**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**

**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.**