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SCHEME OF TEACHING AND EXAMINATION

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SCHEME OF TEACHING AND EXAMINATION

    B.E Chemical Engineering Syllabus

    ENGINEERING MATHEMATICS III

    Subject Code : 10MA31 IA Marks : 25

    No. of Lecture Hours/Week : 04 Exam Hours : 03

    Total No. of Lecture Hours : 52 Exam Marks : 100

    PART A

    UNIT 1:

    Fourier Series: Periodic functions, Fourier expansions, Half range expansions, Complex form of Fourier series, Practical harmonic analysis. 7 Hours

    UNIT 2:

    Fourier Transforms: Finite and Infinite Fourier transforms, Fourier sine and consine transforms, properties. Inverse transforms. 6 Hours

    UNIT 3:

    Partial Differential Equations (P.D.E): Formation of P.D.E Solution of non homogeneous P.D.E by direct integration, Solution of homogeneous P.D.E involving derivative with respect to one independent variable only (Both types with given set of conditions) Method of separation of variables. (First and second order equations) Solution of Lagrange’s linear P.D.E. of the type P p + Q q = R. 6 Hours

    UNIT 4:

    Applications of P.D.E: Derivation of one dimensional wave and heat equations. Various possible solutions of these by the method of separation of variables. D’Alembert’s solution of

    wave equation. Two dimensional Laplace’s equation – various possible solutions. Solution of all these equations with specified boundary conditions. (Boundary value problems). 7 Hours

    PART B

    UNIT 5:

    Numerical Methods: Introduction, Numerical solutions of algebraic and transcendental equations:- Newton-Raphson and Regula-Falsi methods. Solution of linear simultaneous equations : - Gauss elimination and Gauss Jordon methods. Gauss - Seidel iterative method. Definition of eigen values and eigen vectors of a square matrix. Computation of largest eigen value and the corresponding eigen vector by Rayleigh’s power method.

     6 Hours

    UNIT 6:

    Finite Differences (Forward and Backward differences): Interpolation, Newton’s forward

    and backward interpolation formulae. Divided differences Newton’s divided difference

    formula. Lagrange’s interpolation and inverse interpolation formulae. Numerical differentiation

    using Newton’s forward and backward interpolation formulae. Numerical Integration

    Simpson’s one third and three eighth’s value, Weddle’s rule. (All formulae / rules without proof).

     7 Hours

    UNIT 7:

    Calculus of Variations: Variation of a function and a functional Extremal of a functional, Variational problems, Euler’s equation, Standard variational problems including geodesics, minimal surface of revolution, hanging chain and Brachistochrone problems. 6 Hours

    UNIT 8:

Difference Equations and Z-transforms: Difference equations Basic definitions. Z-

    transforms Definition, Standard Z-transforms, Linearity property, Damping rule, Shifting rule, Initial value theorem, Final value theorem, Inverse Z-transforms. Application of Z-transforms to solve difference equations. 7 Hours

Text Book:

    thHigher Engineering Mathematics by Dr. B.S. Grewal (36 Edition Khanna Publishers)

    Reference Books:

    1. Higher Engineering Mathematics by B.V. Ramana (Tata-Macgraw Hill)

    2. Advanced Modern Engineering Mathematics by Glyn James Pearson Education

     Note:

    1. One question is to be set from each unit.

    2. To answer Five questions choosing at least Two questions from each part.

    MOMENTUM TRANSFER

    Subject Code : 10CH32 IA Marks : 25

    No. of Lecture Hours/Week : 04 Exam Hours : 03

    Total No. of Lecture Hours : 52 Exam Marks : 100

    PART A

    UNIT 1:

    Fluid statics and its applications: Concept of unit operations, Concept of Momentum Transfer, Nature of fluids and pressure concept, Variation of pressure with height hydrostatic

    equilibrium, Barometric equation, Measurement of fluid pressure manometers. Continuous

    gravity decanter, decanter, Centrifugal decanter. 6 Hours

UNIT 2:

    Fluid flow phenomena: Types of fluids shear stress and velocity gradient relation, Newtonian and non Newtonian fluids, Viscosity of gases and liquids. Types of flow laminar and

    turbulent flow, Reynolds stress, Eddy viscosity. Flow in boundary layers, Reynolds number, Boundary layer separation and waste formation. 6 Hours

UNIT 3:

    Basic equations of fluid flow: Average velocity, Mass velocity, Continuity equation, Euler and Bernoulli equations, Modified equations for real fluids with correction factors. Pump work in Pernoulli equation. Angular momentum equation. 8 Hours

UNIT 4:

    Flow of incompressible fluids in conduits and thin layer: Laminar flow through circular and

    non-circular conduits. Hagen Poiseuille equation, Laminar flow of non-newtonian liquids, Turbulent flow in pipes and closed channels, Friction factor chart. Friction form change in velocity or direction. Form friction losses in Bernoulli equation. Flow of fluids in thin layers.

