GATE SYLLABUS For Mechanical Engineering

GATE SYLLABUS For Mechanical Engineering

 

Section 1: Engineering Mathematics
Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and
eigenvectors.
Calculus: Functions of single variable, limit, continuity and differentiability, mean
value theorems, indeterminate forms; evaluation of definite and improper integrals;
double and triple integrals; partial derivatives, total derivative, Taylor series (in one
and two variables), maxima and minima, Fourier series; gradient, divergence and
curl, vector identities, directional derivatives, line, surface and volume integrals,
applications of Gauss, Stokes and Green’s theorems.
Differential equations: First order equations (linear and nonlinear); higher order linear
differential equations with constant coefficients; Euler-Cauchy equation; initial and
boundary value problems; Laplace transforms; solutions of heat, wave and
Laplace's equations.
Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s
integral theorem and integral formula; Taylor and Laurent series.
Probability and Statistics: Definitions of probability, sampling theorems, conditional
probability; mean, median, mode and standard deviation; random variables,
binomial, Poisson and normal distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic
equations; integration by trapezoidal and Simpson’s rules; single and multi-step
methods for differential equations.
Section 2: Applied Mechanics and Design
Engineering Mechanics: Free-body diagrams and equilib

Section 3: Fluid Mechanics and Thermal Sciences
Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy, forces on
submerged bodies, stability of floating bodies; control-volume analysis of mass,
momentum and energy; fluid acceleration; differential equations of continuity and
momentum; Bernoulli’s equation; dimensional analysis; viscous flow of
incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes,
head losses in pipes, bends and fittings.
Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance
concept and electrical analogy, heat transfer through fins; unsteady heat
conduction, lumped parameter system, Heisler's charts; thermal boundary layer,
dimensionless parameters in free and forced convective heat transfer, heat transfer
correlations for flow over flat plates and through pipes, effect of turbulence; heat
exchanger performance, LMTD and NTU methods; radiative heat transfer, StefanBoltzmann law, Wien's displacement law, black and grey surfaces, view factors,
radiation network analysis.
Thermodynamics: Thermodynamic systems and processes; properties of pure
substances, behaviour of ideal and real gases; zeroth and first laws of
thermodynamics, calculation of work and heat in various processes; second law of
thermodynamics; thermodynamic property charts and tables, availability and
irreversibility; thermodynamic relations.
Applications: Power Engineering: Air and gas compressors; vapour and gas power
cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel
and dual cycles. Refrigeration and air-conditioning: Vapour and gas refrigeration
and heat pump cycles; properties of moist air, psychrometric chart, basic
psychrometric processes. Turbomachinery: Impulse and reaction principles, velocity
diagrams, Pelton-wheel, Francis and Kaplan turbines.

Section 4: Materials, Manufacturing and Industrial Engineering
Engineering Materials: Structure and properties of engineering materials, phase
diagrams, heat treatment, stress-strain diagrams for engineering materials.
Casting, Forming and Joining Processes: Different types of castings, design of
patterns, moulds and cores; solidification and cooling; riser and gating design.
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. Principles of welding, brazing, soldering and adhesive bonding.
Machining and Machine Tool Operations: Mechanics of machining; basic machine
tools; 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, 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 models; safety stock inventory control systems.
Operations Research: Linear programming, simplex method, transportation,
assignment, network flow models, simple queuing models, PERT and CPM.

