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THEORY


Fibre study

(a) Classification of fibres – study of properties common to protein,

cellulose, mineral and thermoplastic fibres.
(b) Manufacture, uses and properties of Cotton, Jute, Viscose Rayon, Wool, Silk, Nylon, Terylene and Acrylic.
2. Yarn processing – Steps involved in processing cotton yarns – classification of yarns based on direction of twist, count – simple and novelty yarns.
3. Weaving - parts of a loom, basic weaving operation, study of weaves – Basic weaves and figured weaves.
4. Fabric finishing – Purpose and uses of various finishes – singeing, scouring, bleaching, tentering, calendering, sizing, weighting, mercerising, napping, sanforising, crease proofing.
Dyeing and printing
Classification of dyes - Natural and Synthetic – Direct, Basic, Acid, Mordant, Naphthol, Reactive and Vat dyes – Methods of Dyeing - Stock, Top, Yarn and Piece dyeing.
Styles of Printing – Direct, Discharge and Resist method. Methods of printing – Hand methods - Batik, Tie & Dye, Block, Screen Printing; Machine Methods - Roller printing, Screen Printing, Duplex Printing, Transfer Printing and Photo Printing.

REFERENCES
1. Durga Deulkar, (1951). A guide to household textiles and laundry work. Atmaram and Sons, New Delhi.

2. Hess, (1961). Textile fibres and their use. Lippincot Co., New York.

3. Irwin, (1957). Clothing for Moderns. The Macmillan Company, New York.

4. Joseph, M.L., (1977). Introductory Textile Science. Rinehart & Winston.


New York. 3rd Editionl

5. Norma, Hollen & Saddler (1973). Textiles. The Macmillan Co. New York.

6. Potter & Corbman, (1985).Fibre to Fabric. Mc Graw Hill Book Co. New

York.


7. Trotman, E.R. (1994). Dyeing and Chemical Technology of Textile fibres.

6th Edition, B.I. Publications Pvt. Ltd., New Delhi.

8. Wingate, (1976). Textile Fabrics and their selection. Prentice Hall Inc.,

New Jersey.



SEMESTER – VI
ELECTIVE II - CLOTHING CONSTRUCTION

Theory: 4 hours

Practicals: 2 hours

OBJECTIVES:

To help the students to

Study the principles of laundering and use this knowledge in care of Textiles.

Select clothing appropriate for various family members.

Learn the techniques involved in Garment Construction.
THEORY:
Techniques of clothing construction

Selection, use and care of sewing machine and sewing tools.

Study of basic hand stitches-temporary and permanent.

Seams and seam finishes.

Methods of introducing fullness into a fabric-darts,tucks,pleats and gathers.
Principles of Pattern Making, Fabric Preparation, Pattern Layout and Garment Cutting

Steps in preparing the basic bodice, sleeve and skirt pattern for children and adult women based on body measurements.

Steps in fabric preparation.

Pattern Layout.

Methods of transferring pattern markings on to a fabric.

Care of Textiles- Principles of laundering and storing cotton, wool, silk, rayon and synthetic fabrics- study on selection of suitable soaps, bleaches, whitening and stiffening agents.

Family clothing plan-Principles of preparing clothing budget and wardrobe planning-selection and buying of fabrics and ready-mades based on art principles, personal characteristics and other factors.

Application of computer aided designing in textiles.


PRACTICALS:
Fullness - Darts, Tucks, Pleats, Gathers, Frills, Ruffles and Smocking.

Fasteners – Button and Buttonhole, Loops, Press, Buttons, Hooks and Eyes and Eyelets.

Decorative stitches.

Fabric painting

Construction of Salwar Kameez.
REFERENCES:

1. Allyne Bane, 1980, “Creative Sewing”, McGraw & Hill Book Company.

2. Durga Deulkar, 1951, “A guide to household textiles and laundry work”,

Atmaram and sons. New Delhi.

3. Graves Ryan. “Complete Encyclopedia for Stitchery”

4. Hess, 1961, “Textile fibers and their use”, Lippincot Co., New York.

5. Juveka, “Easy Cutting”.

6. Joseph, “Introductory Textile Science”, Rinehart & Winston Inc., New York.

7. Irwin, 1957, “Clothing for Moderns”, The Macmillan Company,

New York.

8. Irwin, “Practical Dress Design”.

9. Lewis, Bowar, Kettunen, 1976, “Clothing Construction and Wardrobe Planning”.


The Macmillan Company. New York.