     8 Hours

    PART B

UNIT 5:

    Flow of compressible fluids: Continuity equation, Concept of Mach number, Total energy balance, Velocity of sound, Ideal gas equations. Flow through variable-area conducts. Adiabatic

    frictional flow. Isothermal frictional flow (elementary treatment only). 6 Hours

UNIT 6:

    Metering of fluids: Pipes, Fitting and valves, Measurement of liquid and gas flow rates by orifice meter, venturi meter, rotameter and pitot tube. Flow through open channels weirs and

    notches. 6 Hours

    Introduction to unsteady state flow: Time to empty the liquid from a tank. 2 Hours

UNIT 7:

    Transportation of fluids: Elementary concept of target meter, vortex sedding meters, turbine meters, positive displacement meters, magnetic meters, coriolis meters and thermal meters. Performance and characteristics of pumps positive displacement and entrifugal pumps. Fans, compressor and blowers. 6 Hours

UNIT 8:

    Dimensional analysis: Dimensional homogeneity, Rayieigh’s and Buckingham’s II – methods.

    Significance of different dimensionless numbers. Elementary treatment of similitude between model and prototype. 4 Hours

Text Books: th1. Unit Operations of Chemical Engineering, McCabe. W.L., et. al. 5 edn., McGraw Hill,

    New York 1993.

2. Engineering Fluid Mechanics, Kumar K. I. Eurasia Publishing House (p) Ltd., New rdDelhi., 3 edn., 1984.

Reference Books: th1. Chemical Engineering, Vol. 1., Coulson J. II and Richardson. J.F.., 5 edn., Asian Books

    (p) Ltd., New Delhi, 1998.

    2. Introduction to Chemical Engineering, Badger. W.I., and Banchero J.T., Tata Mc Graws

    Hill, New York, 1997.

    CHEMICAL PROCESS CALCULATIONS

    Subject Code : 10CH33 IA Marks : 25

    No. of Lecture Hours/Week : 04 Exam Hours : 03

    Total No. of Lecture Hours : 52 Exam Marks : 100

    PART A

UNIT 1:

    Units and dimensions: Fundamental and derived units, Conversion. Dimensional consistency of equations. Dimensionless groups and constants. Conversion of equations. 6 Hours

UNIT 2:

    Basic chemical calculations: Concept of mole, Mole fraction. Compositions of mixtures of solids, liquids and gases. Concept of normality, Molarity, Molality, ppm. Use of semi-log, log-

    log triangular graphs. Ideal gas law calculations, 6 Hours

UNIT 3:

    Vapour pressure concepts, humidity, constant humidity chart, humidification and dehumidification operation. 7 Hours

UNIT 4:

    Material balance without reaction: General material balance equation for steady and unsteady state. Typical steady state material balances in distillation, absorption, extraction, crystallization, drying. 7 Hours

    PART B

UNIT 5:

    Steady state material balance for mixing and evaporation. Elementary treatment of material balances involving bypass. Recycle and purging. 6 Hours

UNIT 6:

    Steady state material balance with reaction: Principles of stoichiometry, Concept of limiting

    and excess reactants and inerts, fractional and percentage conversion, fractional yield and percentage yield, selectivity, related problems. 7 Hours

UNIT 7:

    Ultimate and proximate analyses of fuels, Calculations involving burning of solid, liquid and gaseous fuels, excess air, Air-fuel ratio calculations. 6 Hours

UNIT 8:

    Energy balance: General steady state energy balance equation, Thermo physics. Thermo chemistry and laws. Heat capacity. Enthalpy, Heat of formation, Heat of reaction, Heat of combustion and Calorific values. Heat of solution. Heat of mixing, Heat of crystallization. Determination o at standard and elevated temperatures, Theoretical flame temperature and F

    adiabatic flame temperature. 7 Hours

Text Books:

    1. Stoichiometry (SI Units), Bhatt B.L. and Vora S.M. Third Edition, 1996, Tata McGraw

    Hill Publishing Ltd., New Delhi 1996.