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GATE SYLLABUS FOR Civil Engineering

GATE SYLLABUS FOR Civil Engineering

 

Section 1: 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, local maxima and minima, Taylor and Maclaurin series; Evaluation of definite
and indefinite integrals, application of definite integral to obtain area and volume; Partial
derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities, Directional
derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher
order linear equations with constant coefficients; Euler-Cauchy equations; Laplace
transform and its application in solving linear ODEs; initial and boundary value problems.
Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of onedimensional diffusion equation; first and second order one-dimensional wave equation
and two-dimensional Laplace equation.
Probability and Statistics: Definitions of probability and sampling theorems; Conditional
probability; Discrete Random variables: Poisson and Binomial distributions; Continuous
random variables: normal and exponential distributions; Descriptive statistics - Mean,
median, mode and standard deviation; Hypothesis testing.
Numerical Methods: Accuracy and precision; error analysis. Numerical solutions of linear
and non-linear algebraic equations; Least square approximation, Newton’s and
Lagrange polynomials, numerical differentiation, Integration by trapezoidal and Simpson’s
rule, single and multi-step methods for first order differential equations.

Section 2: Structural Engineering

Engineering Mechanics: System of forces, free-body diagrams, equilibrium equations;
Internal forces in structures; Friction and its applications; Kinematics of point mass and rigid
body; Centre of mass; Euler’s equations of motion; Impulse-momentum; Energy methods;
Principles of virtual work.
Solid Mechanics: Bending moment and shear force in statically determinate beams;
Simple stress and strain relationships; Theories of failures; Simple bending theory
Concrete Structures: Working stress, Limit state and Ultimate load design concepts; Design
of beams, slabs, columns; Bond and development length; Prestressed concrete; Analysis
of beam sections at transfer and service loads.
Steel Structures: Working stress and Limit state design concepts; 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.

Section 3: Geotechnical Engineering
Soil Mechanics: Origin of soils, soil structure and fabric; Three-phase system and phase
relationships, index properties; Unified and Indian standard soil classification system;
Permeability - one dimensional flow, Darcy’s law; Seepage through soils - two-dimensional
flow, flow nets, uplift pressure, piping; Principle of effective stress, capillarity, seepage
force and quicksand condition; Compaction in laboratory and field conditions; Onedimensional consolidation, time rate of consolidation; Mohr’s circle, stress paths, effective
and total shear strength parameters, characteristics of clays and sand.
Foundation Engineering: Sub-surface investigations - scope, drilling bore holes, sampling,
plate load test, standard penetration and cone penetration tests; Earth pressure theories -
Rankine and Coulomb; Stability of slopes - finite and infinite slopes, method of slices and
Bishop’s method; Stress distribution in soils - Boussinesq’s and Westergaard’s theories,
pressure bulbs; Shallow foundations - Terzaghi’s and Meyerhoff’s bearing capacity
theories, effect of water table; Combined footing and raft foundation; Contact pressure;
Settlement analysis in sands and clays; Deep foundations - types of piles, dynamic and
static formulae, load capacity of piles in sands and clays, pile load test, negative skin
friction.

Section 4: Water Resources Engineering
Fluid Mechanics: Properties of fluids, fluid statics; Continuity, momentum, energy and
corresponding equations; Potential flow, applications of momentum and energy
equations; Laminar and turbulent flow; Flow in pipes, pipe networks; Concept of
boundary layer and its growth.
Hydraulics: Forces on immersed bodies; Flow measurement in channels and pipes;
Dimensional analysis and hydraulic similitude; Kinematics of flow, velocity triangles; Basics
of hydraulic machines, specific speed of pumps and turbines; Channel Hydraulics -
Energy-depth relationships, specific energy, critical flow, slope profile, hydraulic jump,
uniform flow and gradually varied flow
Hydrology: Hydrologic cycle, precipitation, evaporation, evapo-transpiration, watershed,
infiltration, unit hydrographs, hydrograph analysis, flood estimation and routing, reservoir
capacity, reservoir and channel routing, surface run-off models, ground water hydrology -
steady state well hydraulics and aquifers; Application of Darcy’s law.
Irrigation: Duty, delta, estimation of evapo-transpiration; Crop water requirements; Design
of lined and unlined canals, head works, gravity dams and spillways; Design of weirs on
permeable foundation; Types of irrigation systems, irrigation methods; Water logging and
drainage; Canal regulatory works, cross-drainage structures, outlets and escapes.

