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
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
Complex variables: Analytic functions, Cauchy’s integral theorem and
integral formula, Taylor’s and Laurent’ series, Residue theorem, solution
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.
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 fitting.
Transducers, Mechanical Measurement and Industrial Instrumentation:
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.
Analog Electronics: 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
Digital Electronics: 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.
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 EMG. Clinical
measurements. Ultrasonic transducers and Ultrasonography. Principles of
Computer Assisted Tomography.