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
Electrical Circuits and Fields: Network
graph, KCL, KVL, node/ cut set, mesh/ tie
set analysis, transient response of d.c. and
a.c. networks; sinusoidal steady-state
analysis; resonance in electrical circuits;
concepts of ideal voltage and current
sources, network theorems, driving point,
immittance and transfer functions of two
port networks, elementary concepts of
filters; three phase circuits; Fourier
series and its application; Gauss theorem,
electric field intensity and potential due
to point, line, plane and spherical charge
distribution, dielectrics, capacitance
calculations for simple configurations;
Ampere's and Biot-Savart's law, inductance
calculations for simple configurations.
Electrical Machines: Single phase
transformer - equivalent circuit, phasor
diagram, tests, regulation and efficiency;
three phase transformers - connections,
parallel operation; auto transformer and
three-winding transformer; principles of
energy conversion, windings of rotating
machines: D. C. generators and motors -
characteristics, starting and speed control,
armature reaction and commutation; three
phase induction motors-performance
characteristics, starting and speed control;
single-phase induction motors; synchronous
generators-performance, regulation, parallel
operation; synchronous motors - starting,
characteristics, applications, synchronous
condensers; fractional horse power motors;
permanent magnet and stepper motors.
Power Systems: Electric power generation -
thermal, hydro, nuclear; transmission line
parameters; steady-state performance of
overhead transmission lines and cables and
surge propagation; distribution systems,
insulators, bundle conductors, corona and
radio interference effects; per-unit
quantities; bus admittance and impedance
matrices; load flow; voltage control and
power factor correction; economic operation;
symmetrical components, analysis of
symmetrical and unsymmetrical faults;
principles of over current, differential and
distance protections; concept of solid state
relays and digital protection; circuit
breakers; concept of system stability-swing
curves and equal area criterion; basic
concepts of HVDC transmission.
Control Systems: Principles of feedback;
transfer function; block diagrams:
steady-state errors; stability-Routh and
Nyquist criteria; Bode plots; compensation;
root loci; elementary state variable
formulation; state transition matrix and
response for Linear Time Invariant systems.
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-meter, oscilloscopes,
potentiometric recorders, error analysis.
Analog and Digital Electronics:
Characteristics of diodes, BJT, FET, SCR;
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, multivibrators,
sample and hold circuits, A/D and D/A
converters; microprocessors and their
applications.
Power Electronics and Electric Drives:
Semiconductor power devices-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, basic concepts of adjustable
speed dc and ac drives.
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