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 in 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 for 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 in 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 in beams, beams with 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 beamspropped cantilevers and fixed beams Columns: Buckling and stability, Euler’s equations for columns with different support conditions,
Preliminaries, Concept of continuum, Properties of fluids – density – pressure – viscosity - surface tension - capillarity - vapour pressure, Fluid statics, Basic equations of fluid statics, Variation of pressure in a fluid, - Manometry - Forces on surfaces and bodies in fluids, Floatation - stability of bodies in fluid -metacentric height and its measurement, Fluids in rigid body motion, Fluid kinematics -Eulerian and Lagrangian description - local and material rates - deformation of a fluid element -strain rate-velocity relations, Graphical description of flow – streamlines - path lines - streak lines - stream tube, Fluid dynamics -concept of the control volume -Reynolds transport equation and its use to formulate fluid mechanicsproblems, Integral and differential forms of the continuity - momentum and energy equations, Illustrativeexamples.
One dimensional flow through pipes, Non viscous equation for the flow through a stream tube and along a stream line – Euler‘s equation – Bernoulli‘s equation, - Energy equation, Applications of the one dimensional equations - velocity and flow measuring devices and quasi steady problems, Laminar and turbulent flow through pipes - Hagen- Poiseuille equation - Darcy-Weisbach equation - pipe friction -Moody‘s chart - minor losses in pipes
Two dimensional incompressible inviscid flows – Vorticity - Vortex tube - Irrotational flow - Velocity potential, Stream function - relation between stream function and potential function in ideal flows -Equation of a streamline - governing equations, Fundamental flow patterns, Combination of basic patterns - Rankine half body - Rankine oval - Doublet and flow over a cylinder, Magnus effect and the calculation of lift on bodies.
Plane viscous flow past bodies, The boundary layer - Prandtl‘s boundary layer equations, Blasius solution for the boundary layer over a flat plate, Karman‘s Momentum Integral equations - Solutions using simple profiles for the boundary layer on flat plate - calculation of skin friction drag.
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 in 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 solid solubility, 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 –case 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 boundaryhardening, 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,
Applications of ferrous and non ferrous alloys-steel- low, medium, high carbon steels-Stainless steels ferritic,austenitic, martensitic, duplex steels-tool steels cast iron- gray, white, ductile cast irons- copper and its alloysaluminium and its alloys-magnesium and alloys- titanium and its alloys-refractories- super alloys-ceramics--composite and glasses-shape memory alloys- Nano materials, bio materials-Optical fibers
Introduction to Machine Drawing: Conversion of pictorial views to orthographic views 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 for 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.