Section 5: Environmental Engineering
Water and Waste Water: 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, 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.

Section 6: Transportation Engineering
Transportation Infrastructure: Highway alignment and engineering surveys; Geometric
design of highways - cross-sectional elements, sight distances, horizontal and vertical
alignments; Geometric design of railway track; Airport runway length, taxiway and exit
taxiway design.
Highway Pavements: Highway materials - desirable properties and quality control tests;
Design of bituminous paving mixes; Design factors for flexible and rigid pavements; Design
of flexible pavement using IRC: 37-2012; Design of rigid pavements using IRC: 58-2011;
Distresses in concrete pavements.
Traffic Engineering: Traffic studies on flow, speed, travel time - delay and O-D study, PCU,
peak hour factor, parking study, accident study and analysis, statistical analysis of traffic
data; Microscopic and macroscopic parameters of traffic flow, fundamental
relationships; Control devices, signal design by Webster’s method; Types of intersections
and channelization; Highway capacity and level of service of rural highways and urban
roads.

Section 7: Geomatics Engineering
Principles of surveying; Errors and their adjustment; Maps - scale, coordinate system;
Distance and angle measurement - Levelling and trigonometric levelling; Traversing and
triangulation survey; Total station; Horizontal and vertical curves.
Photogrammetry - scale, flying height; Remote sensing - basics, platform and sensors,
visual image interpretation; Basics of Geographical information system (GIS) and
Geographical Positioning system (GPS).

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GATE Syllabus for Electronics and Communications Engineering(ECE)

Section 1: Engineering Mathematics

Linear Algebra:

Vector space, basis, linear dependence and independence, matrix algebra, eigen values and eigen vectors, rank, solution of linear equations – existence and uniqueness.

Calculus: Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.

Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations, Cauchy's and Euler's equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.

Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stoke's theorems. Complex Analysis: Analytic functions, Cauchy's integral theorem, Cauchy's integral formula; Taylor's and Laurent's series, residue theorem.

Numerical Methods: Solution of nonlinear equations, single and multi-step methods for differential equations, convergence criteria.

Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions - binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis.

Section 2: Networks, Signals and Systems

Network 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; Time domain analysis of simple linear circuits; Solution of network equations using Laplace transform; Frequency domain analysis of RLC circuits; Linear 2‐port network parameters: driving point and transfer functions; State equations for networks. Continuous-time signals: Fourier series and Fourier transform representations, sampling theorem and applications; Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, Z-transform, interpolation of discrete-time signals; LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay, digital filter design techniques.

Section 3: Electronic Devices

Energy bands in intrinsic and extrinsic silicon; Carrier transport: diffusion current, drift current, mobility and resistivity; Generation and recombination of carriers; Poisson and continuity equations; P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photo diode and solar cell; Integrated circuit fabrication process: oxidation, diffusion, ion implantation, photolithography and twin-tub CMOS process.

Section 4: Analog Circuits

Small signal equivalent circuits of diodes, BJTs and MOSFETs; Simple diode circuits: clipping, clamping and rectifiers; Single-stage BJT and MOSFET amplifiers: biasing, bias stability, mid-frequency small signal analysis and frequency response; BJT and MOSFET amplifiers: multi-stage, differential, feedback, power and operational; Simple op-amp circuits; Active filters; Sinusoidal oscillators: criterion for oscillation, single-transistor and opamp configurations; Function generators, wave-shaping circuits and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation.

Section 5: Digital Circuits

Number systems; Combinatorial circuits: Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers, decoders and PLAs; Sequential circuits: latches and flip‐flops, counters, shift‐registers and finite state machines; Data converters: sample and hold circuits, ADCs and DACs; Semiconductor memories: ROM, SRAM, DRAM; 8-bit microprocessor (8085): architecture, programming, memory and I/O interfacing.

