GATE 2012 Mechanical Syllabus

       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: Peltonwheel, 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.

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GATE 2012 Electrical Syllabus

        SYLLABUS FOR ELECTRICAL ENGINEERING (EE)
                         Engineering Mathematics 
Linear Algebra:
Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus:
Mean value theorems, Theorems of integral calculus, Evaluation of definite and
improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier
series. Vector identities, Directional derivatives, Line, Surface and Volume integrals,
Stokes, Gauss and Green's theorems.
Differential equations:
First order equation (linear and nonlinear), Higher order linear differential equations with
constant coefficients, Method of variation of parameters, Cauchy's and Euler's
equations, Initial and boundary value problems, Partial Differential Equations and
variable separable method.
Complex variables:
Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent'
series, Residue theorem, solution integrals.
Probability and Statistics:
Sampling theorems, Conditional probability, Mean, median, mode and standard
deviation, Random variables, Discrete and continuous distributions, Poisson, Normal
and Binomial distribution, Correlation and regression analysis.
Numerical Methods:
Solutions of non-linear algebraic equations, single and multi-step methods for
differential equations.
Transform Theory:
Fourier transform, Laplace transform, Z-transform.Electrical Engineering
Electric Circuits and Fields: 
Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac
networks; sinusoidal steady-state  analysis, resonance, basic filter concepts; ideal
current and voltage sources, Thevenin's, Norton's and Superposition and Maximum
Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem,
electric field and potential due to point, line, plane and spherical charge distributions;
Ampere's and Biot-Savart's laws; inductance; dielectrics; capacitance.
Signals and Systems: 
Representation of continuous and discrete-time signals; shifting and scaling operations;
linear, time-invariant and causal systems; Fourier series representation of continuous
periodic signals; sampling theorem; Fourier, Laplace and Z transforms.
Electrical Machines: 
Single phase transformer  - equivalent circuit, phasor diagram, tests, regulation and
efficiency; three phase transformers - connections, parallel operation; auto-transformer;
energy conversion principles; DC machines - types, windings, generator characteristics,
armature reaction and commutation, starting and speed control of motors; three phase
induction motors  - principles, types, performance characteristics, starting and speed
control; single phase induction motors; synchronous machines  - performance,
regulation and parallel operation of generators, motor starting, characteristics and
applications; servo and stepper motors.
Power Systems:
Basic power generation concepts; transmission line models and performance; cable
performance, insulation; corona and radio interference; distribution systems; per-unit
quantities; bus impedance and admittance matrices; load flow; voltage control; power
factor correction; economic operation; symmetrical components; fault analysis;
principles of over-current, differential and distance protection; solid state relays and
digital protection; circuit breakers; system stability concepts, swing curves and equal
area criterion; HVDC transmission and FACTS concepts.
Control Systems:
Principles of feedback; transfer function; block diagrams; steady-state errors; Routh and
Niquist techniques; Bode plots; root loci; lag, lead and lead-lag compensation; state
space model; state transition matrix, controllability and observability.
Electrical and Electronic Measurements: Bridges and potentiometers; PMMC, moving iron, dynamometer and induction type
instruments; measurement of voltage, current, power, energy and power factor;
instrument transformers; digital voltmeters and multimeters; phase, time and frequency
measurement; Q-meters; oscilloscopes; potentiometric recorders; error analysis.
Analog and Digital Electronics:
Characteristics of diodes, BJT, FET; amplifiers  - biasing, equivalent circuit and
frequency response; oscillators and feedback amplifiers; operational amplifiers  -
characteristics and applications; simple active filters; VCOs and timers; combinational
and sequential logic  circuits; multiplexer; Schmitt trigger; multi-vibrators; sample and
hold circuits; A/D and D/A converters; 8-bit microprocessor basics, architecture,
programming and interfacing.
Power Electronics and Drives:
Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and
IGBTs  - static characteristics and principles of operation; triggering circuits; phase
control rectifiers; bridge converters  - fully controlled and half controlled; principles of
choppers and inverters; basis concepts of adjustable speed dc and ac drives.