10. Marry Mathews, 1996, “Practical Clothing Construction- Part I and Part II”, cosmic press.

11 Norma, Hollen, Saddler, 1973, “Textiles”, The Macmillan Company, New York.

12. Wingate, 1976, “Textile Fabrics and their selection”, Prentice Hall Inc. New Jersey.




ELECTIVE III - FAMILY STUDIES

[Common Syllabus for B.Sc. (I.D.) and B.Sc. (Clinical Nutrition)]

Theory: 5 hrs/week

OBJECTIVES

To enable students to

1. Help students to gain maturity to face the demands of married life.

2. Take right decisions towards setting up a family


THEORY:

I. FAMILY

a. Characteristics and developmental tasks – types of family – Indian

– Traditional and Modern.


    1. Functions of family – Family in India – Factors influencing the

Indian Family.
II. MARRIAGE AND FAMILY AS BASIC INSTITUTION


  • Motives of Marriage

  • Functions of Marriage


III. Importance of physical, mental health, emotional maturity, personality development in marriage – Factors affecting Marriage relationship – Religion, social, economic status, career and money.
IV. ADJUSTMENT IN MARRIAGE – Adjustment towards male, sex, finance, society, in-law.
V. FAMILY LIFE CYCLE – Stage – beginning family, expanding family, contracting family – adjustment in different stages.
VI. CRISIS IN THE FAMILY - Critical Family situation, alcoholism, widowhood etc. – their effects on children.
VII. Maternal and paternal deprivation and their effect on the child growth and development.
VIII. Parental attitudes and their influence on children – styles of parenting.
IX. Small family norms – concept, advantages and limitations.


PRACTICALS
1. Study on qualities preferred by Adolescents in their life partner.

2. Survey on in-law relationships.

3. Survey on different types of family.
REFERENCES
1. Christensen, H.T. (1964). Handbook of Marriage and the Family – Rand

Mc Nally Co.

2. Christensen, H.T. and Johnson, K.P. (1971) – Marriage and the Family –

Ronald Press Co, 3rd Edition.

3. Desouza, A (1973). Women in contemporary India – Manohar Book

Service.


4. Duvall, E.M. (1977) – Marriage and Family development, J.B. Lippincott Company, Philadelphia.

5. Goode, W.J. (1965) – The Family. Prentice Hall of India.

6. Kapadia, K.M. (1972) – Marriage and Family in India – Oxford University Press, Bombay.

7. Landis F. and Landis M.D. (1935) – Personal Adjustments in Marriage and Family living – Prentice Hall Inc. of New York.

8. Laudir J.T. and Landis M.D. (1978) Marriage and Family – Prentice Hall Inc. of New York., 6th edition.

9. Stinnet, N and Walters, J (1977) Relationships in Marriage and Family – Macmillan Publishing.

10. Sussman, M.D. (1953) – Source Book on Marriage and Family – Houghton Mifflin Co, New York.

11. B.Sc. DEGREE COURSE IN MATHEMATICS

SYLLABUS
CORE SUBJECT : PAPER – V
DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS

Credits - 4 Instructional Hours – 4


First order but of higher degree equations – solvable for p, solvable for x, solvable for y, clairaut’s form – simple problems.
Second order differential equations with constant coefficients with particular integrals for eax, xm, eax sinmx, eax cosmx
Second order differential equations with variable coefficients ;

Method of variation of parameters; Total differential equations, simple problems.


Partial Differential equations :-

Formation of P.D.E by eliminating arbitrary constants and arbitrary functions; complete integral; Singular integral ; general integral; Charpit’s method and standard types f(p,q)=0, f(x,p,q)=0, f(y,p,q)=0, f(z,p,q)=0, f(x,p)= f(y,q); Clairaut’s form and Lagrange’s equations Pp+Qq=R – simple problems.


