__
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.

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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 twintub 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
waveshaping 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, z-transform. 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.