Section 6: Control Systems

Basic control system components; Feedback principle; Transfer function; Block diagram representation; Signal flow graph; Transient and steady-state analysis of LTI systems; Frequency response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; Lag, lead and lag-lead compensation; State variable model and solution of state equation of LTI systems.

Section 7: Communications

Random processes: autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems; Analog communications: amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers, circuits for analog communications; Information theory: entropy, mutual information and channel capacity theorem; Digital communications: PCM, DPCM, digital modulation schemes, amplitude, phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, calculation of bandwidth, SNR and BER for digital modulation; Fundamentals of error correction, Hamming codes; Timing and frequency synchronization, inter-symbol interference and its mitigation; Basics of TDMA, FDMA and CDMA.

Section 8: Electromagnetics

Electrostatics; Maxwell’s equations: differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector; Plane waves and properties: reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth; Transmission lines: equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart; Waveguides: modes, boundary conditions, cut-off frequencies, dispersion relations; Antennas: antenna types, radiation pattern, gain and directivity, return loss, antenna arrays; Basics of radar; Light propagation in optical fibers.

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GATE SYLLABUS FOR ELECTRICAL ENGINEERING EE

GATE SYLLABUS FOR ELECTRICAL ENGINEERING

Electric Circuits Syllabus for gate electrical 
Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac
networks, Sinusoidal steady‐state analysis, Resonance, Passive filters, Ideal current and
voltage sources, Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum
power transfer theorem, Two‐port networks, Three phase circuits, Power and power factor
in ac circuits.

 

Electromagnetic Fields
Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence,
Electric field and potential due to point, line, plane and spherical charge distributions,
Effect of dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law,
Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force,
Reluctance, Magnetic circuits,Self and Mutual inductance of simple configurations.

 

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, Applications of Fourier Transform, Laplace Transform
and z-Transform.

 

Electrical Machines
Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit
tests, regulation and efficiency; Three phase transformers: connections, parallel operation;
Auto‐transformer, Electromechanical energy conversion principles, DC machines:
separately excited, series and shunt, motoring and generating mode of operation and
their characteristics, starting and speed control of dc motors; Three phase induction
motors: principle of operation, types, performance, torque-speed characteristics, no-load
and blocked rotor tests, equivalent circuit, starting and speed control; Operating principle
of single phase induction motors; Synchronous machines: cylindrical and salient pole
machines, performance, regulation and parallel operation of generators, starting of
synchronous motor, characteristics; Types of losses and efficiency calculations of electric
machines.

 

Power Systems
Power generation concepts, ac and dc transmission concepts, Models and performance
of transmission lines and cables, Series and shunt compensation, Electric field distribution
and insulators, Distribution systems, Per‐unit quantities, Bus admittance matrix, GaussSeidel and Newton-Raphson load flow methods, Voltage and Frequency control, Power
factor correction, Symmetrical components, Symmetrical and unsymmetrical fault
analysis, Principles of over‐current, differential and distance protection; Circuit breakers,
System stability concepts, Equal area criterion.

 

Control Systems
Mathematical modeling and representation of systems, Feedback principle, transfer
function, Block diagrams and Signal flow graphs, Transient and Steady‐state analysis of
linear time invariant systems, Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci,
Stability analysis, Lag, Lead and Lead‐Lag compensators; P, PI and PID controllers; State
space model, State transition matrix.

 

Electrical and Electronic Measurements
Bridges and Potentiometers, Measurement of voltage, current, power, energy and power
factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and
Frequency measurement; Oscilloscopes, Error analysis.

 

Analog and Digital Electronics
Characteristics of diodes, BJT, MOSFET; Simple diode circuits: clipping, clamping, rectifiers;
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, Demultiplexer,
Schmitt trigger, Sample and hold circuits, A/D and D/A converters, 8085Microprocessor:
Architecture, Programming and Interfacing.

