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
Transformers : working principles and elementary theory of an ideal transformer,Constructional features of single phase transformer, emf equation, turns ratio, vector diagram, equivalent circuit, impedence transformation, transformer losses, flux leakage,efficiency, open circuit and short circuit test, load test. Auto transformer – working principle and saving copper, basic idea of current transformer and potential transformer,distribution and power transformer, applications, standard rating, IS specifications.
Basic principles of electrical machines: Concepts of motoring and generating action,DC machines: Main constructional features, principles of operation, types of generators,emf equation, characteristics, applications, armature reaction and commutation, types of efficiency, speed control, testing, load of dc machines.
AC Machines : Alternator- rotating field, speed and frequency, effect of distribution of winding, coil span, characteristics, emf equation, losses and efficiency, regulation (emf method only), applications, synchronous motor-principles of operation, over excited and under excited, starting, applications, synchronous capacitor.Induction Motor: Induction motor, principles of operation, constructional features of squirrel cage and slip ring motors, torque-slip characteristics, starting, speed control,losses and efficiency.
Generation, transmission & distribution of electrical energy: Different methods of power generation-thermal, hydro-electric, nuclear, diesel, gas turbine stations(general idea only), electrical equipment i power stations, concept of bus bar, load dispatching, methods of transmission, transmission lines, overhead lines and insulators, corona and skin effect of DC & AC distribution, substation (elementary idea only)
Tension, Compression, and Shear: Normal stress and strain, stress-strain diagrams,elasticity and plasticity, linear elasticity and Hooke’s law, shear stress and strain,allowable stresses Axially loaded members: Deflections of axially loaded members, statically indeterminate structures, temperature and pre-strain effects, strain energy Analysis of stress and strain: Plane stress, plane strain, principal stresses and maximum shear stresses, Mohr’s circle fr plane stress, spherical & cylindrical pressure vessels
Torsion : Torsion of circular bars, pure shear, relation between modulus of elasticity and modulus of rigidity, power transmission, strain energy i torsion Shear force and Bending moment: Types of beams, shear force and bending moment,relation ship among load, shear force, and bending moment, shear force and bending moment diagrams
Stresses in beams: Normal strains in beams, normal stresses in beams, cross sectional shapes of beams, shear stresses i beams, beams wit axial loads, Combined axial,bending, and torsional loads.Theories of failure: Various theories of failure and their applications to ductile and brittle materials.
Deflections of beams: Differential equations of the deflection curve, deflections by integration, Macaulay’s method, moment area method, deflections of non prismatic beams, deflections of statically indeterminate beams- proped cantilevers and fixed beams Columns: Buckling and stability, Euler’s equations fr columns wth different support conditions,
Introduction to Fluid flows - distinction between fluids and solids - viscosity and its effects – forces i fluids – surface tension and its effects – basic equations of fluid static– pressure- variation of pressure i a stati fluid- absolute and gauge pressuremeasurement of gauge pressure- – pressure i the atmosphere – hydrostatic forces on plane and curved surfaces-centre of pressure – buoyancy and stability of submerged and floating bodies- metacentric height – Eulerian and Lagrangian methods – Classification of fluid flow – steady and unsteady flow – uniform and non-uniform flow – rotational and irrotational flows-one, two and three dimensional flows- stream lines – path lines –stream tube – stream surfaces – streak lines – Control volume – Reynolds Transport Equation
Basic equation for one-dimensional flow through a stream tube and along a streamline – Euler’s equation – Bernoulli’s equation and its limitations-measurement of velocity-Pitot tube-Venturimeter - Orificemeter –Rotameter-Flow through orifice-Hydraulic coefficients-Experimental determination of hydraulic coefficients-Time of emptying a tank through an orifice at its bottom-Notches and weirs - fully developed flow through pipes-Reynold’s experiment-laminar and turbulent flow- general equation fr friction –laminar flow i circular pipes – Darcy Weisbach equation – friction factor – minor losses i pipes