Laplace transform; inverse Laplace transform(usual types); applications of Laplace transform to solution of first and second order linear differential equations (constant coefficients) and simultaneous linear differential equations – simple problems.
Reference Books :-

  1. Engineering Mathematics volume 3 : M.K. Venkataraman(National Publishing Co.)




  1. Engineering Mathematics Volume 3 : P.Kandasamy and others(S.Chand and Co.)

  2. Integral Calculus and differential equations : Dipak Chatterjee (Tata McGraw Hill Publishing Company Ltd.)




  1. Advanced Engineering Mathematics : Erwin Kreyszig (John Wiley and sons New York 1999)

  2. Calculus : Narayanan and others (S.Viswanathan Publishers)

  3. Differential Equations and Integral Transforms : Dr.S.Sudha (Emerald Publishers)


Core Subject - Paper VI
COORDINATE GEOMETRY OF 3 DIMENSIONS AND PROBABILITY
Credits - 4 Instructional Hours – 5
Planes and Lines : Planes and Lines - Reduction to symmetric form of a line given by a pair of planes; conditions for 2 lines to be coplanar and the equation of the plane containing the lines; length and equation of the shortest distance between 2 skew lines; image of a point and a line w. r. t. a plane, bisector planes.
Sphere :-

Equation of a sphere ; general equation ; section of a sphere by a plane ; tangent plane ; radical plane ; coaxal system of spheres; orthogonal spheres.


Probability :-

Probability space; total probability ; multiplication law on probability; conditional probability ; independent events; Baye’s Theorm.

Random variables; discrete and continuous ; distribution functions ; expected value ; moments; moment generating function; probability generating function.

Reference Books :


  1. Differential Equations, Fourier series and Analytical Solid Geometry : P.R.Vittal (Margham Publishers)

  2. Engineering Mathematics volume 3 : M.K. Venkataraman(National Publishing Co.)

  3. Engineering Mathematics volume 3 : P.Kandasamy and others(S.Chand and Co.)

  4. Advanced Engineering Mathematics : Stanley Grossman and William R.Devit(Harper and Row publishers)

  5. Fundamentals of Mathematical Statistics : S.C.Gupta and V.K. Kapoor (S.Chand and Co.)

  6. Mathematical Statistics and Probability by P.R.Vittal (Margham Publishers)

Core Subject - Paper – VII
VECTOR CALCULUS, FOURIER SERIES AND FOURIER TRANSFORMS

Credits - 4 Instructional Hours – 5


Vector Differentiation :-

Gradient , divergence, curl, directional derivative, unit normal to a surface.


Vector integration: line, surface and volume integrals; theorems of Gauss, Stokes and Green. (without proof) – simple problems.
Fourier Series: Expansions of periodic function of period 2π ; expansion of even and odd functions; half range series.
Fourier Transform: Infinite Fourier transform (Complex form, no derivation); sine and cosine transforms; simple properties of Fourier Transforms; Convolution theorem; Parseval’s identity.
Reference Books :-

  1. Engineering Mathematics Volume 3 : M. K. Venkataraman (National Publishing Co.)

  2. Engineering Mathematics Volume 3 : P. Kandasamy and others (S. Chand and Co.)

  3. Vector Analysis : Murray Spiegel (Schaum Publishing company, New York)

  4. Vector Analysis : P. Duraipandian and Laxmi Duraipandian (Emerald Publishers).



Core Subject – Paper- VIII
STATICS

Credits – 4 Instructional hours : 4


Forces: Types of forces, Magnitude and direction of the resultant of the forces acting on a particle, Lami’s Theorem, equilibrium of a particle under several coplanar forces, parallel forces, moments, couples-simple problems.
Friction: Laws of friction, angle of friction, equilibrium of a body on a rough inclined plane acted on by several forces, centre of gravity of simple uniform bodies, triangular lamina, rods forming a triangle, trapezium, centre of gravity of a circular arc, elliptic quadrant, solid and hollow hemisphere, solid and hollow cone, catenary-simple problems.

Reference Book:

  1. Mechanics – P. Duraipandian and others, S. Chand & Co.

  2. Statics – K. Viswanatha naik and M. S. Kasi, Emerald Publishers.

  3. Statics – S. Narayanan and others, S. Chand and Co.

  4. Statics – A. V. Dharmapadam, S. Viswanathan and Co.

Core Subject – PAPER- IX

ALGEBRAIC STRUCTURES -I
Credits – 4 Instructional hours : 6
Groups: Subgroups, cyclic groups and properties of cyclic groups – simple problems; Lagrange’s Theorem; Normal subgroups; Homomorphism; Automorphism ; Cayley’s Theorem, Permutation groups.
Rings: Definition and examples, Integral domain, homomorphism of rings, Ideals and quotient Rings, Prime ideal and maximum ideal; the field and quotients of an integral domain, Euclidean Rings.
Reference Book:

Contents and treatment as in “Topic in Algebra” – I. N. Hesteien, Wiley Eastern Ltd.