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GATE 2012 Electronics and Communication Syllabus

Engineering Mathematics 
SYLLABUS FOR ELECTRONICS AND
COMMUNICATION ENGINEERING (EC)
Linear Algebra:
Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus:
Mean value theorems, Theorems of integral calculus, Evaluation of definite and
improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier
series. Vector identities, Directional derivatives, Line, Surface and Volume integrals,
Stokes, Gauss and Green's theorems.
Differential equations:
First order equation (linear and nonlinear), Higher order linear differential equations with
constant coefficients, Method of variation of parameters, Cauchy's and Euler's
equations, Initial and boundary value problems, Partial Differential Equations and
variable separable method.
Complex variables:
Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent'
series, Residue theorem, solution integrals.
Probability and Statistics:
Sampling theorems, Conditional probability, Mean, median, mode and standard
deviation, Random variables, Discrete and continuous distributions, Poisson, Normal
and Binomial distribution, Correlation and regression analysis.
Numerical Methods:
Solutions of non-linear algebraic equations, single and multi-step  methods for
differential equations.
Transform Theory:Fourier transform, Laplace transform, Z-transform.
Electronics and Communication Engineering
Networks:
Network graphs: matrices associated with graphs; incidence, fundamental cut set and
fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network
theorems: superposition, Thevenin and Norton's maximum power transfer, Wye-Delta
transformation. Steady state sinusoidal analysis using phasors. Linear constant
coefficient differential equations; time domain analysis of simple RLC circuits, Solution
of network equations using Laplace transform: frequency domain analysis of RLC
circuits. 2-port network parameters: driving point and transfer functions. State equations
for networks.
Electronic Devices: 
Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon:
diffusion current, drift current, mobility, and resistivity. Generation and recombination of
carriers. p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor,
MOSFET, LED, p-I-n and avalanche photo diode, Basics of LASERs. Device
technology: integrated circuits fabrication process, oxidation, diffusion, ion implantation,
photolithography, n-tub, p-tub and twin-tub CMOS process.
Analog Circuits:
Small Signal Equivalent circuits of diodes, BJTs, MOSFETs and analog CMOS. Simple
diode circuits, clipping, clamping, rectifier. Biasing and bias stability of transistor and
FET amplifiers. Amplifiers: single-and multi-stage, differential and operational, feedback,
and power. Frequency response of amplifiers. Simple op-amp circuits. Filters.
Sinusoidal oscillators; criterion for oscillation; single-transistor and op-amp
configurations. Function generators and wave-shaping circuits, 555 Timers. Power
supplies.
Digital circuits:
Boolean algebra, minimization of Boolean functions; logic gates; digital IC families (DTL,
TTL, ECL, MOS, CMOS). Combinatorial circuits: arithmetic circuits, code converters,
multiplexers, decoders, PROMs and PLAs. Sequential circuits: latches and flip-flops,
counters and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor
memories. Microprocessor(8085): architecture, programming, memory and I/O
interfacing.
Signals and Systems:
Definitions and properties of Laplace transform, continuous-time and discrete-time
Fourier series, continuous-time and discrete-time Fourier Transform, DFT and FFT, ztransform. Sampling theorem. Linear Time-Invariant (LTI) Systems: definitions and
properties; causality, stability, impulse response, convolution, poles and zeros, parallel
and cascade structure, frequency response, group delay, phase delay. Signal
transmission through LTI systems.
Control Systems:
Basic control system components; block diagrammatic description, reduction of block
diagrams. Open loop and closed loop (feedback) systems and stability analysis of these
systems. Signal flow graphs and their use in determining transfer functions of systems;
transient and steady state analysis of LTI control systems and frequency response.
Tools and techniques for LTI control system analysis: root loci, Routh-Hurwitz criterion,
Bode and Nyquist plots. Control system compensators: elements of lead and lag
compensation, elements of Proportional-Integral-Derivative (PID) control. State variable
representation and solution of state equation of LTI control systems.
Communications:
Random signals and noise: probability, random variables, probability density function,
autocorrelation, power spectral density. Analog communication systems: amplitude and
angle modulation and demodulation systems, spectral analysis of these operations,
superheterodyne receivers; elements of hardware, realizations of analog
communication systems; signal-to-noise ratio (SNR) calculations for amplitude
modulation (AM) and frequency modulation (FM) for low noise conditions.
Fundamentals of information theory and channel capacity theorem. Digital
communication systems: pulse code modulation (PCM), differential pulse code
modulation (DPCM), digital modulation schemes: amplitude, phase and frequency shift
keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth consideration
and probability of error calculations for these schemes. Basics of TDMA, FDMA and
CDMA and GSM.
Electromagnetics: 
Elements of vector calculus:  divergence and curl; Gauss' and Stokes' theorems,
Maxwell's equations: differential and integral forms. Wave equation, Poynting vector.
Plane waves: propagation through various media; reflection and refraction; phase and
group velocity; skin depth. Transmission lines: characteristic impedance; impedance
transformation; Smith chart; impedance matching; S parameters, pulse excitation.
Waveguides: modes in rectangular waveguides; boundary conditions; cut-off
frequencies; dispersion relations. Basics of propagation in dielectric waveguide and
optical fibers. Basics of Antennas: Dipole antennas; radiation pattern; antenna gain.

