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.
Cauchy's integral theorem and integral formula
Taylor's and Laurent's series
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
Divergence and Curl, Vector identities
Line, Surface and Volume integrals
Gauss and Green's theorems.
mode and standard deviation
discrete and continuous distributions
Poisson and binomial distributions
solutions of non-linear algebraic equations
Iterative methods for solving differential equations
Regression and correlation analysis
Voltage and current sources
ideal and practical v – i relationships of resistor
mutual inductor and capacitor
transient analysis of RLC circuits with dc excitation.
mesh and nodal analysis
Thevenin, Norton, maximum power transfer and reciprocity theorems.
Peak-, average- and rms values of ac quantities
active- and reactive power
impedance and admittance
series and parallel resonance
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
Fourier and z – transforms
frequency response of first and second order linear time invariant systems
impulse response of systems
Discrete time system
pulse transfer function
DFT and FFT
basics of IIR and FIR filters.
signal flow graph
steady – state – errors
phase and gain margin
Routh and Nyquist criteria
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
on-off, P, P – I, P – I – D
cascade, feedforward, and ratio controllers.
Characteristics and applications of diode
BJT and MOSFET
small signal analysis of transistor circuits
Characteristics of operational amplifiers
applications of opamps
active filters and other circuits
Oscillators, signal generators
voltage controlled oscillators and phase locked loop.
Combinational logic circuits
minimization of Boolean functions
TTL and CMOS
multi – vibrators
timers and counter
sample – and – hold circuit
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
memory and input-output interfacing; basics of data acquisition systems.
systematic and random errors in measurement
expression of uncertainty – accuracy and precision index
propagation of errors
PMMC, MI and dynamometer type instruments
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
timer / counter
phase and frequency measurements
shielding and grounding.
Resistive -, capacitive -, inductive -, piezoelectric -, Hall effect sensors and associated signal conditioning circuits
transducers for industrial instrumentation
displacement ( linear and angular )
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 )
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
laser, photo – diode
light dependent resistor and their characteristics
applications in metrology
basics of fiber optic sensing.