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
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,
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.
Basics of Circuits and Measurement Systems:
Kirchoff’s laws, mesh and nodal Analysis. Circuit theorems.
One-port and two-port Network Functions. Static and dynamic
characteristics of Measurement Systems. Error and
uncertainty analysis. Statistical analysis of data and curve
Transducers, Mechanical Measurement and Industrial
Resistive, Capacitive, Inductive and
piezoelectric transducers and their signal conditioning.
Measurement of displacement, velocity and acceleration
(translational and rotational), force, torque, vibration and
shock. Measurement of pressure, flow, temperature and liquid
level. Measurement of pH,
conductivity, viscosity and humidity.
Characteristics of diode, BJT, JFET and MOSFET. Diode
circuits. Transistors at low and high frequencies,
Amplifiers, single and multi-stage. Feedback amplifiers.
Operational amplifiers, characteristics and circuit
configurations. Instrumentation amplifier. Precision
rectifier. V-to-I and I-to-V converter. Op-Amp based active
filters. Oscillators and signal generators.
Combinational logic circuits, minimization of Boolean
functions. IC families, TTL, MOS and CMOS. Arithmetic
circuits. Comparators, Schmitt trigger, timers and
mono-stable multi-vibrator. Sequential circuits, flip-flops,
counters, shift registers. Multiplexer, S/H circuit.
Analog-to-Digital and Digital-to-Analog converters. Basics
of number system. Microprocessor applications, memory and
input-output interfacing. Microcontrollers.
Signals, Systems and Communications:
Periodic and aperiodic signals. Impulse response, transfer function
and frequency response of first- and second order systems.
Convolution, correlation and characteristics of linear time
invariant systems. Discrete time system, impulse and
frequency response. Pulse transfer function. IIR and FIR
filters. Amplitude and frequency
modulation and demodulation. Sampling theorem, pulse code
modulation. Frequency and time division multiplexing.
Amplitude shift keying, frequency shift keying and pulse
shift keying for digital modulation.
Electrical and Electronic Measurements:
Bridges and potentiometers, measurement of R,L and C. Measurements
of voltage, current, power, power factor and energy. A.C &
D.C current probes. Extension of instrument ranges. Q-meter
and waveform analyzer. Digital voltmeter and multi-meter.
Time, phase and frequency measurements. Cathode ray
oscilloscope. Serial and
parallel communication. Shielding and grounding.
Control Systems and Process Control:
Feedback principles. Signal flow graphs. Transient Response,
steady-state-errors. Routh and Nyquist criteria. Bode plot,
root loci. Time delay systems. Phase and gain margin. State
space representation of systems. Mechanical, hydraulic and
pneumatic system components. Synchro pair, servo and step
motors. On-off, cascade, P, PI, P-I-D, feed forward and
derivative controller, Fuzzy controllers.
Analytical, Optical and Biomedical Instrumentation:
Mass spectrometry. UV, visible and IR spectrometry. X-ray and
nuclear radiation measurements. Optical sources and
detectors, LED, laser, Photo-diode, photo-resistor and their
characteristics. Interferometers, applications in metrology.
Basics of fiber optics. Biomedical instruments, EEG, ECG and
measurements. Ultrasonic transducers and Ultrasonography.
Principles of Computer Assisted Tomography.