Chapter 2 : Section – 2.1 , 2.2 , 2.3 , 2.4 , 2.5 , 2.6 , 2.7 (Omit Sections 1 and 2)

2.8 , 2.9 , 2.10

Chapter 3 : Section – 3.1 , 3.2 , 3.3 , 3.4 , 3.5 , 3.6 , 3.7.
Core Subject – PAPER-X

REAL ANALYSIS -I
Credits – 4 Instructional hours : 6


Sets and Functions :
Sets and elements; Operations on sets; functions; real valued functions; equivalence; countability; real numbers; least upper bounds.
Sequences of Real Numbers: Definition of a sequence and subsequence; limit of a sequence; convergent sequences; divergent sequences; bounded sequences; monotone sequences; operations on convergent sequences; operations on divergent sequences; limit superior and limit inferior; Cauchy sequences.
Series of Real Numbers : Convergence and divergence; series with non-negative numbers; alternating series; conditional convergence and absolute convergence; tests for absolute convergence; series whose terms form a non-increasing sequence; the class I2.

Limits and metric spaces : Limit of a function on a real line; metric spaces; limits in metric spaces.
Reference Book :-


  1. Treatment as in “Methods of Real Analysis” : Richard R. Goldberg (Oxford and IBH Publishing Co.)




  1. Chapter 1 – (full), Chapter 2 – Sections 2.1 to 2.10

3. Chapter 3 – Section 3.1 to 3.4, 3.6 , 3.7 , 3.10 , Chapter 4 – full.




Core Subject – PAPER- XI

DYNAMICS
Credits – 4 Instructional hours : 6
Kinematics : kinematics of a particle, velocity, acceleration, relative velocity, angular velocity, Newton’s laws of motion, equation of motion, rectilinear motion under constant acceleration, simple harmonic motion.
Projectiles : Time of flight, horizontal range, range in an inclined plane. Impulse and impulsive motion, collision of two smooth spheres, direct and oblique impact-simple problems.
Central forces : Central orbit as plane curve, p-r equation of a central orbit, finding law of force and speed for a given central orbit, finding the central orbit for a given law of force.
Moment of inertia : Moment of inertia of simple bodies, theorems of parallel and perpendicular axes, moment of inertia of triangular lamina, circular lamina, circular ring, right circular cone, sphere (hollow and solid).
Reference Books :


  1. Mechanics – P. Duraipandian and others, S. Chand and Co.

  2. Dynamics – K. Viswanatha Naik and M. S. Kasi, Emerald Publishers.

  3. Dynamics – A. V. Dharmapadam, S. Viswanathan Publishers.



Core Subject – PAPER- XII
PROGRAMMING LANGUAGE ‘C’ WITH MATHEMATICAL

PRACTICALS

THEORY


Credits – 4 Instructional hours : 6

Introduction-Constants- Variables- Data-types-Operators-Precedence of operators – Library functions –Input statements- Output statements-Escape sequences-Formatted outputs – Storage classes – Command line arguments – Preprocessor directives.


Control statements – if statement – if else statement – nested if statement – switch case statement – conditional operator – go to statement –while statement – do while statement – for statement – nested for – continue –exit – break.
Arrays – one dimensional arrays – declarations – initialization of arrays – two dimensional arrays – multidimensional arrays – pointers – functions – function definition – function declaration – calling a function – call by reference - call by value.
Categories of functions – nesting of functions – recursion – function with arrays – strings – arithmetic operators on characters – comparing strings – string handling functions.
Structure – structure definition – structure initialization – union – enumerations – user defined data types(typedef) – files – open – close - input – output – operations on files.
Reference Books :


  1. Programming in ANSI C 2nd edition, E. Balaguruswamy, Tata-Mcgraw Hill Publishing Company.

  2. Venugopal, programming in C

  3. Gottfied, B.S. : programming with C , Schaum’s outline series, TMH 2001


Practicals
Writing ‘C’ programs for the following :