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GATE 2012 Civil Syllabus

             SYLLABUS FOR CIVIL ENGINEERING (CE)
                               Engineering Mathematics

Linear Algebra:

Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

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.

                                       Structural Engineering

Mechanics:
Bending moment and shear force in statically determinate beams. Simple stress and

strain relationship: Stress and strain in two dimensions, principal stresses, stress

transformation, Mohr's circle.  Simple bending theory, flexural and shear stresses,

unsymmetrical bending, shear centre. Thin walled pressure vessels, uniform torsion,

buckling of column, combined and direct bending stresses.

Structural Analysis:

Analysis of statically determinate trusses, arches, beams, cables and frames,

displacements in statically determinate structures and analysis of statically

indeterminate structures by force/ energy methods, analysis by displacement methods

(slope deflection and moment distribution methods), influence lines for determinate and

indeterminate structures. Basic concepts of matrix methods of structural analysis.

Concrete Structures:

Concrete Technology- properties of concrete, basics of mix design. Concrete designbasic working stress and limit state design concepts, analysis of ultimate load capacity

and design of members subjected to flexure, shear, compression and torsion by limit

state methods. Basic elements of prestressed concrete, analysis of beam sections at

transfer and service loads.

Steel Structures:

Analysis and design of tension and compression members, beams and beam- columns,

column bases. Connections- simple and eccentric, beam'column connections, plate

girders and trusses. Plastic analysis of beams and frames.

Geotechnical Engineering

Soil Mechanics:

Origin of soils, soil classification, three-phase system, fundamental definitions,

relationship and interrelationships, permeability & seepage, effective stress principle,

consolidation, compaction, shear strength.

Foundation Engineering:

Sub-surface investigations- scope, drilling bore holes, sampling, penetration tests, plate

load test. Earth pressure theories, effect of water table, layered soils. Stability of slopesinfinite slopes, finite slopes. Foundation types-foundation design requirements. Shallow

foundations-bearing capacity, effect of shape, water table and other factors, stress

distribution, settlement analysis in sands & clays. Deep foundations pile types, dynamic

& static formulae, load capacity of piles in sands & clays, negative skin friction.Water Resources Engineering

Fluid Mechanics and Hydraulics:

Properties of fluids, principle of conservation of mass, momentum, energy and

corresponding equations, potential flow, applications of momentum and Bernoulli's

equation, laminar and turbulent flow, flow in pipes, pipe networks. Concept of boundary

layer and its growth. Uniform flow, critical flow and gradually varied flow in channels,

specific energy concept, hydraulic jump. Forces on immersed bodies, flow

measurements in channels, tanks and pipes. Dimensional analysis and hydraulic

modeling. Kinematics of flow, velocity triangles and specific speed of pumps and

turbines.

Hydrology:

Hydrologic cycle, rainfall, evaporation, infiltration, stage discharge relationships, unit

hydrographs, flood estimation, reservoir capacity, reservoir and channel routing. Well

hydraulics.

Irrigation:

Duty, delta, estimation of evapo-transpiration. Crop water requirements. Design of: lined

and unlined canals, waterways, head works, gravity dams and  spillways. Design of

weirs on permeable foundation. Types of irrigation system, irrigation methods. Water

logging and drainage, sodic soils.

                                           Environmental Engineering

Water requirements:

Quality standards, basic unit processes and operations for water treatment. Drinking

water standards, water requirements, basic unit operations and unit processes for

surface water treatment, distribution of water. Sewage and sewerage treatment,

quantity and characteristics of wastewater. Primary, secondary and tertiary treatment of

wastewater, sludge disposal, effluent discharge standards. Domestic wastewater

treatment, quantity of characteristics of domestic wastewater, primary and secondary

treatment Unit operations and unit processes of domestic wastewater, sludge disposal.

