Matrices and Vector spaces: Rank of matrix, Echelon and normal form, Solutions of linear systems of algebraic equations, Eigen values and Eigen vectors, Cayley- Hamilton theorem (no proof). Vector Spaces- Subspaces,-Linear Independence of vectors-Linearspan-Dimension and Basis. Linear transformations.
Fourier series and Fourier integrals: Fourier series of Periodic functions-Euler formulae for Fourier coefficients- functions having period 2π , arbitrary period- even and odd functions-half range expansions, Fourier integral, Fourier cosine and sine transformations, linearity property, transform of derivatives, convolution theorem (no proof)
Laplace transforms: Linearity property, transforms of elementary functions, Laplace transforms of derivatives and integrals, differentiation and integration of transforms,convolution theorm (no proof), use of Laplace transforms in the solution of initial value problems, unit step function, impulse function - transform of step functions, transforms of periodic functions.
Vector calculus : Scalar and Vector point functions-Gradient and directional derivative of a scalar point functions.- Divergence and Curl of a vector point functions- their physical meanings.Evaluation of line integral, surface integral and volume integrals, Gauss’s divergence theorem,. Stoke’s theorem (No Proof of these theorem), conservative force fields,scalar potential.
1. R.K. Jain, S.R.K Iyengar: Advanced Engineering Mathematics, Narosa publishers.19912. C.R. Wilie & L.C. Barrett: Advanced Engineering Mathematics, MGH Co.
1. Larry C Andrews, Ronald C Philips: Mathematical Techniques fo Engineers & Scientists, PHI2. M.C. Potter, J.L. Goldberg: Advanced Engineering Mathematics, Oxford universitypress3. B. S. Grewal: Higher Engineering Mathematics, Khanna publishers,1986
Conducting materials: Review of metallic conduction on the basis of free electron theory- Fermi-Dirac distribution – variation of conductivity with temperature and composition, Materials for electric resistances- general electric properties: brushes of electrical machines, lamp filaments, fuses and solder.Semiconductors: Compound semiconductors – basic ideas of amorphous and organic semiconductor – preparation of semiconductor materials – zone-refining technique – fabrication of p-n-p junction.Magnetic materials: Classification of magnetic materials – origin of permanent magnetic dipoles – ferromagnetism - hysterisis curve – hard and soft magnetic materials – magnetic material used in electrical machines, instruments and relays.
Dielectrics: dielectric polarization under static fields – electronic, ionic and dipolar polarizations – behavior of dielectrics in alternating fields – mechanism of breakdown in gases, liquids and solids - factors influencing dielectric strength – capacitor materials Insulating materials – complex dielectric constant – dipolar relaxation dielectric loss insulator materials used – inorganic materials (mica, glass, porcelain, asbestos) – organic materials (paper, rubber, cotton silk, fibre, wood, plastics, bakelite)- resins and varnishes – liquid insulators (transformer oil) – gaseous insulators (air, SF6, and hydrogen ) – ageing of insulators.
Materials for special applications: materials for solar cells/fuels cells/battery- materials for coatings for enhanced solar thermal energy collection – solar selective coatings- cold mirror coatings- heat mirror coatings – antireflection coatings, Sintered alloys for breaker/switch contacts – arcing tips.
Modern techniques for Material Studies: optical microscopy – electron microscopy – photoelectron spectroscopy – atomic absorption spectroscopy – magnetic resonance – nuclear magnetic resonance – electron spin resonance – ferromagnetic resonance.
Fluids and their properties: Fluids, shear stress in a moving fluid, viscosity, Newtonian and non-Newtonian fluids, viscosity in liquids and gases. Fluid statics: pressure, variation of pressure in a static fluid, absolute and gauge pressure, measurement of gauge pressure.Kinematics of fluid flow: Eulerian and Langragain approaches, classification of fluid flow as steady and unsteady flow, uniform and non uniform flow, laminar and turbulent flow, Path line, stream line, streak line and stream tube, one, two, and three dimensional flow, velocity and accelerations in steady and unsteady flow. Basic Hydrodynamics: Ideal fluids, equations of continuity in the differential form, rotational and irrotational flow, circulation and vorticity, Stream function, Velocity potential, one dimensional flow along a stream line, Bernoulli’s equation and its limitations, measurement of velocity, Pitot tube and Pitot-static tube, venturi meter, orifice meter, flow nozzles, notches and weirs.
Steady flow of incompressible fluids in pipes: Laminar and turbulent flows, critical Reynolds number, hydraulic radius, general equation for friction, laminar flow in circular pipes, Darcy- Weisbach equation, friction factor, equivalent pipes, minor losses in pipes, Development of boundary layer. Dimensional Analysis & Similitude: Rayleigh’s method, Buckingharm’s Pi theorem, nondimensional parameters in fluid mechanics and machinery – principles of similitude – geometric, kinematic and dynamics similarities – model studies. Physical meaning of important dimensional groups of fluid mechanics and their practical use.
Dynamic action of fluid: Momentum equation applied to a control volume, impact of jets, flow of an incompressible fluid over fixed and moving vanes, work done and efficiency.Hydraulic turbines: velocity triangles, impulse and reaction turbines, Pelton wheel, Francis turbine and Kaplan turbine, their constructional features and performance characteristics – non dimensional parameters for comparative study of turbine performance, theory of draft tubes, speed regulation of turbines, selection of type and speed of turbines.
