycle, heat pumps, gas refrigeration, Reverse
Brayton cycle; moist air: psychrometric chart, basic psychrometric
processes. *Turbomachinery:*Pelton-wheel, Francis and Kaplan turbines — impulse and reaction principles, velocity diagrams.

#### MANUFACTURING AND INDUSTRIAL ENGINEERING

**Engineering Materials**: Structure and properties of engineering materials, heat treatment, stress-strain diagrams for engineering materials.

**Metal Casting:** Design of patterns, moulds and cores; solidification and cooling; riser and gating design, design considerations.

**Forming:** 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.

**Joining:** Physics of welding, brazing and soldering; adhesive bonding; design considerations in welding.

**Machining and Machine Tool Operations:** Mechanics of
machining, 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,
principles of design of jigs and fixtures

**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.

**Computer Integrated Manufacturing:** Basic concepts of CAD/CAM and their integration tools.

**Production Planning and Control:** Forecasting models, aggregate production planning, scheduling, materials requirement planning.

**Inventory Control:** Deterministic and probabilistic models; safety stock inventory control systems.

**Operations Research:** Linear programming, simplex and
duplex method, transportation, assignment, network flow models, simple
queuing models, PERT and CPM.