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 differential equations.
Transform Theory: Fourier transform,Laplace transform,
Z-transform.
INSTRUMENTATION
ENGINEERING
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 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 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, P-I, 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.