Pumping machinery: general features of positive displacement and rotodynamic pumps, cetrifugal pumps, classification, principle of working, velocity diagrams, losses in pumps, circulatory flow, multistage pumps, propeller pumps, priming, cavitation and its significance.Reciprocating pumps: Acceleration head, effect of friction, use of air vessels, efficiencies, pump characteristics.
Review of network theorem – steady state AC analysis-mesh and node analysis, mesh and node analysis by inspection, superposition theorem, reciprocity theorem, Thevenin’s theorem, Norton’s theorem, maximum power transfer theorem.
Network topology – definition of graph,tree, incidence matrix, tie-set matrix, cut-set matrix, application of graph theoretic methods to formulation of network equation, current variable and voltage variable methods.Coupled circuit – self and mutual inductance analysis of coupled coils, dot rule, conductively coupled equivalent circuits, coupling coefficient, linear transformer, ideal transformer.
Polyphase systems – balanced and unbalanced loads – unbalanced three wire and four wire star connected load, displacement neutral method, power measurement using wattmeter.Circuit transients – direct current transients - RL, RC, RLC transients, alternating current transients – application of Laplace transform for transients analysis.
Fourier method of waveform analysis – frequency spectrum of periodic signals, trigonometric Fourier series, exponential Fourier series.Fourier transform and inverse Fourier transform – properties of Fourier transforms, continuous amplitude and phase spectra.
General Principles of Measurements, Standards: Absolute and Working Standards, Calibration of Meters, Qualities of Measurements, Characteristics, Errors in Measurement and its Analysis, Direct Deflecting Instruments. Moving Coil, Moving Iron, Dynamo Meter, Induction, Thermal, Electrostatic and Rectifier Type, Shunts and Multipliers, Various Types of Galvanometers.
Measurement of Current, Voltage and Resistance, Measurement of Insulation Resistance, Earth Resistance, Earth Tester; Measurement of Power and Energy, Dynamometer Type Wattmeter, Error and Compensation, Ampere Hour Meter, Single and Three Phase Energy Meters (Induction Type), Calibration, Trivector Meter, Frequency Meters, Power Factor Meters, Current Transformers and Potential Transformers.
Null Deflection Method – Measurement of Resistance; Current, Voltage and Power – Direct Current Potentiometer-Wheatstone Bridge-Kevin Double Bridge-Carry Foster Slide Wire Bridge-Bridge Current Limitations-Localization of Cable Fault by Murray and Varley Loop Tests-A.C Potentiometers-Various A.C Bridges and Measurement of Inductance & Capacitance; Magnetic Measurements: Classification-Measurement of Flux and Permeability-Hibbert’s Magnetic Standard –Flux Meter, Hall Effect Gauss meter, Ballistic Galvanometer, Calibration-Vibration Galvanometer-B.H. Curve and Permeability and Measurement on bar and ring specimens-Hysteresis Measurement- Core Loss Measurement with Lloyd Fishes square
Illumination: Laws of Illumination- Polar Curves- Photometry- Luminous Efficiency- Measurement of Illumination of Different Light Sources- Illumination of Surfaces- Levels of Illumination; Digital Measurements and Meters; Oscilloscope- Basic Principle of Signal Display- Triggered Sweep CRO- Trigger Pulse Circuit- Delay Line in Triggered Sweep- Sync- Selector for continuous Sweep CRO- Dual Beam CRO- Dual Trace Oscilloscope-Applications.
DC power supplies - power transformers - rectification - half wave, full wave, bridge - expression for ripple factor, efficiency, comparison, diode ratings. filters - capacitor - inductor LC filters- use of bleeder resistor - voltage multipliers - dual power supplies - zener and avalanche diodes - simple and series voltage regulator. Special semiconductor devices: Principles and operation of photodiodes, PIN diodes, phototransistors, LED, UJT. MOSFET- Enhancement and depletion type NMOS, PMOS AND CMOS - basic principles & characteristics.
Small Signal amplifiers: Bipolar junction transistor – configurations, characteristics - current amplification factors - relations between alpha & beta – comparison. BJT amplifiers: Biasing techniques of BJT- stabilization of operating point - h-parameters - CE RC coupled amplifier - concept of load lines- frequency response of RC coupled amplifier - frequency analysis of R C coupled amplifier - lower cut-off frequency - upper cut-off frequency - 3 db bandwidth.FET Amplifiers: Principle of operation, characteristics, Common source amplifier- design, frequency response-applications
Power amplifier - classification - class A, B, AB and C power amplifiers-tuned amplifier- pushpull and complementary symmetry power amplifier –Harmonic distortion– Heat sinks.Feed-back amplifiers: concept of Negative and positive feedback – Bark Hausen criteria -low frequency sinusoidal oscillators High frequency oscillators – types- LC, Crystal oscillators –circuit diagram-description-applications
Pulse Circuits:-Different types Pulse circuits - pulse characteristics - Pulse shaping using RC circuits - Differentiating and integrating circuits –applications. Clipping and clamping circuits using diodes - Transistor as a switch– simple sweep circuits-bootstrap sweep.Multivibrators-astable, monostable and bistable ciruits using BJTs-applications