ENGINEERING MATHEMATICS
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
Measurement Basics and Metrology: Static and
dynamic characteristics of measurement
systems. Standards and calibration. Error
and uncertainty analysis, statistical
analysis of data, and curve fitting. Linear
and angular measurements; Measurement of
straightness, flatness, roundness and
roughness.
Transducers, Mechanical Measurements and
Industrial Instrumentation: Transducers -
elastic, resistive, inductive, capacitive,
thermo-electric, piezoelectric,
photoelectric, electro-mechanical,
electro-chemical, and ultrasonic.
Measurement of displacement, velocity
(linear and rotational), acceleration,
shock, vibration, force, torque, power,
strain, stress, pressure, flow, temperature,
humidity, viscosity, and density. energy
storing elements, suspension systems and
dampers.
Analog Electronics: Characteristics of
diodes, BJTs, JFETs and MOSFETs; Diode
circuits; Amplifiers: single and
multi-stage, feedback; Frequency response;
Operational amplifiers - design,
characteristic, linear and non-linear
applications: difference amplifiers;
instrumentation amplifiers; precision
rectifiers, I-to-V converters, active
filters, oscillators, comparators, signal
generators, wave shaping circuits.
Digital Electronics: Combinational logic
circuits, minimization of Boolean functions;
IC families (TTL, MOS, CMOS), arithmetic
circuits, multiplexer and decoders.
Sequential circuits: flip-flops, counters,
shift registers. Schmitt trigger, timers,
and multivibrators. Analog switches,
multiplexers, S/H circuits.
Analog-to-digital and digital-to-analog
converters. Basics of computer organization
and architecture. 8-bit microprocessor
(8085), applications, memory, I/O
interfacing, and microcontrollers.
Signals and Systems: Vectors and matrices;
Fourier series; Fourier transforms; Ordinary
differential equations. Impulse and
frequency responses of first and second
order systems. Laplace transform and
transfer function, convolution and
correlation. Amplitude and frequency
modulations and demodulations. Discrete time
systems, difference equations, impulse and
frequency responses; Z-transforms and
transfer functions; IIR and FIR filters.
Electrical and Electronic Measurements:
Measurement of R, L and C; bridges and
potentiometers. Measurement of voltage,
current, power, power factor, and energy;
Instrument transformers; Q meter, waveform
analyzers. Digital volt-meters and
multi-meters. Time, phase and frequency
measurements; Oscilloscope. Noise and
interference in instrumentation.
Control Systems & Process Control:
Principles of feedback; transfer function,
signal flow graphs. Stability criteria, Bode
plots, root-loci, Routh and Nyquist
criteria. Compensation techniques; State
space analysis. System components:
mechanical, hydraulic, pneumatic, electrical
and electronic; Servos and synchros; Stepper
motors. On-off, cascade, P, PI, PID and
feed-forward controls. Controller tuning and
general frequency response.
Analytical, Optical and Biomedical
Instrumentation: Principles of spectrometry,
UV, visible, IR mass spectrometry, X-ray
methods; nuclear radiation measurements,
gas, solid and semi conductor lasers and
their characteristics, interferometers,
basics of fibre optics, transducers in
biomedical applications, cardiovascular
system measurements, instrumentation for
clinical laboratory.
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