  1. To convert centigrade to Fahrenheit

  2. To find the area, circumference of a circle

  3. To convert days to months and days

  4. To solve quadratic equations

  5. To find sum of n numbers

  6. To find the largest and smallest numbers

  7. To evaluate the sine series, cosine series

  8. To evaluate the power series

  9. To generate Pascal’s triangle, Floyd’s triangle

  10. To add and subtract two matrices

  11. To multiply two matrices

  12. To evaluate Fibonacci series using functions

  13. To evaluate compound interest using functions

  14. To add complex numbers using functions

  15. To use string functions


SEMESTER VI

CORE SUBJECT – PAPER- XIII
ALGEBRAIC STRUCTURES-II

Credits – 4 Instructional hours : 6


Vector Spaces : Definition and examples, linear dependence and independence, dual spaces, inner product spaces.
Linear Transformations : Algebra of linear transformations, characteristic roots, matrices, canonical forms, triangular forms.
Treatment and content as in “Topics in Algebra” – I. N. Herstein-Wiley Eastern Ltd.

Chapter 4 – Sections 4.1 to 4.4

Chapter 6 – Sections 6.1 to 6.4
Reference Books:


  1. University Algebra – N. S. Gopalakrishnan – New Age International Publications, Wiley Eastern Ltd.

  2. First course in Algebra – John B. Fraleigh, Addison Wesley.

  3. Text Book of Algebra – R. Balakrishna and N. Ramabadran, Vikas publishing Co.

  4. Algebra – S. Arumugam, New Gamma publishing house, Palayamkottai.

CORE SUBJECT- XIV
REAL ANALYSIS II

Credits – 4 Instructional hours : 6



Continuous functions on Metric Spaces: Functions continuous at a point on the real line, reformulation, functions continuous on a metric space, open sets, closed sets, discontinuous functions on the real line.
Connectedness Completeness and compactness: More about open sets, connected sets, bounded sets and totally bounded sets, complete metric spaces, compact metric spaces, continuous functions on a compact metric space, continuity of inverse functions, uniform continuity.
Calculus : Sets of measure zero, definition of the Riemann integral, existence of the Riemann integral (statement only) properties of Riemann integral, derivatives, Rolle’s theorem, Law of mean, Fundamental theorems of calculus, Taylor’s theorem.

Sequences and Series of Functions.

Pointwise convergence of sequences of functions, uniform convergence of sequences of functions.
Treatment as in “Methods of Real Analysis”- Richard R. Goldberg (Oxford and IBH Publishing Co)

Chapter 5 and 6 full, Chapter 7, section 7.1 to 7.8, Chapter 8, section 8.5 only, Chapter 9, sections 9.1 and 9.2 0nly








CORE SUBJECT – PAPER – XV
COMPLEX ANALYSIS


Credits – 4 Instructional hours : 6


Complex numbers : Point at infinity , Stereographic projection
Anlaytic functions : Functions of a complex variable , mappings, limits , theorems of limits without proof, continuity, derivatives, differentiation formula , Cauchy-Riemann equations , sufficient conditions Cauchy-Riemann equations in polar form, analytic functions, harmonic functions.
Mappings by elementary functions: linear functions, the function 1/z,linear fractional transformations , the functions w=zn, w=ez, special linear fractional transformations.
Integrals : definite integrals, contours , line integrals, Cauchy-Goursat theorem(without proof), Cauchy integral formula, derivatives of analytic functions, maximum moduli of functions.
Series : convergence of sequences and series (theorems without proof),Taylor’s series, Laurent’s series, zero’s of analytic functions.
Residues and poles : residues, the residue theorem, the principal part of functions, poles, evaluation of improper real integrals, improper integrals, integrals involving trigonometric functions, definite integrals of trigonometric functions
Content and Treatment as in “Complex Variables and Applications” – Ruel V. Churchill, James W. Brown and Roger F.Verhey-McGrawhill International student edition.
Reference Books :-

  1. Theory and problems of Complex Variables – Murray R.Spiegel ,Schaum outline series

  2. Complex Analysis – P.Duraipandian

  3. Introducation to Complex Analysis S. Ponnuswamy , Narosa Publishers 1993



Elective Subjects may be chosen from the following list.
List of Elective subjects.


  1. Operations Research – I

  2. Graph Theory – I

  3. Special Functions – I

  4. Astronomy - I

  5. Operations Research – II (pre-requisite Operations Research –I)

  6. Graph Theory – II(pre-requisite Graph theory – I)

  7. Special Functions – II(pre-requisite Special Functions – I)

  8. Astronomy – II (pre-requisite Astronomy – I)

  9. Discrete Mathematics

  10. Elementary Number Theory



OPERATIONS RESEARCH – I

Credits – 5 Instructional hours : 6


Linear programming – formulation – graphical solution – simplex method
Big-M method – Two-phase method-duality- primal-dual relation – dual simplex method – revised simplex method – Sensitivity analysis.
Transportation problem – assignment problem.
Sequencing problem – n jobs through 2 machines – n jobs through 3 machines – two jobs through m machines – n jobs through m machines
Books for reference :

1.Gauss S.I. Linear programming , McGraw-Hill Book Company.