Air Pollution:

Types of pollutants, their sources and impacts, air pollution meteorology, air pollution

control, air quality standards and limits.

Municipal Solid Wastes:Characteristics, generation, collection and transportation of solid wastes, engineered

systems for solid waste management (reuse/ recycle, energy recovery, treatment and

disposal).

Noise Pollution:

Impacts of noise, permissible limits of noise pollution, measurement of noise and control

of noise pollution.

Transportation Engineering

Highway Planning:

Geometric design of highways, testing and specifications of paving materials, design of

flexible and rigid pavements.

Traffic Engineering:

Traffic characteristics, theory of traffic flow, intersection design, traffic signs and signal

design, highway capacity.

Surveying

Importance of surveying, principles and classifications, mapping concepts, coordinate

system, map projections, measurements of distance and directions, leveling, theodolite

traversing, plane table surveying, errors and adjustments, curves.

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GATE 2012 CS & IT Syllabus

Mathematical Logic:

Propositional Logic; First Order Logic.

Probability:

Conditional Probability; Mean, Median, Mode and Standard Deviation; Random Variables; Distributions; uniform, normal, exponential, Poisson, Binomial.

Set Theory & Algebra:

Sets; Relations; Functions; Groups; Partial Orders; Lattice; Boolean Algebra.

Combinatorics:

Permutations; Combinations; Counting; Summation; generating functions; recurrence relations; asymptotics.

Graph Theory:

Connectivity; spanning trees; Cut vertices & edges; covering; matching; independent sets; Colouring; Planarity; Isomorphism.

Linear Algebra:

Algebra of matrices, determinants, systems of linear equations, Eigen values and Eigen vectors.

Numerical Methods:

LU decomposition for systems of linear equations; numerical solutions of non-linear algebraic equations by Secant, Bisection and Newton-Raphson Methods; Numerical integration by trapezoidal and Simpson's rules.

Calculus:

Limit, Continuity & differentiability, Mean value Theorems, Theorems of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives, maxima & minima.

Computer Science And Information Technology

Digital Logic:

Logic functions, Minimization, Design and synthesis of combinational and sequential circuits; Number representation and computer arithmetic (fixed and floating point).

Computer Organization and Architecture:

Machine instructions and addressing modes, ALU and data-path, CPU control design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and main memory, Secondary storage.

Programming and Data Structures:

Programming in C; Functions, Recursion, Parameter passing, Scope, Binding; Abstract data types, Arrays, Stacks, Queues, Linked Lists, Trees, Binary search trees, Binary heaps.

Algorithms:

Analysis, Asymptotic notation, Notions of space and time complexity, Worst and average case analysis; Design: Greedy approach, Dynamic programming, Divide-and-conquer; Tree and graph traversals, Connected components, Spanning trees, Shortest paths; Hashing, Sorting, Searching. Asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, Basic concepts of complexity classes  P, NP, NP-hard, NP-complete.

Theory of Computation:

Regular languages and finite automata, Context free languages and Push-down automata, Recursively enumerable sets and Turing machines, Undecidability.

Compiler Design:

Lexical analysis, Parsing, Syntax directed translation, Runtime environments, Intermediate and target code generation, Basics of code optimization.

Operating System:

Processes, Threads, Inter-process communication, Concurrency, Synchronization, Deadlock, CPU scheduling, Memory management and virtual memory, File systems, I/O systems, Protection and security.

Databases:

ER-model, Relational model (relational algebra, tuple calculus), Database design (integrity constraints, normal forms), Query languages (SQL), File structures (sequential files, indexing, B and B+ trees), Transactions and concurrency control.

Information Systems and Software Engineering:

information gathering, requirement and feasibility analysis, data flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project, design, coding, testing, implementation, maintenance.

Computer Networks:

ISO/OSI stack, LAN technologies (Ethernet, Token ring), Flow and error control techniques, Routing algorithms, Congestion control, TCP/UDP and sockets, IP(v4), Application layer protocols (icmp, dns, smtp, pop, ftp, http); Basic concepts of hubs, switches, gateways, and routers. Network security  basic concepts of public key and private key cryptography, digital signature, firewalls.

Web technologies:

HTML, XML, basic concepts of client-server computing.

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