SECTIONS 
SYLLABUS 
Engineering Mathematics 
 Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigenvalues and Eigenvectors, rank, solution of linear equations – existence and uniqueness.

Calculus: Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.

Differential Equations: First order equations (linear and nonlinear), higherorder linear differential equations, Cauchy’s and Euler’s equations, methods of solution using a variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.

Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss’s, Green’s and Stoke’s theorems.
 Complex Analysis: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula; Taylor’s and Laurent’s series, residue theorem.

Numerical Methods: Solution of nonlinear equations, single and multistep methods for differential equations, convergence criteria.

Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions – binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis.

Networks, Signals, and Systems 

Network 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; Timedomain analysis of simple linear circuits; Solution of network equations using Laplace transform; Frequency domain analysis of RLC circuits; Linear 2‐port network parameters: driving point and transfer functions; State equations for networks.

Continuoustime signals: Fourier series and Fourier transform representations, sampling theorem and applications; Discretetime signals: discretetime Fourier transform (DTFT), DFT, FFT, Ztransform, interpolation of discretetime signals; LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay, digital filter design techniques.

Electronic Devices 

Energy bands in intrinsic and extrinsic silicon; Carrier transport: diffusion current, drift current, mobility and resistivity; Generation and recombination of carriers; Poisson and continuity equations; PN junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photodiode and solar cell; Integrated circuit fabrication process: oxidation, diffusion, ion implantation, photolithography and twintub CMOS process.

Analog Circuits 

Small signal equivalent circuits of diodes, BJTs and MOSFETs; Simple diode circuits: clipping, clamping and rectifiers; Singlestage BJT and MOSFET amplifiers: biasing, bias stability, midfrequency smallsignal analysis and frequency response; BJT and MOSFET amplifiers: multistage, differential, feedback, power and operational; Simple opamp circuits; Active filters; Sinusoidal oscillators: criterion for oscillation, singletransistor and opamp configurations; Function generators, waveshaping circuits and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation.

Digital Circuits 

Number systems; Combinatorial circuits: Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers, decoders and PLAs; Sequential circuits: latches and flip‐flops, counters, shift‐registers and finite state machines; Data converters: sample and hold circuits, ADCs and DACs; Semiconductor memories: ROM, SRAM, DRAM; 8bit microprocessor (8085): architecture, programming, memory and I/O interfacing.

Control Systems 

Basic control system components; Feedback principle; Transfer function; Block diagram representation; Signal flow graph; Transient and steadystate analysis of LTI systems; Frequency response; RouthHurwitz and Nyquist stability criteria; Bode and rootlocus plots; Lag, lead and laglead compensation; State variable model and solution of state equation of LTI systems.

Communications 

Random processes: autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems; Analog communications: amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, super heterodyne receivers, circuits for analogue communications; Information theory: entropy, mutual information and channel capacity theorem.

Digital communications: PCM, DPCM, digital modulation schemes, amplitude, phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, calculation of bandwidth, SNR and BER for digital modulation; Fundamentals of error correction, Hamming codes; Timing and frequency synchronization, intersymbol interference and its mitigation; Basics of TDMA, FDMA and CDMA.

Electromagnetics 

Electrostatics; Maxwell’s equations: differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector; Plane waves and properties: reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth;

Transmission lines: equations, characteristic impedance, impedance matching, impedance transformation, Sparameters, Smith chart

Waveguides: modes, boundary conditions, cutoff frequencies, dispersion relations; Antennas: antenna types, radiation pattern, gain and directivity, return loss, antenna arrays; Basics of radar; Light propagation in optical fibers.
