India Education

aayush_005 · #1 (**permalink**) 10-15-2008, 04:21 PM

ENGINEERING MATHEMATICS
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
GATE 2009 GRADUATE APTITUDE TEST IN ENGINEERING
Organizing Institute: IIT, Roorkee 27/80
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: singleand
multi-stage, differential and operational, feedback, and power. Frequency response of amplifiers. Simple opamp
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.
GATE 2009 GRADUATE APTITUDE TEST IN ENGINEERING
28/80 Organizing Institute: IIT, Roorkee
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.