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.
separation of variables
solutions of onedimensional diffusion equation
first and second order one – dimensional wave equation and two-dimensional Laplace equation.
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 Greens theorems.
Definitions of probability and sampling theorems
Conditional probability
Discrete Random variables
Poisson and Binomial distributions
Continuous random variables
normal and exponential distributions
Descriptive statistics – Mean, median, mode and standard deviation
Hypothesis testing.
Accuracy and precision
error analysis
Numerical solutions of linear and non – linear algebraic equations
Least square approximation
Newtons and Lagrange polynomials
numerical differentiation
Integration by trapezoidal and Simpsons rule
single and multi – step methods for first order differential equations.
Network graph
KCL, KVL
Node and Mesh analysis
Transient response of dc and ac networks
Sinusoidal steady ‐ state analysis
Resonance
Passive filters
Ideal current and voltage sources
Thevenins theorem, Nortons theorem, Superposition theorem, Maximum power transfer theorem
Two port networks, Three phase circuits, Power and power factor in ac circuits.
Coulombs Law
Electric Field Intensity
Electric Flux Density
Gausss Law
Divergence
Electric field and potential due to point line
plane and spherical charge distributions
Effect of dielectric medium
Capacitance of simple configurations
Biot ‐ Savarts law
Amperes law
Curl, Faradays law
Lorentz force
Inductance
Magnetomotive force
Reluctance
Magnetic circuits
Self and Mutual inductance of simple configurations.
Representation of continuous and discrete ‐ time signals
Shifting and scaling operations
Linear Time Invariant and Causal systems
Fourier series representation of continuous periodic signals
Sampling theorem
Applications of Fourier Transform
Laplace Transform and z – Transform.
Single phase transformer
equivalent circuit
phasor diagram
open circuit and short circuit tests
regulation and efficiency;
Three phase transformers
connections parallel operation
Auto ‐ transformer
Electromechanical energy conversion principles
DC machines
separately excited
series and shunt motoring and generating mode of operation and their characteristics
starting and speed control of dc motors
Three phase induction motors
principle of operation
Types
Performance
torque – speed characteristics
no – load and blocked rotor tests
equivalent circuit
starting and speed control
Operating principle of single phase induction motors
Synchronous machines
cylindrical and salient pole machines
Performance
regulation and parallel operation of generators
starting of synchronous motor
characteristics
Types of losses and efficiency calculations of electric machines.
Power generation concepts
ac and dc transmission concepts
Models and performance of transmission lines and cables
Series and shunt compensation
Electric field distribution and insulators
Distribution systems Per ‐ unit quantities
Bus admittance matrix
Gauss – Seidel and Newton – Raphson load flow methods
Voltage and Frequency control
Power factor correction
Symmetrical components
Symmetrical and unsymmetrical fault analysis
Principles of over - current
differential and distance protection
Circuit breakers
System stability concepts
Equal area criterion.
Mathematical modeling and representation of systems
Feedback principle
transfer function
Block diagrams and Signal flow graphs
Transient and Steady ‐ state analysis of linear time invariant systems
Routh – Hurwitz and Nyquist criteria
Bode plots
Root loci
Stability analysis
Lag, Lead and Lead ‐ Lag compensators
P, PI and PID controllers
State space model
State transition matrix.
Bridges and Potentiometers
Measurement of voltage
current, power, energy and power factor
Instrument transformers
Digital voltmeters and multimeters
Phase, Time and Frequency measurement
Oscilloscopes
Error analysis.
Characteristics of diodes
BJT, MOSFET
Simple diode circuits
clipping, clamping, rectifiers
Amplifiers
Biasing
Equivalent circuit and Frequency response
Oscillators and Feedback amplifiers
Operational amplifiers: Characteristics and applications
Simple active filters
VCOs and Timers
Combinational and Sequential logic circuits
Multiplexer, Demultiplexer
Schmitt trigger
Sample and hold circuits
A / D and D / A converters
8085 Microprocessor
Architecture
Programming and Interfacing.
Characteristics of semiconductor power devices
Diode]
Thyristor
Triac, GTO, MOSFET, IGBT
DC to DC conversion
Buck
Boost and Buck – Boost converters
Single and three phase configuration of uncontrolled rectifiers
Line commutated thyristor based converters
Bidirectional ac to dc voltage source converters
Issues of line current harmonics
Power factor
Distortion factor of ac to dc converters
Single phase and three phase inverters
Sinusoidal pulse width modulation.
Basic of sensors, Transducers.
Basic of data acquisition systems.
Discrete cosine transform
FIR, IIR, filter
Bilinear transformation
SHIVAM SINGH
ALL INDIA 1st RANK(EEE)
GATE-2017
SARFARAJ NAWAZ
ALL INDIA 4th RANK(EEE)
GATE-2017
ADARSH RAHUL
ALL INDIA 7th RANK(CSE)
GATE-2017
HARSH GUPTA
ALL INDIA 1st RANK(CH)
GATE-2017
MRIDUL RAKESH MISHRA
ALL INDIA 1st RANK(CE)
GATE-2017
BOBADE PRADIP
ALL INDIA 3rd RANK(ME)
GATE-2017
THADURI NAVEEN
ALL INDIA 1st RANK(IN)
GATE-2017
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