Sections

Topics

Section 1 – Engineering Mathematics

 Linear Algebra: Matrix algebra, systems of linear equations, Eigenvalues and Eigenvectors.
 Calculus: Mean value theorems, theorems of integral calculus, partial derivatives, maxima and minima, multiple integrals, Fourier series, vector identities, line, surface and volume integrals, Stokes, Gauss and Green’s theorems.
 Differential equations: First order linear and nonlinear differential equations, higher order linear differential equations with constant coefficients, method of separation of variables, Cauchy’s and Euler’s equations, initial and boundary value problems, solution of partial differential equations.
 Analysis of complex variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’s series, residue theorem.
 Probability and Statistics: Sampling theorems, conditional probability, mean, median, mode and standard deviation, random variables, discrete and continuous distributions: normal, Poisson and binomial distributions. Tests of Significance, statistical power analysis, and sample size estimation.
 Linear Regression and correlation analysis;
 Numerical Methods: Matrix inversion, numerical solutions of nonlinear algebraic equations, iterative methods for solving differential equations, numerical integration.

Section 2 – Electrical Circuits

 Voltage and current sources – independent, dependent, ideal and practical; vi relationships of resistor, inductor and capacitor; transient analysis of RLC circuits with de excitation; Kirchoffs laws, superposition, Thevenin, Norton, maximum power transfer and reciprocity theorems; Peak, average and rms values of ac quantities; apparent, active and reactive powers; phasor analysis, impedance and admittance; series and parallel resonance, realization of basic filters with R, L and C elements, Bode plot.

Section 3 – Signals and Systems

 Continuous and Discrete Signal and Systems – Periodic, aperiodic and impulse signals; Sampling theorem; Laplace and Fourier transforms; impulse response of systems; transfer function, frequency response of first and second order linear time invariant systems, convolution, correlation. Discrete time systems – impulse response, frequency response, DFT, Z – transform; basics of IIR and FIR filters.

Section 4 Analog and Digital Electronics

 Basic characteristics and applications of diode, BJT and MOSFET; Characteristics and applications of operational amplifiers difference amplifier, adder, subtractor, integrator, differentiator, instrumentation amplifier, buffer, filters and waveform generators. Number systems, Boolean algebra; combinational logic circuits – arithmetic circuits, comparators, Schmitt trigger, encoder/decoder, MUX/DEMUX, multivibrators; Sequential circuits – latches and flipflops, state diagrams, shift registers and counters; Principles of ADC and DAC; Microprocessor architecture, interfacing memory and input output devices.

Section 5 – Measurements and Control Systems

 SI units, systematic and random errors in measurement, expression of uncertainty – accuracy and precision index, propagation of errors; PMMC, MI and dynamometer type instruments; de potentiometer; bridges for measurement of R, Land C, Qmeter. Basics of control system – transfer function.