Introduction to two dimensional inviscid incompressible flows – equation of continuity in the differential form – velocity and acceleration-velocity potential functions and stream functions-vortex flow-uniform flow-source flow-sink flow- concept of stream functions – rotational and irrotational of flow – velocity and acceleration i steady and unsteady flow - circulation and vorticity – stream functions – velocity potential – one dimensional flow along a stream line – uniform flow – source and sink flow – free and forced vortex flow – Doublet flow – Vortex pair – Rankine half body – flow around cylinders –Magnus effect
Introduction to Boundary layers – development of boundary layer – boundary layer thickness – displacement thickness – momentum thickness – drag on a flat plate –boundary layer separation – control of separation – wakes-Navier Stokes equation –Blassius solutions fr flow over a flat plate - turbulent flow – Karman vortex street –Vortex shedding – vortex sheet – vortex filament – flow visualization technique –Subsonic Wind Tunnel testing, Heleshaw experiment
Crystallography : crystal structure, space lattice, crystal systems, miller indices of crystal planes and directions, atomic density of crystallographic planes and lines, atomic packing factor, coordination number, inter planar spacing.Solidification of metals : homogenous and heterogeneous nucleation, crystal growth, grains and grain boundaries, equi-axed and columnar grains, dendritic pattern, polymorphism.Crystal imperfections : point defect, line defect, edge dislocation, screw dislocation, interaction between dislocation, planar defects, stacking faults, grain boundary, twist and twin boundaries,volume defects.Diffusion : mechanism of diffusion n crystals, types of diffusion, factors affecting diffusion, Fick’s law of diffusion, metallurgical application of diffusion.
Phase: Equilibrium between phases, Gibb’s phase rule, solid solution,interstitial, substitutional, ordered and disordered types, Hume – Rothery rules,equilibrium phase diagrams of binary alloys complete solid solubility, partial solidsolubility, no solid solubility,: eutectic, peritectic and eutectoid reactions, Cu- Ni, Cd-Bi,Pb-Sn, Ag-Pt, and Fe-C systems as examples.Heat treatment of steel: Definition and aims of heat treatment, T T T diagram, isothermal and continuous cooling, annealing, normalizing, hardening, tempering, austempering, martempering,hardenability of steels, jomini test, surface treatments –cases hardening, carburising, cyaniding,nitriding, flame hardening, induction hardening, metal coating- hot dipping, electro plating, metal cladding, impregnation, metal spraying.
Deformation of metals : Elastic, anelastic and visco elastic behaviour,plastic deformation, mechanism of slip, slip planes and slip directions, mechanism of twinning, strengthening mechanisms, work hardening, grain boundary hardening,precipitation hardening, cold working, hot working, recovery, recrystalisation and grain growth.Failure of metals : creep, mechanism of creep, creep curves, creep resistant materials, fracture,brittle fracture, Griffith’s theory, ductile fracture, ductile-brittle transition, protection against fracture, fatigue, mechanism of fatigue, S-N Curve.
Cast Irons : classification- grey, white, malleable, and spheroidal graphite cast irons, composition, properties and uses.Steels : Classification of steels, functions of alloying elements of steels, composition and properties of common commercially important alloy steels.Non-ferrous alloys :
Screwed fastenings: Screw thread forms, V and Square threads, Conventional representation of threads, Hexagonal headed bolt and nut, Square headed bolt, Nut locking arrangements, Foundation bolts- ray bolt and Lewis foundation bolt.Cotter and Pin joints: Socket and Spigot joints, Gib and Cotter joint fr rectangular rods, Sleeve and Cotter joints, Knuckle joint.
Pipe joints : Coupler joints, Nipple joints, Union, Socket and Spigot joints, Integral flanged joints and Hydraulic joints.Couplings: Parallel and Tapered sunk keys, Saddle keys, Feather keys and Pin keys,Muff coupling, Protected type flange coupling, Pin type flexible coupling.Bearings : Solid journal bearings, Bushed bearings, Plummer block, Foot step bearing,Thrust bearings.
Assembly of machine parts: Machine Vice, Tail-Stock of Lathe Steam Engine parts: Stuffing box, Cross head.I.C. engine: Piston and Connecting rod.Valves: Steam stop valve, Spring loaded safety valve, Lever safety valve, Ramsbottom safety valve.