    2. Chemical Process Principles Part I Material and Energy Balances, Second edition,

    Hougen O.A., Waston K.M. and Ragatz R.A., CBS publishers and distributors, New Delhi,

    1995. th3. Basic Principles and Calculations in Chemical Engineering, 6 Edn. Himmelblau D.M.,

    Prentice Hall of India, New Delhi 1997. nd4. Bioprocess Engineering Basic Concepts, 2 Edn. Shuler M.L., and Kargi F., Prentice

    Hall of India Ltd., 2002.

Note: Question paper shall contain at least 30% theory, and questions from all the chapters.

    TECHNICAL CHEMISTRY

    Subject Code : 10CH34 IA Marks : 25

    No. of Lecture Hours/Week : 04 Exam Hours : 03

    Total No. of Lecture Hours : 52 Exam Marks : 100

    PART A

     UNIT 1:

    Colligative properties: Concept of mole and mole fraction. Colligative properties - Meaning and types, Lowering of vapour pressure, Raoult’s law - statement, limitations. Determination of

    molecular weight by lowering of vapour pressure, problems. Ostwald’s and Walker’s method, Elevation in boiling point of a solvent derivation, Experimental determination of molecular

    weight by ebulliscopic method, problems. Isotonic solutions abnormal molecular weight.

    Osmosis and Osmotic pressure - Explanation of the terms, effect of concentration and temperature and simultaneous effect of concentration and temperature on osmotic pressure. Determination of molecular weight - Berkeley and Hartley’s method and problems. 8 Hours

    UNIT 2:

    Principles of valence bond theory and molecular orbital theory: Introduction to chemical

    bonding - Formation of ionic bond, covalent bond and co-ordinate bond with examples; Energies of covalent bond formation, Valence bond theory postulates and explanation, Types

    of covalent bonds: --ry postulates, Linear combination

    of atomic orbitals (LCAO), conditions for effective combination of atomic orbitals. Molecular orbital configuration of simple molecules ( H and He) ; Similarities and distinctions between 22

    valence bond theory and molecular orbital theory; Polar and non polar covalent bonds. 6 Hours

UNIT 3:

    Surface chemistry: Introduction, Types of adsorption Physisorption and chemisorption,

    adsorption isotherm, isobar, isotere, Langmuir adsorption isotherm, BET isotherm, BET equation for surface area, Langmuir-Hinshelwood, and Langmuir-Rideal mechanisms, kinetic effects of surface heterogeneity, surface inhibition and activation energies, unimolecular and bimolecular surface reactions, reactions between two adsorbed molecules, Transition state theory of surface reactions, Mechanism of chemisorption and rates of chemisorption and desorption. 7 Hours

UNIT 4:

    Catalysis: Basic principles, classification of catalytic systems; Homogeneous catalysis:

    Homogeneous catalysis involving gases, Homogeneous catalysis in the liquid phase with examples including Wilkinson’s catalyst; Heterogeneous catalysis- Explanation with examples

    including Ziegler-Natta catalyst; Mechanism of acid-base catalysis, Catalytic reactions- Hydrogenation, transfer hydrogenation, hydroformylation, isomerization, Wacker’s process-

    acetic acid from ethylene; Negative catalysis and its mechanism. 6 Hours

    PART B

UNIT 5:

    Dyes: Colour and constitution - chromophore, and auxochrome theory , modern theory of colour, classification of dyes - by structure and by methods of application. Synthesis of dyes - Methyl orange, Congo red, Malachite green, Indigo and Alizarin. 6 Hours

    UNIT 6:

    Reaction mechanism: Concept of reactive intermediates- carbanions, carbocations, inductive and resonance effects; Mechanism of nucleophilic substitution (SNand SN) in alkyl halides; 1 2

    Mechanistic concept of elimination reactions (E and E); Mechanism of 12

    electrophilic substitution in benzene - Nitration, sulphonation, halogenation, Friedel-Crafts alkyl and acylation reactions; Electronic interpretation of orienting influences of substituents in aromatic electrophilic substitution of toluene, chlorobenzene, phenol and nitrobenzene. 7

    Hours

UNIT 7:

    Insecticides: Definition, classification i) Internal or Stomach insecticide

    ii) External or Contact Insecticides iii) Fumigants -

    Explanation with examples; Organic insecticides DDT, Chlordane, Nitrophenol, BHC

    (Gammexane), Aldrin, Schradan, Parathion, Malathion and Baygon - synthesis and their applications; Rodenticides, Fungicides, and Herbicides Definition, examples and their

    applications. 6 Hours

    UNIT 8:

    Oils and fats-Vegetable oils- Examples; Analysis of oils- Saponification value,iodine value and acid value - their determination, Extraction of oils- Solvent extraction, Refining of oils, Hydrogenation - manufacture of Vanaspati.

