Complex Analytic functions and conformal mapping: curves and regions in the complex plane, complex functions, limit, derivative, analytic function, Cauchy - Riemann equations, Elementary complex functions such as powers, exponential function,logarithmic, trigonometric and hyperbolic functions. Conformal mapping: Linear fractional transformations, mapping by elementary functions like Z2, ez, sin z, cos z, sin hz, and Cos hz, Z+1/Z.
Complex integration: Line integral, Cauchy's integral theorem, Cauchy's integral formula, Taylor's series, Laurent's series, residue theorem, evaluation of real integrals using integration around unit circle, around the semi circle, integrating contours having poles, on the real axis.
Partial differential equations:Formation of partial differential equations. Solutions of equations of the form F(p, q) = 0, F(x,p,q)=0, F(y,p,q)=0, F(z,p,q)=0, F1(x,p) = F2 (y,q),Lagrange’s form Pp+Qq = R. Linear homogeneous partial differential equations with constant co-effients.
Vibrating string : one dimensional wave equation, D’Alembert’s solution, solution by the method of separation of variables. One dimensional heat equation, solution of the equation by the method of separation of variables, Solutions of Laplace’s equation over a rectangular region and a circular region by the method of separation of variables.
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. Ervin Kreyszig, Wiley Eastern - Advanced Engineering Mathematics2. Churchill R.V- Complex Variables & Applications: MGH Publishers.3. M.C.Potter - Advanced Engineering Mathematics, , J.L.Goldberg Oxford University Press
Transister Amplifiers : need for blacing, stabilization concepts of load line, small signal amplifiers, h parameters model, working principle or RC coupled amplifiers, frequency response, power amplifier, classification, theory of operation and comparison, expression fr gain Zin, Zo.Concepts of Feedback: positive and negative feedback (voltage shunt and current series feedback configuration only)
Wave shaping networks: RC differentiator and integrator, clipping and clamping circuits using diodes, differential amplifier, common mode and differential mode operations,characteristics of OPAMP, applications, summer, Integrater, Differentiator and scale changes.
p>Oscillators: sinusoidal and non sinusoidal oscillation, conditions for oscillation, basics of RC and LC oscillators (RC phase shift Oscillator and Hartely Oscillator) transister as switchs, classification, transistorized sweep generator Multivibrators : Monostables, bistables, astable generator, working principle of astable multivibrators only.
Thyristers : classifications, SCR, series and parallel operation of SCR. Single phase controlled rectifier, half wave and full wave. Half controlled and fully controlled-wave forms. Power suppliers: - Transisterised regulated power supply using Zener diodes, theory of operation, regulation characteristics.SMPS – UPS (Basic concept and block diagram treatment only)Industrial heating: Induction heating, dielectric heating, principle and applications, application of power electronics i welding.
2D problems in Cartesian co-ordinates:stress & strain at a point, components of stress & strain , Hooks law plane stress & plane strain, measurement of surface strains, construction of Mohr circle fr stress & strain strain rosettes, differential equations of equilibrium , boundary conditions, compatibility equations, stress functions. Solution by polynomials, St.Venant’s principle, bending of a cantilever loaded at the end.
2D problems in polar co-ordinates General equations n polar co-ordinates. Stress distribution symmetrical about an axis pure bending of curved bars. Strain components i polar coordinates, displacement fr symmetrical stress distribution, rotating disks, thick cylinders, pure bending of curved bars.
Analysis of stress & strain in 3D Principal stresses, stress ellipsoid, stress invariants, maximum shearing stress,homogenous deformation. Strain at a point, rotation, differential equations of equilibrium,compatibility. Equations of equilibrium n terms of displacements Stretching of a prismatic bar by its own weight Energy methods: principle of virtual work, reciprocal theorems, strain energy methods,Castigliano’s theorems.
Unsymmetric bending, shear flow, shear centre.Torsion of noncircular straight bars, elliptic cross sections. Membrane analogy. Torsion of thin tubes, open and closed sections.
First and second law of thermodynamics, Carnot theorem, Thermodynamic temperature scale, Internal Energy and entropy, Claussius inequality, entropy charge n various thermodynamic processes of ideal gases, Application of first and second law of thermodynamics fr steady flow processes, reversibility, irreversibility & Availability,Tds equations, (Helmoholtz, Gibbs functions & Maxwell relations) Claussius clapeyron equations.
