Applied Mathematics - II

Differential Equations

1. Exact diff. Equation & those which can be made exact by use of integrating factor. Integrating factor by inspection, Linear equations & reducible to linear ( Bernoulli eqn.), method of substitution to reduce the eqn. to one of the above forms.

2. Linear Diff. Eqn. of nth order with constant coefficients, complimentary function & particular integral when the function of the integral on the R.H.S. are exponential, Sin(ax + b), Cos(ax + b).Cauchys Linear equation( Homogenous eqn.). The Legendre Linear equation, Variation of parameters & method of undetermined coefficients.

3. Elementary application of above diff. Eqn. in solving engineering

problems from Electrical Engg., Chemical Engg., Mechanical Engg., Civil Engg. Etc.

Integral Calculus

Rectification of plane curves, Double and Triple integrals, Their geometrical interpretation & evaluation. Evaluation of double integrals by change of order and change to polar. Application of double and triple integrals to areas, volumes & mass.

Beta & Gamma Functions

1. Beta & Gamma function & their properties, relation between Beta & Gamma functions.

2. Error Functions.

3. Differentiation under the integral sign.

RECOMMENDED BOOKS : =

1. Applied Mathematics               -     Wartikar (vol.1 & vol.2 )
2. Integral Calculus                 -     Shanti Narayan
3. Engineering Mathematics         -     R.M.Baphana
4. Engineering Mathematins         -     M.L.Bhatia   

Applied Physics II

Theory of production of X-rays.

Continuous and Characteristic X-rays spectra, X-ray diffraction, Laue spots, Braggs law and Moseleys law. Determination of crystal structure. Braggs spectrometer method and power method.

Optics.

Interference in thin film, Newtons rings and fringes in wedge shaped films. Fraunhoffer diffraction grating ( with derivation of formula ).

Principles of Laser.

Spontaneous and Stimulated radiation, Population inversion, Pumping methods. Ruby and He-Ne laser, Carbon dioxide laser, Semiconductor lasers ( Dye lasers and holography ).

Fibre Optics.

Types of optical fibres, step index and graded index, numerical aperture.

Communication through optical fibres

Dual nature of matter.

DeBroglie waves, Verification of matter waves, uncertainty principle, electron microscope- Introduction and application.

Detection and measurement of radiation.

Structure of nuclear binding energy, Nuclear fission. Nuclear reactors, Nuclear fusion. Detection and measurement of nuclear radiation by emulsion plates, cloud chamber & Bubble chamber.

Super Conductivity

Applied Chemistry II

Phase rule

Basic principles of phase rule, application of phase rule to water system.

Condensed phase rule, allotropes of iron, study of iron-carbon equilibrium diagram.

Corrosion

Definition, electrochemical theory of corrosion, factors affecting the rate of corrosion, different types of corrosion, protection against corrosion, factors affecting the rate of corrosion - design and selection. Cathodic and anodic protection, protective coatings- metallic, inorganic, organic coatings, corrosion inhibitors.

Fuels.

Classification, calorific value, determination by bomb calorimeter and Dulongs formulae, problems based on calorific value, characteristics of fuel, types of coal and its analysis. Preparation and properties of metallurgical coke. Liquid fuels, classification, refining of petroleum, thermal and catalytic cracking, synthetic gasoline, purification of gasoline, knocking, octane and cetane number, anti knock agents. Gaseous fuels - natural gas, coal gas, producer gas, water gas.

Problems based on combustion of fuels.

Cement.

Raw materials, composition, method of manufacture : wet and dry process.

Properties of cement, setting and hardening of cement, testing of cement.

Alloys.

Introduction, purpose of making alloys, composition. Properties and uses of plain carbon steels and alloy steels - heat resistant steel, shock resistant steels, magnetic steels, corrosion resistant steels, tool steels. Non Ferrous alloys - Copper(Brass, Bronze, German Silver), Nickel(Nichrome, Monel), Aluminium (Duralumin, Y-alloy, Magnalium), Lead and Tin (Solders, Brazing alloys, type metal, wood metal ).

Biotechnology.

Engineering Drawing II

Development of lateral surfaces of solids when cutting plane is perpendicular to H.P. or V.P. including curved cuts.

Intersection of surfaces of solids- prism, pyramid, cone or cylinder penetrated by any prism or cylinder.

Isometric & Oblique parallel projections, simple block and cylindrical type objects & spheres.

Primary auxiliary views of machine parts involving inclined surfaces.

Reading of orthographic projections, drawing of missing views & converting into sectional views.

Free hand sketches of the following machine elements

1. Rivet heads and riveted joints.

2. Thread profiles of IS V & square threads, metric, buttress, acme, knuckle, I.S. convention of representing external and internal V and square threads.