    Soaps and detergents Manufacture of soap by hot process; Types of soaps - Liquid soap, Toilet soaps-opaque and transparent; Mechanism of cleansing action of soap; Synthetic detergents Ionic detergents-anionic and cationic; Nonionic detergents-Manufacture. 6 Hours

Text Books:

    th1. Organic Chemistry, Morrision B.R. and Boyd L.L., 6 Edition, ELBS, New Delhi, 1999. th2. Physical Chemistry, Puri L.R. and Sharma B.R., 14 Edition, Chand S. and Co., New

    Delhi 1998.

Reference Books:

    1. Modern Synthetic Reactions, House, H.O., ULBS Publishers, New Delhi.

    2. Organic Reactions Mechanism, Sykes Peter, ULBS Publishers, New Delhi.

    3. Organic Chemistry Vol I and II, Finar, ULBS Publishers, New Delhi. th4. Industrial Chemistry, Sharma B.K., 11 Edition, Chand S. and Co. New Delhi, 2001. th5. Organic Chemistry, Tiwari Melhrotra and Vishnoi, 7 edition, Chand S. and Co., New

    Delhi, 1996. th6. A Text Book of Organic Chemistry, Arun Bahl and Bahl B.S., 15 Edition. S. Chand

    and Company, New Delhi, 1998.

    7. Surface Chemistry: Theory and applications by J.J. Bikerman, Academic press, New

    York, 1972.

    8. Physical Chemistry of Surfaces by A.W. Adamson, Interscience publishers Inc., New

    York.

    MECHANICAL OPERATIONS

    Subject Code : 10CH35 IA Marks : 25

    No. of Lecture Hours/Week : 04 Exam Hours : 03

    Total No. of Lecture Hours : 52 Exam Marks : 100

    PART A

UNIT 1:

    Particle technology: Particle shape, particle size, different ways of expression of particle size, shape factor, sphericity, mixed particles size analysis, mixed particles size analysis, screens

    ideal and actual screens, Differential and cumulative size analysis, Effectiveness of screen, Specific surface of mixture of particles, Number of particles in a mixture, standard screens industrial screening equipment, Motion of screen, Grizzly, Gyratory screen, Vibrating screen, Trommels, Sub sieve analysis Air permeability method, Sedimentation and elutriation methods.

     8 Hours

UNIT 2:

    Size reduction: Introduction Types of forces used for comminution, Criteria for communition, characteristics of comminuted products, Laws of size reduction, Work Index, Energy utilization, Methods of operating crushers Free crushing, Choke feeding, Open circuit grinding, Closed

    circuit grinding, Wet and dry grinding, Equipment for size reduction Blake jaw crusher,

    Gyratory crusher, Smooth roll crusher, Toothed roll crusher, Impactor, Attrition mill, Ball mill, Critical speed of ball mill, Ultra fine grinders, Fluid energy mill, Colloid mill, Cutters Knife

    cutter. 6 Hours

UNIT 3:

    Flow of fluid past immersed bodies: Drag, Drag coefficient, Pressure drop Kozeny-Carman

    equation, Blake-Plummer, Ergun equation, Fluidizaion, Conditions for fluidization, Minimum fluidization veleocity, Types of fluidization, Applications of fluidization, Slurry transport, Pneumatic conveying. 6 Hours

UNIT 4:

    Motion of particles through fluids: Mechanics of particle motion, equation for one

    dimensional motion of particles through a fluid in gravitational and centrifugal field, Terminal velocity, Drag coefficient, Motion of spherical particles in Stoke’s region, Newtons region and

    Intermediate region, Criterion for settling regime, Hindered settling, Modification of equation for hindered settling, Centrifugal separators, Cyclones and Hydro cyclones. 6 Hours

    PART B

UNIT 5:

    Sedimentation: Batch settling test, Application of batch settling test to design of a continuous thickener, Coe and Clevenger theory, Kynch theory, Thickener design, Determination of thickener area. 6 Hours

UNIT 6:

