The syllabus is the set of information regarding the topics which will be asked in the examination. It consists of all the area from where the questions will be asked. This article will give you complete information regarding the GATE Production and Industrial Engineering Syllabus.

**GATE Production and Industrial Engineering Syllabus (PI)**

GATE Production and Industrial Engineering (PI) Sections consists of some of the Arithmetic Problems, **Engineering Mathematics** and Production and Industrial Engineering (PI).

### GATE Engineering Mathematics Syllabus

### Linear Algebra

**Algebra of matrices:** Inverse and rank of a matrix; System of linear equations; Symmetric, skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvectors, Diagonalisation of matrices; Cayley-Hamilton Theorem.

### Calculus

**Functions of single variable:** Limit, continuity and differentiability; Mean value theorems, Indeterminate forms and L’Hospital’s rule; Maxima and minima; Taylor’s theorem, Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes.

**Functions of two variables:** Limit, continuity and partial derivatives; Directional derivative, Total derivative; Tangent plane and normal line; Maxima, minima and saddle points, Method of Lagrange multipliers; Double and triple integrals, and their applications.

**Sequence and series:** Convergence of sequence and series; Tests for convergence, Power series; Taylor’s series; Fourier Series; Half range sine and cosine series.

### Vector Calculus

Gradient, divergence and curl; Line and surface integrals; Green’s theorem, Stokes theorem and Gauss divergence theorem (without proofs).

### Complex Variable

Analytic functions; Cauchy-Riemann equations; Line integral, Cauchy’s integral theorem and integral formula (without proof); Taylor’s series and Laurent series; Residue theorem (without proof) and its applications.

### Ordinary Differential Equation

First-order equations (linear and nonlinear); Higher order linear differential equations with constant coefficients; Second-order linear differential equations with variable coefficients; Method of variation of parameters; Cauchy-Euler equation; Power series solutions; Legendre polynomials, Bessel functions of the first kind and their properties.

### Partial Differential Equation

Classification of second-order linear partial differential equations; Method of separation of variables; Laplace equation; Solutions of one-dimensional heat and wave equations.

### Probability

Axioms of probability; Conditional probability; Bayes’ Theorem; Discrete and continuous random variables: Binomial, Poisson and normal distributions; Correlation and linear regression.

### Numerical Methods

The solution of systems of linear equations using LU decomposition, Gauss elimination and Gauss-Seidel methods; Lagrange and Newton’s interpolations, Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical integration by trapezoidal rule, Simpson’s rule and Gaussian quadrature rule; Numerical solutions of first-order differential equations by Euler’s method and 4th order Runge-Kutta method.

**GATE Production and Industrial Engineering Syllabus (PI) – General Engineering**

**Engineering Materials:** Structure and properties correlation; engineering materials (metals, ceramics, polymers and composites) – properties and applications; stress train behaviour of metals and alloys;iron-carbon phase diagram, heat treatment of metals and alloys, its influence on mechanical properties.

**Applied Mechanics:** Engineering mechanics – equivalent force systems, free body concepts, equations of equilibrium; trusses; strength of materials – stress, strain and their relationship; failure theories, Mohr’s circle(stress), deflection of beams, bending and shear stress, Euler’s theory of columns.

**Theory of Machines and Design:** Analysis of planar mechanisms, cams and followers; governors and flywheels; design of bolted, riveted and welded joints; interference/shrink-fit joints; design of shafts, keys, spur gears, belt drives, brakes and clutches; pressure vessels.

**Thermal and Fluids Engineering:** Fluid mechanics – fluid statics, Bernoulli’s equation, flow through pipes, equations of continuity and momentum, capillary action, contact angle and wetting; thermodynamics – zeroth, first and the second law of thermodynamics, thermodynamic system and processes, calculation of work and heat for systems and control volumes; air standard cycles; heat transfer –basic applications of conduction, convection and radiation.

**Manufacturing Processes I**

**Casting:** types of casting processes and applications; patterns – types and materials; allowances; moulds and cores – materials, making, and testing; casting techniques of cast iron, steels and nonferrous metals and alloys; analysis

of solidification and microstructure development; design of gating and riser; the origin of defects

**Metal Forming:** Stress-strain relations in elastic and plastic deformation; the concept of flow stress; hot and cold working – forging, rolling, extrusion and wire drawing; sheet metal working processes – blanking, bending and deep drawing; ideal work and slab analysis; the origin of metalworking defects.

