Sections 
Topics 
Section 1: Engineering Mathematics

Linear Algebra: Matrix algebra, systems of linear equations, consistency and rank, Eigen values, and Eigen vectors.
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 equation (linear and nonlinear), second order linear differential equations with constant coefficients, method of variation of parameters, Cauchy’s and Euler’s equations, initial and boundary value problems, solution of partial differential equations: variable separable method.
Analysis of complex variables: Analytic functions, Cauchy’s integral theorem, and integral formula, Taylor’s and Laurent’s series, residue theorem, solution of integrals.
Probability and Statistics: Sampling theorems, conditional probability, mean, median, mode, standard deviation, and variance; random variables: discrete and continuous distributions: normal, Poisson, and binomial distributions.
Numerical Methods: Matrix inversion, solutions of nonlinear algebraic equations, iterative methods for solving differential equations, numerical integration, regression, and correlation analysis.

Section 2: Electricity and Magnetism

Coulomb’s Law, Electric Field Intensity, Electric Flux Density, Gauss’s Law, Divergence, Electric field and potential due to point, line, plane, and spherical charge distributions, Effect of the dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.

Section 3: Electrical Circuits and Machines

Voltage and current sources: independent, dependent, ideal, and practical; vi relationships of resistor, inductor, mutual inductance, and capacitor; transient analysis of RLC circuits with dc excitation.
Kirchoff’s laws, mesh and nodal analysis, 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, locus diagrams, the realization of basic filters with R, L, and C elements. transient analysis of RLC circuits with ac excitation.
Oneport and twoport networks, driving point impedance, and admittance, open, and short circuit parameters.
Single phase transformer: equivalent circuit, phasor diagram, open circuit, and short circuit tests, regulation and efficiency; Three phase induction motors: the principle of operation, types, performance, torquespeed characteristics, noload and blocked rotor tests, equivalent circuit, starting and speed control; Types of losses and efficiency calculations of electric machines.

Section 4: Signals and Systems

Periodic, aperiodic, and impulse signals; Laplace, Fourier, and ztransforms; transfer function, the frequency response of first and second order linear timeinvariant systems, the impulse response of systems; convolution, correlation.Discretetime system: impulse response, frequency response, pulse transfer function; DFT and FFT; basics of IIR and FIR filters.

Section 5: Control Systems

Feedback principles, signal flow graphs, transient response, steadystateerrors, Bode plot, phase and gain margins, Routh and Nyquist criteria, root loci, design of lead, lag and leadlag compensators, statespace representation of systems; timedelay systems; mechanical, hydraulic and pneumatic system components, synchro pair, servo, and stepper motors, servo valves; onoff, P, PI, PID, cascade, feedforward, and ratio controllers, tuning of PID controllers and sizing of control valves.

Section 6: Analog Electronics

Characteristics and applications of the diode, Zener diode, BJT, and MOSFET; small signal analysis of transistor circuits, feedback amplifiers. Characteristics of ideal and practical operational amplifiers; applications of opamps: adder, subtractor, integrator, differentiator, difference amplifier, instrumentation amplifier, precision rectifier, active filters, oscillators, signal generators, voltage controlled oscillators, and phase locked loop, sources, and effects of noise and interference in electronic circuits.

Section 7: Digital Electronics

Combinational logic circuits, minimization of Boolean functions. IC families: TTL and CMOS. Arithmetic circuits, comparators, Schmitt trigger, multivibrators, sequential circuits, flip flops, shift registers, timers, and counters; sampleandhold circuit, multiplexer, analogtodigital (successive approximation, integrating, flash and sigmadelta) and digitaltoanalog converters (weighted R, R2R ladder and current steering logic). Characteristics of ADC and DAC (resolution, quantization, significant bits, conversion/settling time); basics of number systems, Embedded Systems: Microprocessor and microcontroller applications, memory and inputoutput interfacing; basics of data acquisition systems, basics of distributed control systems (DCS) and programmable logic controllers (PLC).

Section 8: Measurements

SI units, standards (R, L, C, voltage, current, and frequency), systematic and random errors in measurement, expression of uncertainty – accuracy and precision, propagation of errors, and linear and weighted regression.
Bridges: Wheatstone, Kelvin, Megohm, Maxwell, Anderson, Schering, and Wien for measurement of R, L, C and frequency, Qmeter. Measurement of voltage, current, and power in single and threephase circuits; ac and DC probes; true RMS meters, voltage and current scaling, instrument transformers, timer/counter, time, phase and frequency measurements, digital voltmeter, digital multimeter; oscilloscope, shielding, and grounding.

Section 9: Sensors and Industrial Instrumentation

Resistive, capacitive, inductive, piezoelectric, Hall effect sensors, and associated signal conditioning circuits; transducers for industrial instrumentation: displacement (linear and angular), velocity, acceleration, force, torque, vibration, shock, pressure (including low pressure), flow (variable head, variable area, electromagnetic, ultrasonic, turbine, and open channel flow meters) temperature (thermocouple, bolometer, RTD (3/4 wire), thermistor, pyrometer, and semiconductor); liquid level, pH, conductivity and viscosity measurement. 420 twowire transmitters.

Section 10: Communication and Optical Instrumentation

Amplitude and frequency modulation and demodulation; Shannon’s sampling theorem, pulse code modulation; frequency and time division multiplexing, amplitude, phase, frequency, quadrature amplitude, pulse shift keying for digital modulation; optical sources and detectors: LED, laser, photodiode, light dependent resistor, square law detectors, and their characteristics; interferometer: applications in metrology; basics of fibre optic sensing. UVVIS Spectrophotometers, Mass spectrometers.
