# (Syllabus) GATE Examination (Mechanical Engineering)

**GATE Syllabus
Mechanical Engineering**

**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, stressstrain
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.