 

Power Electronics
Characteristics of semiconductor power devices: Diode, Thyristor, Triac, GTO, MOSFET,
IGBT; DC to DC conversion: Buck, Boost and Buck-Boost converters; Single and three
phase configuration of uncontrolled rectifiers, Line commutated thyristor based
converters, Bidirectional ac to dc voltage source converters, Issues of line current
harmonics, Power factor, Distortion factor of ac to dc converters, Single phase and three
phase inverters, Sinusoidal pulse width modulation.

Engineering Mathematics
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.
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 integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Green’s theorem.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.
Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.
Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step methods for differential equations.
Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.

GATE SYLLABUS FOR ELECTRICAL ENGINEERING BY

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GATE SYLLABUS FOR ELECTRICAL ENGINEERING(EE)

GATE SYLLABUS FOR ELECTRICAL ENGINEERING

Electric Circuits
Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac
networks, Sinusoidal steady‐state analysis, Resonance, Passive filters, Ideal current and
voltage sources, Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum
power transfer theorem, Two‐port networks, Three phase circuits, Power and power factor
in ac circuits.

 

Electromagnetic Fields
Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence,
Electric field and potential due to point, line, plane and spherical charge distributions,
Effect of dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law,
Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force,
Reluctance, Magnetic circuits,Self and Mutual inductance of simple configurations.

 

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, Applications of Fourier Transform, Laplace Transform
and z-Transform.

 

Electrical Machines
Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit
tests, regulation and efficiency; Three phase transformers: connections, parallel operation;
Auto‐transformer, Electromechanical energy conversion principles, DC machines:
separately excited, series and shunt, motoring and generating mode of operation and
their characteristics, starting and speed control of dc motors; Three phase induction
motors: principle of operation, types, performance, torque-speed characteristics, no-load
and blocked rotor tests, equivalent circuit, starting and speed control; Operating principle
of single phase induction motors; Synchronous machines: cylindrical and salient pole
machines, performance, regulation and parallel operation of generators, starting of
synchronous motor, characteristics; Types of losses and efficiency calculations of electric
machines.

 

Power Systems
Power generation concepts, ac and dc transmission concepts, Models and performance
of transmission lines and cables, Series and shunt compensation, Electric field distribution
and insulators, Distribution systems, Per‐unit quantities, Bus admittance matrix, GaussSeidel and Newton-Raphson load flow methods, Voltage and Frequency control, Power
factor correction, Symmetrical components, Symmetrical and unsymmetrical fault
analysis, Principles of over‐current, differential and distance protection; Circuit breakers,
System stability concepts, Equal area criterion.

 

Control Systems
Mathematical modeling and representation of systems, Feedback principle, transfer
function, Block diagrams and Signal flow graphs, Transient and Steady‐state analysis of
linear time invariant systems, Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci,
Stability analysis, Lag, Lead and Lead‐Lag compensators; P, PI and PID controllers; State
space model, State transition matrix.

 

Electrical and Electronic Measurements
Bridges and Potentiometers, Measurement of voltage, current, power, energy and power
factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and
Frequency measurement; Oscilloscopes, Error analysis.

 

Analog and Digital Electronics
Characteristics of diodes, BJT, MOSFET; Simple diode circuits: clipping, clamping, rectifiers;
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, Demultiplexer,
Schmitt trigger, Sample and hold circuits, A/D and D/A converters, 8085Microprocessor:
Architecture, Programming and Interfacing.

 

Power Electronics
Characteristics of semiconductor power devices: Diode, Thyristor, Triac, GTO, MOSFET,
IGBT; DC to DC conversion: Buck, Boost and Buck-Boost converters; Single and three
phase configuration of uncontrolled rectifiers, Line commutated thyristor based
converters, Bidirectional ac to dc voltage source converters, Issues of line current
harmonics, Power factor, Distortion factor of ac to dc converters, Single phase and three
phase inverters, Sinusoidal pulse width modulation.

