GATE 2012
ENGINEERING MATHAMATICS
Linear Algebra:
Ø Matrix Algebra,
Ø Systems of linear equations,
Ø Eigen values and eigen vectors.
Calculus:
Ø Mean value theorems,
Ø Theorems of integral calculus,
Ø Evaluation of definite and improper integrals,
Ø Partial Derivatives,
Ø Maxima and minima,
Ø Multiple integrals,
Ø Fourier series
Ø Vector identities,
Ø Directional derivatives,
Ø Line, Surface and Volume integrals,
Ø Stokes, Gauss and Green's theorems.
Differential equations:
Ø First order equation (linear and nonlinear),
Ø Higher order linear differential equations with constant coefficients,
Ø Method of variation of parameters,
Ø Cauchy's and Euler's equations,
Ø Initial and boundary value problems,
Ø Partial Differential Equations and variable separable method.
Complex variables:
Ø Analytic functions,
Ø Cauchy's integral theorem and integral formula,
Ø Taylor's and Laurent' series,
Ø Residue theorem,
Ø solution integrals.
Probability and Statistics:
Ø Sampling theorems,
Ø Conditional probability,
Ø Mean, median, mode and standard deviation,
Ø Random variables,
Ø Discrete and continuous distributions,
Ø Poisson, Normal and Binomial distribution,
Ø Correlation and regression analysis.
Numerical Methods:
Ø Solutions of non-linear algebraic equations,
Ø single and multi-step methods for differential equations.
Transform Theory:
Ø Fourier transform,
Ø Laplace transform,
Ø Z-transform
ELECTRICAL ENGINEERING
Electric Circuits and Fields:
Ø Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks
Ø sinusoidal steady-state analysis, resonance, basic filter concepts
Ø ideal current and voltage sources, Thevenin's , Norton's and Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits
Ø Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions
Ø Ampere's and Biot-Savart's laws
Ø Inductance
Ø Dielectrics
Ø Dielectrics
Signals and Systems:
Ø Representation of continuous and discrete-time signals
Ø shifting and scaling operations
Ø linear, time-invariant and causal systems
Ø Fourier series representation of continuous periodic signals
Ø sampling theorem
Ø Fourier, Laplace and Z transforms
Electrical Machines:
Ø Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency
Ø three phase transformers - connections, parallel operation
Ø auto-transformer; energy conversion principles
Ø DC machines - types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors
Ø three phase induction motors - principles, types, performance characteristics, starting and speed control
Ø single phase induction motors
Ø synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications
Ø servo and stepper motors.
Power Systems:
Ø Basic power generation concepts
Ø transmission line models and performance
Ø cable performance, insulation
Ø corona and radio interference
Ø distribution systems
Ø per-unit quantities
Ø bus impedance and admittance matrices
Ø load flow
Ø voltage control
Ø power factor correction
Ø economic operation
Ø symmetrical components
Ø fault analysis
Ø principles of over-current, differential and distance protection
Ø solid state relays and digital protection
Ø circuit breakers
Ø system stability concepts, swing curves and equal area criterion
Ø HVDC transmission and FACTS concepts.
Control Systems:
Ø Principles of feedback
Ø transfer function
Ø block diagrams
Ø steady-state errors
Ø Routh and Niquist techniques
Ø Bode plots
Ø root loci
Ø lag, lead and lead-lag compensation
Ø state space model
Ø state transition matrix, controllability and observability.
Electrical and Electronic Measurements:
Ø Bridges and potentiometers
Ø PMMC, moving iron, dynamometer and induction type instruments
Ø measurement of voltage, current, power, energy and power factor
Ø instrument transformers
Ø digital voltmeters and multimeters
Ø phase, time and frequency measurement
Ø Q-meters
Ø oscilloscopes
Ø potentiometric recorders
Ø error analysis.
Analog and Digital Electronics:
Ø Characteristics of diodes, BJT, FET
Ø amplifiers - biasing, equivalent circuit and frequency response
Ø oscillators and feedback amplifiers
Ø operational amplifiers - characteristics and applications
Ø simple active filters
Ø VCOs and timers
Ø combinational and sequential logic circuits
Ø multiplexer
Ø Schmitt trigger
Ø multi-vibrators
Ø sample and hold circuits
Ø A/D and D/A converters
Ø 8-bit microprocessor basics, architecture, programming and interfacing.
Power Electronics and Drives:
Ø Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and principles of operation
Ø triggering circuits
Ø phase control rectifiers
Ø bridge converters - fully controlled and half controlled
Ø principles of choppers and inverters
Ø basis concepts of adjustable speed dc and ac drives.
0 comments:
Post a Comment