Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
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
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.
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.
Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.
Fourier transform, Laplace transform, Z-transform
Electronics and Communication Engineering
Network graphs, matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network theorems: superposition, The venin and Norton's maximum power transfer, Wyes-Delta transformation. Steady state sinusoidal analysis using phases. 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.
Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon: diffusion current
drift current, mobility, 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, photolithography, n-tub, p-tub and twin-tub CMOS process.
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 andop-amp configurations, Function generators and wave-shaping 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.
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 Rough-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.
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, super heterodyne 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