**Joining of materials:** Principles of fusion welding processes(manual metal arc, MIG, TIG, plasma arc, submerged arc welding processes)–different heat sources (flame, arc, resistive, laser, electron beam), and heat transfer and associated losses, flux application, feeding of filler rod; Principles of solid-state welding processes (friction, explosive welding, ultrasonic welding processes); Principles of adhesive, brazing and soldering processes; Origins of welding defects.

**Powder processing:** Production of metal/ceramic powders, compaction and sintering of metals and ceramic powders.

**Polymers and Composites:** Plastic processing – injection, compression and blow moulding, extrusion, calendaring and thermoforming; moulding of composites.

**Manufacturing Processes II**

**Machine Tools and Machining:** Basic machine tools like centre lathe, milling machine, and drilling machine – construction and kinematics; machining processes – turning, taper turning, thread cutting, drilling, boring, milling, gear cutting, thread production, grinding; the geometry of single-point cutting tools, chip formation, cutting forces, specific cutting energy and power requirements, Merchant’s analysis; the basis of selection of machining parameters; tool materials, tool wear and tool life, the economics of machining, thermal aspects of machining, cutting fluids, machinability; Jigs and fixtures – principles, applications, and design.

**Non-traditional Manufacturing:** Principles, applications, the effect of process parameters on MRR and product quality of non-traditional machining processes – USM, AJM, WJM, AWJM, EDM and Wire cut EDM, LBM, EBM, PAM, CHM, ECM.

**Computer Integrated Manufacturing:** Basic concepts of CAD – geometric modelling, CAM – CNC and robotics – configurations, drives and controls, Group Technology and its applications – CAPP, cellular manufacturing and FMS.

**Quality and Reliability**

**Metrology and Inspection:** Limits, fits, and tolerances, gauge design, interchangeability, selective assembly; linear, angular, and form measurements(straightness, squareness, flatness, roundness, and cylindricity) by

mechanical and optical methods; inspection of screw threads and gears; surface finish measurement by contact and non-contact methods; tolerance analysis in manufacturing and assembly.

**Quality management:** Quality – concept and costs; quality assurance; statistical quality control, acceptance sampling, zero defects, six sigma; total quality management; ISO 9000.

**Reliability and Maintenance:** Reliability, availability and maintainability; distribution of failure and repair times; determination of MTBF and MTTR, reliability models; determination of system reliability; preventive maintenance and replacement.

**Industrial Engineering **

**Product Design and Development:** Principles of good product design, tolerance design; quality and cost considerations; product life cycle; standardization, simplification, diversification, value engineering and analysis, concurrent engineering; comparison of production alternatives.

**Work System Design:** Taylor’s scientific management, Gilbreths’s contributions; productivity – concepts and measurements; method study, micro-motion study, principles of motion economy; work measurement –time study, work sampling, standard data, PMTS; ergonomics; job evaluation, merit rating, incentive schemes, and wage administration.

**Facility Design:** Facility location factors and evaluation of alternate locations; types of plant layout and their evaluation; computer-aided layout design techniques; assembly line balancing; materials handling systems.

**Operations research and Operations management **

**Operation Research:** Linear programming – problem formulation, simplex method, duality and sensitivity analysis; transportation and assignment models; network flow models, constrained optimization and Lagrange multipliers; Markovian queuing models; dynamic programming; simulation – manufacturing applications.

**Engineering Economy and Costing:** Elementary cost accounting and methods of depreciation; break-even analysis, techniques for evaluation of capital investments, financial statements, time-cost trade-off, resource-levelling.

**Production control:** Forecasting techniques – causal and time series models, moving average, exponential smoothing, trend and seasonality; aggregate production planning; master production scheduling; MRP and MRP-II; routing, scheduling and priority dispatching; Push and pull production systems, the concept of JIT manufacturing system; Logistics, distribution, and supply chain management; Inventory – functions, costs, classifications, deterministic inventory models, quantity discount; perpetual and periodic inventory control systems.

**Project management** – PERT and CPM.

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