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Section 1: Engineering Mathematics

**Linear Algebra**:

- Matrix Algebra
- Systems of linear equations
- Eigenvalues
- Eigenvectors

**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 integral, Surface integral
- Volume integral
- Stokes’s theorem
- Gauss’s theorem
- Green’s theorem

**Differential equations**:

- First order equations (linear and nonlinear)
- Higher order linear differential equations with constant coefficients
- Method of variation of parameters
- Cauchy’s equation
- Euler’s equation
- Initial and boundary value problems
- Partial Differential Equations
- Method of separation of variables

**Complex variables**:

- Analytic functions
- Cauchy’s integral theorem
- Cauchy’s integral formula
- Taylor series
- Laurent series
- Residue theorem
- Solution integrals

**Probability and Statistics**:

- Sampling theorems
- Conditional probability
- Mean, Median, Mode
- Standard Deviation
- Random variables
- Discrete and Continuous distributions
- Poisson distribution
- Normal distribution
- Binomial distribution
- Correlation analysis
- Regression analysis

**Numerical Methods**:

- Solutions of nonlinear algebraic equations
- Single and Multi-step methods for differential equations

**Transform Theory**:

- Fourier Transform
- Laplace Transform

Section 2: Electric Circuits

- 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,
- Thevenin’s theorem,
- Norton’s theorem,
- Superposition theorem,
- Maximum power transfer theorem,
- Two-port networks,
- Three phase circuits,
- Power and power factor in AC circuits.

Section 3: Electromagnetic Fields

- Coulomb’s Law
- Electric Field Intensity
- Electric Flux Density
- Gauss’s Law
- Divergence
- Electric field and potential due to point
- line, plane and spherical charge distributions
- Effect of dielectric medium
- Capacitance of simple configurations
- BiotSavart’s law
- Ampere’s law, Curl
- Faraday’s law
- Lorentz force
- Inductance
- Magnetomotive force
- Reluctance
- Magnetic circuits
- Self and Mutual inductance of simple configurations

Section 4: Signals and Systems

- 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

Section 5: Electrical Machines

- Single phase transformer:
- equivalent circuit, phasor diagram
- open circuit and short circuit tests
- regulation and efficiency

- Three phase transformers:
- connections
- parallel operation
- Autotransformer
- 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:
- the 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 the synchronous motor, characteristics
- Types of losses and efficiency calculations of electric machines

Section 6: Power Systems

- 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 overcurrent
- differential and distance protection
- Circuit breakers
- System stability concepts
- Equal area criterion

Section 7

*:*Control Systems- 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 LeadLag compensators
- P, PI, and PID controllers
- State space model, State transition matrix

Section 8

*:*Electrical and Electronic Measurements

- 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

Section 9

*:*Analog and Digital Electronics- 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

Section 10

*:*Power Electronics- 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

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