    Filtration: Introduction, Classification of filtration, Cake filtration, Clarification, Batch and continuous filtration, pressure and vacuum filtration Constant rate filtration and cake filtration, characteristics of filter media, industrial filters, sand filter, Filter press, leaf filter, Rotary drum filter, Horizontal belt filter, Beg filter, Centrifugal filtration Suspended batch centrifuge, Filter

    aids, Application of filter aids, Principles of cake filtration, Modification of Kozeny Carman

    for filtration. 6 Hours

UNIT 7:

    Agitation and mixing: Application of agitation, Agitation equipment, Types of impellers

    Propellers, Paddles and Turbines, Flow patterns in agitated vessels, Prevention of swirling, Standard turbine design, Power correlation and power calculation, Mixing of solids, Types of mixers Change can mixers, Muller mixers, Mixing index, Ribbon lender, Internal screw mixer, Tumbling mixer. 6 Hours

UNIT 8:

    Sampling and storage and conveying of solids: Sampling of solids, storage of solids, Open

    and closed storage, Bulk and bin storage, Conveyors Belt conveyors, Chain conveyors, Apron

    conveyor, Bucket conveyor, Bucket elevators, Screw conveyor. 4 Hours

    Miscellaneous separation: Magnetic separation, electrostatic separation, Jigging, Heavy media separation, Froth floatation process, Additives used during flotation, Floatation cells, Typical floatation circuits, Size enlargement (only principle and equipment) Flocculation, Briquetting,

    Pelletization, Granulation. 4 Hours

Text Books:

1. Unit Operations of Chemical Engineering”, McCabe W.L., et.al., V Edn., McGraw

    Hill International, Singapore 2000.

    2. “Introduction to Chemical Engineering” III Edn., Badger, W.L. and Banchero J.T.

    McGraw Hill International Edition, Singapore 1999.

    3. Coulson and Richardson’s Chemical Engineering Vol. 2 Particle Technology and

    Separation Processes” IV Edn.,Coulson J.M. and Richardson J.F., Asian Books Pvt. Ltd.

    New Delhi, 1998.

Reference Books:

    1. “Unit Operations” I Edn., Brown. G.G. et.al., CBS Publishers, New Delhi, 1995. 2. Perry’s Chemicl Engineers’ Hand book”, VII Edn., Perry R.. and Green W.D.,

    McGraw Hill International Edn., New York, 2000.

    3. Fuels and Combustion”, II Edn., Sarkar Samir, orient longman, NewDelhi New York,

    2000.

    4. Principles of Unit Operations” III Edn., Foust A. S. et.al John Wiley and Sons, New

    York, 1977.

    COMPUTER AIDED CHEMICAL EQUIPMENT DRAWING

    Subject Code : 10CH36 IA Marks : 25

    No. of Practical Hours/Week : 03 Exam Hours : 03

    Total No. of Hours : 39 Exam Marks : 50

    Sectional views: Representation of the sectional planes, Sectional lines and hatching, selection of section planes and types of sectional views. 6 Hours

Proportionate drawing of process equipment: Equipment and piping symbols, Vessel

    component; Vessel opening, Manholes, Vessel enclosures, Vessel support, Jackets, Shell and tube heat exchanger, Reaction vessel and Evaporator. 12 Hours

    Assembly drawing: (i) Joints: Cotter joint with sleeve, cotter joint, Socket and Spigot joint, Flanged pipe joint, Union joint, Stuffing box and Expansion joint (Screw type or Flanged type).

    (ii) Valves: Stop valve, Globe valve, Stop cock and Gate valve, Screw down Stop valve, Rams Bottom safety valve, Non-return valve.

    (iii) Pumps: Centrifugal pump, Gear pump. 21 Hours

Note:

    1. First angle projection to be followed.

    2. Examination consists of one question on proportionate drawing (30 marks) and one

    question on Assembly drawing (70 Marks).

Software: Solid Edge

    Text Books: th1. .“Machine Drawing”, 9 Edn., Gopal Krishna, K.R, Subhas Stores, Bangalore 1995. th2. “Machine Drawing”, 29 Edn., Bhatt, N.D., Charotar Publishing House, Anand, 1995. rd3. “Process Equipment Design”, 3 End, Joshi, M.V., Macmillian India publication”, New

    Delhi.

Reference Books:

    1. Chemical Process Equipment”, Walas, S.M., Butterworth Heinemann Pub. 1999. rd2. Applied Process Design” 3 edn., Ludwig E.E., Gulf Professional Publising, New Delhi,

    1994.

