**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.

**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 usingLaplace
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
ofLaplace 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.