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GATE SYLLABUS FOR Engineering Mathematics

GATE SYLLABUS FOR Engineering Mathematics

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.
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 integral, Surface integral, Volume
integral, Stokes’s theorem, Gauss’s theorem, Green’s theorem.

Differential equations: First order equations (linear and nonlinear), Higher order linear
differential equations with constant coefficients, Method of variation of parameters,
Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial
Differential Equations, Method of separation of variables.

Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral
formula, Taylor series, Laurent series, Residue theorem, Solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median,
Mode, Standard Deviation, Random variables, Discrete and Continuous distributions,
Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis,
Regression analysis.

Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step
methods for differential equations.

Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.

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GATE SYLLABUS FOR ELECTRICAL ENGINEERING

GATE SYLLABUS FOR ELECTRICAL ENGINEERING

Engineering Mathematics

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.
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 integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Green’s theorem.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.
Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.
Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step methods for differential equations.
Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.

 Electrical Engineering
Electric Circuits
Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac networks, Sinusoidal steady‐state analysis, Resonance, Passive filters, Ideal current and voltage sources, Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum power transfer theorem, Two‐port networks, Three phase circuits, Power and power factor in ac circuits.

Electromagnetic Fields
Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence, Electric field and potential due to point, line, plane and spherical charge distributions, Effect of dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits,Self and Mutual inductance of simple configurations.

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, Applications of Fourier Transform, Laplace Transform and z-Transform.

 Electrical Machines
Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit
tests, regulation and efficiency; Three phase transformers: connections, parallel operation;
Auto‐transformer, Electromechanical energy conversion principles, DC machines:
separately excited, series and shunt, motoring and generating mode of operation and
their characteristics, starting and speed control of dc motors; Three phase induction
motors: principle of operation, types, performance, torque-speed characteristics, no-load
and blocked rotor tests, equivalent circuit, starting and speed control; Operating principle
of single phase induction motors; Synchronous machines: cylindrical and salient pole
machines, performance, regulation and parallel operation of generators, starting of
synchronous motor, characteristics; Types of losses and efficiency calculations of electric
machines.

Power Systems
Power generation concepts, ac and dc transmission concepts, Models and performance
of transmission lines and cables, Series and shunt compensation, Electric field distribution
and insulators, Distribution systems, Per‐unit quantities, Bus admittance matrix, Gauss-
Seidel and Newton-Raphson load flow methods, Voltage and Frequency control, Power
factor correction, Symmetrical components, Symmetrical and unsymmetrical fault
analysis, Principles of over‐current, differential and distance protection; Circuit breakers,
System stability concepts, Equal area criterion.

Control Systems
Mathematical modeling and representation of systems, Feedback principle, transfer
function, Block diagrams and Signal flow graphs, Transient and Steady‐state analysis of
linear time invariant systems, Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci,
Stability analysis, Lag, Lead and Lead‐Lag compensators; P, PI and PID controllers; State
space model, State transition matrix.

 Electrical and Electronic Measurements
Bridges and Potentiometers, Measurement of voltage, current, power, energy and power
factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and
Frequency measurement; Oscilloscopes, Error analysis.

Analog and Digital Electronics
Characteristics of diodes, BJT, MOSFET; Simple diode circuits: clipping, clamping, rectifiers;
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, Demultiplexer,
Schmitt trigger, Sample and hold circuits, A/D and D/A converters, 8085Microprocessor:
Architecture, Programming and Interfacing.

 Power Electronics
Characteristics of semiconductor power devices: Diode, Thyristor, Triac, GTO, MOSFET,
IGBT; DC to DC conversion: Buck, Boost and Buck-Boost converters; Single and three
phase configuration of uncontrolled rectifiers, Line commutated thyristor based
converters, Bidirectional ac to dc voltage source converters, Issues of line current
harmonics, Power factor, Distortion factor of ac to dc converters, Single phase and three
phase inverters, Sinusoidal pulse width modulation.

 

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