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 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
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.
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 signal generators.
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
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
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.