    MOMENTUM TRANSFER LAB

    Subject Code : 10CHL37 IA Marks : 25

    No. of Practical Hours/Week : 03 Exam Hours : 03

    Total No. of Hours : 39 Exam Marks : 50

The experiment should be based on the following topics;

1. Friction in circular pipes

    2. Friction in non circular pipes

    3. Friction in helical / spiral coils

    4. Flow rate measurement using venturi / orifice meters (incompressible fluid) 5. Local velocity measurement using pitot tube

    6. Flow over notches

    7. Hydraulic coefficients open orifice

    8. Packed bed

    9. Fluidized bed

    10. Study and development of characteristics for centrifugal pump 11. Study of various pipe fittings and their equivalent lengths 12. Compressible fluid flow measurement using venturi / orifice meters 13. Reynolds apparatus

    14. Air lift pump

Note: Minimum of 10 experiments are to be conducted.

    TECHNICAL CHEMISTRY LAB I

    Subject Code : 10CHL38 IA Marks : 25

    No. of Practical Hours/Week : 03 Exam Hours : 03

    Total No. of Hours : 39 Exam Marks : 50

The experiment should be based on the following topics;

1. Estimation of HCl and CHCOOH in a given acid mixture conductometrically. 3

    2. Determination of sulphate and nitrate in the given sample of water using Nephelometer

    and spectrophotometer.

    3. Determination of chloride content in the given sample of water using N/40 AgNO 3

    solution and KCl crystals.

    4. Determination of partition coefficient of iodine between water and carbon tetrachloride. 5. Study of kinetics of the reaction between KSO and KI. 228

    6. Determination of percentage of nitrogen in ammonium fertilizers, using 1 N

    NaOH solution and standard HCl solution.

    7. Determination of percentage composition of binary mixture using Ostwald’s viscometer.

    8. Effect of salt on the critical solution temperature of phenol-water system. 9. Determination of molecular weight of a non-volatile solute by elevation in boiling point.

    (Using McCoy’s apparatus).

    10. Determination of nickel as nickel dimethylglyoximate gravimetrically (after separating

    iron) in the given stainless steel solution.

11. Determination of iron as ferric oxide gravimetrically (after separating copper) in the given

    chalcopyrites ore solution.

    12. Determination of zinc in the given brass solution volumetrically (after separating copper).

Note: Minimum of 10 experiments are to be conducted.

    ENGINEERING MATHEMATICS - IV

    Subject Code : 10MA41 IA Marks : 25

    No. of Lecture Hours/Week : 04 Exam Hours : 03

    Total No. of Lecture Hours : 52 Exam Marks : 100

    PART A

    UNIT 1:

    Numerical Methods: Numerical solutions of first order and first degree ordinary differential

    equations Taylor’s series method, Modified Euler’s method, Runge – Kutta method of fourth

    order, Milne’s and Adams-Bashforth predictor and corrector methods (All formulae without Proof). 6 Hours

    UNIT 2:

    Complex Variables: Function of a complex variable, Limit, Continuity Differentiability

    Definitions. Analytic functions, Cauchy Riemann equations in cartesian and polar forms, Properties of analytic functions. Conformal Transformation Definition. Discussion of 2ztransformations: W = z, W = e, W = z + (I/z), z ? 0 Bilinear transformations. 7 Hours

    UNIT 3:

    Complex Integration: Complex line integrals, Cauchy’s theorem, Cauchy’s integral formula. Taylor’s and Laurent’s series (Statements only) Singularities, Poles, Residues,

    Cauchy’s residue theorem (statement only).

     6 Hours

    UNIT 4:

    Series solution of Ordinary Differential Equations and Special Functions: Series solution

    Frobenius method, Series solution of Bessel’s D.E. leading to Bessel function of fist

    kind. Equations reducible to Bessel’s D.E., Series solution of Legendre’s D.E. leading to Legendre Polynomials. Rodirgue’s formula. 7

    Hours

    PART B

     UNIT 5:

    Statistical Methods: Curve fitting by the method of least squares: y = a + bx, y = a + bx + 2bxbxcx, y = ax y = ab, y = ae, Correlation and Regression.

    Probability: Addition rule, Conditional probability, Multiplication rule, Baye’s theorem.

     6 Hours

    UNIT 6:

    Random Variables (Discrete and Continuous) p.d.f., c.d.f. Binomial, Poisson, Normal and

    Exponential distributions. 7 Hours

     UNIT 7:

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