2.Gupta P.K. and Hira D.S. Problems in Operations Research , S.Chand & Co.

3. Kanti Swaroop, Gupta P.K and Manmohan , problems in operations Research,

Sultan Chand & Sons

4. Ravindran A., Phillips D.T. and Solberg J.J., Operations research, John wiley

& Sons.

5. Taha H.A. Operation Research, Macmillan pub. Company, New York.



6. Linear Programming, transporation, assignment game by Dr.Paria, Books and

Allied(p) Ltd.,1999.


GRAPH THEORY –I

Credits – 5 Instructional hours : 6


Graphs, subgraphs, degree of a vertex, isomorphism of graphs, independent sets

and coverings, intersection graphs and line graphs, adjacency and incidence

matrices, operations on graphs, degree sequences and graphic sequences –

simple problems.

Connectedness, walks, trails,paths, components, bridge, block, connectivity – simple problems. Eulerian and Hamiltonian graphs, trees – simple problems
Content and treatment as in Invitation to Graph Theory by S.Arumugam and S.Ramachandran, New Gamma Publishing House, Palayamkottai
Chapters 1, 2(omit 2.5),3,4,5,6.
Reference books:-

1. A first book at graph theory by John Clark and Derek Allan Holton, Allied publishers

2. Graph Theory by S.Kumaravelu and susheela Kumaravelu,Publishers authors C/o 182

Chidambara Nagar, Nagarkoil




SPECIAL FUNCTIONS – I

Credits – 5 Instructional hours : 6


Simultaneous linear differential equation – particular solution of variation of parameter – Numerical methods for solving ordinary differential equations – Use of Taylor series – Adams method-Runge-kutta method - Picards methods – Extrapolation with differences.
Series solution of differential equations – properties of power series – singular points of linear second order differential equation – the method of Frobenius – Bessel Functions – Properties of Bessel Functions – Differential equation satisfied by Bessel Functions – Legender Functions.
Book for study:

Advanced Calculus of Application, F. B. Hilder brandt

(Section: 1.8, 1.9,3.1 to 3.4,4.1 to 4.8, 4.10, 4.12)

Book for reference:


  1. Differential Equations and Calculus of Variations – L. Els golts

  2. Differential Equations – Diwan and Agashe.

  3. Numerical Analysis – Sea borough





ASTRONOMY – I

Credits – 5 Instructional hours : 6

Spherical trigonometry – Celestial sphere and Diurnal motion – The Earth. Zones of earth, variations of Day and night, Dip and Tuei light – Astronomical Refraction – Geocentric Parallax-Keplers laws, Newton’s deductions and Anomalies – The solar system.
Treatment and Content : “Astronomy” by S. Kumara velu and Susheela Kumaravelu.

OPERATIONS RESEARCH - II

Credits – 5 Instructional hours : 6


PERT and CPM : project network diagram – Critical path (crashing excluded) – PERT computations.
Queuing theory – Basic concepts – Steady state analysis of M/M/1 and M/M/systems with infinite and finite capacities.
Inventory models : Basic concepts - EOQ models : (a) Uniform demand rate infinite production rate with no shortages (b) Uniform demand rate Finite production rate with no shortages – Classical newspaper boy problem with discrete demand – purchase inventory model with one price break.
Game theory : Two-person Zero-sum game with saddle point – without saddle point – dominance – solving 2 x n or m x 2 game by graphical method.
Integer programming : Branch and bound method.
Books for References :

