Matrix algebra
Systems of linear equations
Eigen values and Eigen vectors
First order ( linear and non – linear ) equations
higher order linear equations with constant coefficients
Euler – Cauchy equations
Laplace transform and its application in solving linear ODEs
Initial and boundary value problems.
Analytic functions
Cauchy's integral theorem and integral formula
Taylor's and Laurent's series
residue theorem
solution of integrals.
Functions of single variable
Limit, continuity and differentiability
Mean value theorems
local maxima and minima
Taylor and Maclaurin series
Evaluation of definite and indefinite integrals
application of definite integral to obtain area and volume
Partial derivatives
Total derivative
Gradient
Divergence and Curl, Vector identities
Directional derivatives
Line, Surface and Volume integrals
Stokes
Gauss and Green's theorems.
Sampling theorem
conditional probability
mean
median
mode and standard deviation
random variable
discrete and continuous distributions
normal
Poisson and binomial distributions
Matrix inversion
solutions of non-linear algebraic equations
Iterative methods for solving differential equations
numerical integration
Regression and correlation analysis
Voltage and current sources
Independent dependent
ideal and practical v – i relationships of resistor
inductor
mutual inductor 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 power
phasor analysis
impedance and admittance
series and parallel resonance
locus diagrams
realization of basic filters with R, L and C elements.
One – port and two – port networks,
driving point impedance and admittance
open-, and short circuit parameters.
Periodic, aperiodic and impulse signals
Laplace
Fourier and z – transforms
transfer function
frequency response of first and second order linear time invariant systems
impulse response of systems
Convolution
correlation.
Discrete time system
impulse response
frequency response
pulse transfer function
DFT and FFT
basics of IIR and FIR filters.
Feedback principles
signal flow graph
transient response
steady – state – errors
Bode plot
phase and gain margin
Routh and Nyquist criteria
root loci
design of lead, lag and lead – lag compensators
state – space representation of systems
time – delay systems
mechanical, hydraulic and pneumatic system components
synchro pair, servo and stepper motors
servo valves
on-off, P, P – I, P – I – D
cascade, feedforward, and ratio controllers.
Characteristics and applications of diode
Zener diode
BJT and MOSFET
small signal analysis of transistor circuits
feedback amplifiers.
Characteristics of operational amplifiers
applications of opamps
difference amplifier
Adder
Subtractor
Integrator
Differentiator
instrumentation amplifier
precision rectifier
active filters and other circuits
Oscillators, signal generators
voltage controlled oscillators and phase locked loop.
Combinational logic circuits
minimization of Boolean functions
IC families
TTL and CMOS
Arithmetic circuits
Comparators
Schmitt trigger
multi – vibrators
sequential circuits
flipflop
shift registers
timers and counter
sample – and – hold circuit
Multiplexer
analog to digital ( successive approximation, integrating, flash and sigma – delta ) and digital to analog converters ( weighted R, R – 2R ladder and current steering logic ).
Characteristics of ADC and DAC ( resolution, quantization, significant bits, conversion / settling time )
basics of number systems, 8 – bit microprocessor and microcontroller
Applications
memory and input-output interfacing; basics of data acquisition systems.
SI units
systematic and random errors in measurement
expression of uncertainty – accuracy and precision index
propagation of errors
PMMC, MI and dynamometer type instruments
dc potentiometer
bridges for measurement of R, L and C, Q – meter
Measurement of voltage
current and power in single and three phase circuit
ac and dc current 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.
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 ( differential pressure, 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.
Amplitude – and frequency modulation and demodulation
Shannon's sampling theorem
pulse code modulation
frequency and time division multiplexing
amplitude -, phase -, frequency -, pulse shift keying for digital modulation
optical sources and detectors
LED
laser, photo – diode
light dependent resistor and their characteristics
Interferometer
applications in metrology
basics of fiber optic sensing.