Pure substance – PV, PT and TS systems – PVT surface – Properties of steam – steam table and Mollier diagram – Analysis of vapour process – thermodynamic analysis of steam power cycles – Rankine, reheat, and regenerative – binary vapour cycles – modern steam generators – performance calculations of boilers.
Ideal, perfect and real gases, Properties of Mixtures of Gases and Gas and vapours:Dalton’s law of Partial Pressure, Amagat’s law of Partial volume, Volumetric and Gravimetric analysis of Gas mixtures, Gibb’s Dalton Law, Mean value of Gas constant,Equivalent Molecular weight, Density, Specific volume, specific heat and Molar heat capacity of gas mixture, Advanced Problem on Adiabatic Mixing.Air compressors – Reciprocating and rotary compressors
Fuels and combustion – Solid, liquid and gaseous fuels – calorific value – calorimeter –combustion equation – Air – Fuel ratio gravimetric & volumetric analysis – excess air Enthalpy and Internal Energy of Combustion – application of first law of thermodynamics to chemical reaction (combustion), adiabatic flame temperature –application of second law of thermodynamics to chemical reaction.
Dimensional Analysis & Similitude : Rayleigh’s method, Buckingham’s Pi theorem,nondimensional parameters i fluid mechanics and machinery – principles of similitude –geometric, kinematic and dynamic 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: Impulse and Reaction turbines, Pelton wheel, Francis turbine and Kaplan turbine, their constructional features, Velocity triangles, Performance characteristics – non dimensional parameters fr comparative study of turbine study of turbine performance, Specific speed, Unit speed, Unit power, theory of draft tubes, speed regulation of turbines, Cavitation, Selection of type and speed of turbines.
Pumping machinery: general features of positive displacement and rotodynamic pumps,centrifugal pumps, classification, principle of working, velocity diagrams, work done,efficiency, minimum speed, specific speed, losses n pumps, circulatory flow, multistage pumps, propeller pumps, priming, Cavitation and its significance.Reciprocating pumps: Working, single acting and double acting pumps, Slip,Acceleration head, effect of friction, use of air vessels, Indicator diagrams, efficiencies,pump characteristics.
Hydraulic Press, Hydraulic Ram, Hydraulic Intensifier, Hydraulic lift, Hydraulic Accumulator, Hydraulic Crane, Hydraulic Coupling, Hydraulic Torque Converter, Surge tank, Vane pump, gear pump, Working principles of axial and radial pumps, Application to hydraulic devices, Fluid transients, Free and Forced Vortex Apparatus
Metal casting process: Introduction-advantages and limitations-applications-casting terms Patterns: Pattern allowance-pattern materials-types of patterns- colour codes Moulding materials: Moulding sand composition-testing sand properties-sand preparation-moulding sand properties-types of sand moulds-moulding machines Cores: Core sand, types of cores, core prints, chaplets, forces acting on the moulding flasks Gating system: Elements of gating system, gates, pouring time, sprue, gating ratio, slag trap system, risering design-caine’s method, modulus method, chills-feeding aids
Product design for sand casting: designing for economical moulding –designing for eliminating defects-features to aid handling Casting cleaning and casting defects-fettling-defects n casting Special casting process: Shell moulding –precision investment casting –permanent mould casting –die casting –centrifugal casting-continuous casting Casting metallurgy
Metal forming process: nature of plastic deformation-hot working and cold working Rolling: principle, rolling stand arrangement, rolling load, roll passes Forging: operations, smith forging, drop forging, press forging, machine forging, forging defects, forging design Extrusion-hot and cold extrusion, tube extrusion, wire drawing swaging Sheet metal operation- shearing operation, drawing, spinning, bending, stretch forming,embossing and coining
Metal fabrication process: introduction to fabrication process, gas welding and cutting.Electric arc welding-principle of arc, arc welding equipment, electrodes, carbon arc welding, TIG GMAW, SAW, arc cutting Resistance welding: principle –spot, seam, projection, upset, flash welding Other welding process: Thermit welding, electro slag welding, EBW, laser beam welding, forge welding, friction welding, diffusion welding, explosion welding Welding design: heat input, heat flow, distortion, metallurgy of welding, defects n welding, brazing, braze welding and soldering