3. Bolts- hexagonal, square-prevention of rotation of bolts.

4. Nuts-hexagonal, square, wingnut locking by lock nuts, castle nut, split pin lock plate.

5. Studs- plain- collar.

6. Washer-plain, chamfered & spring washer.

7. Set screws.

8. Foundation bolts-rag, eye.

Engineering Mechanics II

Kinematics of a particle.

Velocity and acceleration in terms of rectangular co-ordinate system. Rectilinear motion, motion along plane curved path., tangential & normal components of acceleration, acceleration-time, velocity-time graphs and their uses, projectile motion, simple harmonic motion.

Kinematics of rigid bodies.

Translation, pure rotation & plane motion of rigid bodies, link mechanism, instantaneous centre of rotation for the velocity & velocity diagrams for bodies in plane motion, acceleration in plane motion, relative velocities.

Kinetics of particles and kinetics of rigid bodies.

D'Alemberts principle, equation of dynamic equilibrium, linear motion, curvilinear motion, mass moment of inertia about centroidal axis & about any other axis. D'Alemberts principle for bodies under the motion of rotation about a fixed axis and plane motion. Application to motion of bars, cylinders, spheres.

Momentum and Energy principles.

Linear momentum, principle of conservation of momentum, work done by a force. Work-energy equation, principle of conservation of energy, potential and kinetic

energy & power, impact of solid bodies, elastic impact, semi elastic and plastic impact.

Simple Lifting Machines.

Mechanical Advantage, Velocity Ratio & efficiency of the machine, law of machine, condition of maximum efficiency, self locking of the machine.

Following machines will be studied- a) Single purchase crab, b) Double purchase crab, c) Differential wheel and axle, d) Differential pulley block, e) worm and worm wheel, f) Simple screw jack.

Stress & Strain.

Stress, Strain, modulus of elasticity, Bulk modulus, yield stress, ultimate stress, factor of safety, shear stress, Poissons ratio, Bars of varying section, composite sections, temperature stresses.

Belt Friction.

Transmission of power by belts and ropes, centrifugal and initial tension in the belts or ropes. Condition for maximum power transmission. Flat belts on flat pulleys & ropes on grooved pulleys.

Communication Skills I .

Communication

What is communication ? , importance of communication, barriers tocommunication, verbal and non verbal communication, oral and written communication ,techniques to improve communication, internal and external communication.

Business correspondence

Principles of correspondence, language style, format of the business letter, types of business letters, application letter with bio data. enquiries, reply to enquiry, claims, adjustments, sales letters.

Group Discussion

Importance of group discussion, techniques of group discussion.

Precis Writing

Computer Programming II

Flow of control in Pascal, the compound statement, the iterative statement, conditional statements, unconditional branching, avoidance of unconditional branching.

Structured Data types, Arrays and multidimensional arrays, Packed arrays, records and sets.

Functions and Subprograms, parameter passing.

Debugging and testing, documentation and maintenance.

Problem design methods, Top-down modular programming.

Basic Electricity and Electronics II

AC Circuits.

Sinusoidal voltage and current, waveforms, RMS and average value, form factor, crest factor, frequency, periodic time, behaviour of resistance, inductance and

capacitance in AC circuit, RLC series and parallel circuit, phasor diagram, resonance, bandwidth and quality factor.

Polyphase Circuits.

Three phase system of voltages and currents, star and delta connection, balanced three phase circuit, relationship between line and phase currents and voltages, phasor diagram, power in three phase circuits, measurement of power by one wattmeter, two wattmeter and three wattmeter methods.

Transformers.

Construction of single phase transformers, function and working principle,

development of equivalent circuit, phasor diagram, O.C. and S.C. tests, efficiency and regulation, all day efficiency, condition for maximum efficiency.

Semiconductor Electronics.

PN diode construction, characteristics, effect of temperature on diode,

rectification using diodes, C, L, LC and PI filters. BJT construction, characteristics, CE, CB and CC configuration.

Basic Workshop Practice.

Fitting

Use of setting and fitting tools for chipping, cutting, filling, marking,

Center punching, drilling , tapping, die threading etc.

Carpentry

Use and setting of hand tools like hacksaws, jack planes, chisels and gauges for construction of various joints, wood turning, modern wood working methods, joining methods

Welding

Use of welding machine. electric arc welding, edge preparation for welding, types of joints, Sheet metal working and brazing: use of sheet metal working hand tools, cutting, bending, spot welding and brazing.

Forging and Smithy

Use and setting of hand tools such as hammers, chisels, flat and swages,

use of hearth, anvil etc.

Machine tools and machining processes

Lathes, milling machines, drilling machines, grinding machines, operations