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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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