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.
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 twin-tub 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 wave-shaping 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.