  1. Gauss S. I., Linear Programming, Mcgraw-hill Book Company.

  2. Gupta P. K. and Hira D. S., problems in operations research, S. Chand & Co.

  3. Kanti Swaroop, Gupta P. K. and Manmohan, Problems in Operations Research, Sultan Chand & Sons.

  4. Ravindran A., Philips D. T. and Solberg J. J., Operations Research, John Wiley & Sons.

  5. Taha H. A., Operations Research, Macmilliam Publishing Company, New York.


GRAPH THEORY – II

Credits – 5 Instructional hours : 6

Planarity: Definition and properties, characterization of planar graphs, colourabiliry, chromatic number and index, the five colour theorem, four colour problem, chromatic polynomials directed graphs : Definition and basic properties, paths and connectedness, digraphs and matrices, tournaments, some application connector problem, shortest path problem, one way traffic system; traveling sales man problem.
Tretement as in Invitation to Graph Theory by S. Arumugam and S. Ramachandran, Chapters 7 (omit 7.3), Chapters : 8, 9, 10.1 to 10.5.
Matching : Maximum matching, augmenting path, Bergi’s theorem, Hall’s theorem, Marriage problem, matching and covering: Kongi’s minimax theorem, odd and even components, Tuttes theorem.
Chapter 14 in Graph Theory by S. Kumaravelu and Susheela Kumaravelu.
SPECIAL FUNCTIONS – II

Credits – 5 Instructional hours : 6

Partial Differential equations – Definition and example.
Transverse vibration of a string – solution of wave equations by separation of variables – displacement expressed in Fourier series.
One dimensional heat flow – Heat equation and its solution.
Two dimensional heat flow (steady state only)
Laplace equation in two dimensions and its solutions.

Temperature distribution in rectangular plates.

Laplace’s equation in polar coordinates and its solution.

Temperature distribution in circular annulus.

Laplace transform method of solving partial differential equation.
Books for Reference:


  1. Advanced Calculus for application – F. B. Hilder Brandt.

  2. Differential Equations – Diwan and Agashe.

  3. Mathematics for Engineers and Physicists –Louis Rpes

  4. Mathematics for Engineers – Sckolnikoff.

  5. Alaigal – T. R. Balakrishnan, Tamil Nadu Test book society.

ASTRONOMY – II

Credits – 5 Instructional hours : 6


Equation of time, seasons, calendar and conversion of time – Heliocentric parallax, Annual parallax and aberration – procession and nutation – the moon-Eclipses-Planetary motion.


Treatment and Content : “Astronomy” by S. Kumaravelu & Susheela Kumaravelu.

DISCRETE MATHEMATICS

Credits – 5 Instructional hours : 6


Integers, sets, integers, divisibility of integers, mathematical induction, representation of positive integers.

Boolean algebra and its applications.

Recurrence relation and generating functions

Introduction to graph theory.

Contents and treatment as in introduction to Discrete Mathematics, 2nd edition, 2002 by M. K. Sen and B. C. Chakraborthy Books and Allied private Ltd., Kolkata.

Chapter 1, Chapter 6 (omit 6.4 and 6.6), Chapter 7 and 8.

Reference Books:


  1. Discrete mathematics for computer scientists and mathematicians by J. L. Mertt, Abraham Kendel and T. P. Baker prentice-hall, India.

  2. Discrete mathematics for computer scientists by John Truss-Addision Wesley.

  3. Elements of Discrete Mathematics, C. L. Liu, New York Mcgraw-Hill, 1977.

  4. Discrete mathematical structures with applications to computer science, J. T. Tremblay and R. P. Manohar, New York, Mcgraw-hill, 1975.

  5. Discrete mathematical structures, Bernard Kolman, Robert C. Busby, Shron Ross, 3rd edition, 1998, Prentice hall of India, New Delhi.


ELEMENTARY NUMBER THEORY

Credits – 5 Instructional hours : 6

An introduction top the Theory of Numbers (Vth edition) by Ivan Niven, Herbert S. Zuckarman and Hugh L. Montgometry John Wiley & Sons, Inc.2001.
Chapter 1 : Divisibility

Chapter 2 : 2.1 Congruences

2.2 Solution of Congruences

2.3 Chinese Remaining Theorem

2.8 From Page 97 to 104 (cor 2.42, Th 2.43 and cor 2.44 are

omitted)


2.10 Number Theory from an Algebric view point.

2.11 Groups, rings and fields.

Chapter 3 : 3.1 Quadratic Residues

3.2 Quadratic reciprocity

3.3 The Jacobi Symbol

Chapter 4 : 4.1 Greatest Integer Function

4.2 Arithmetic function

4.3 The Mobius Inversion formula

4.5 Combinational Number Theory (4.4 is omitted)

Chapter 5 : 5.1 The equation ax+by=c

5.2 Simultaneous Linear Equations

5.3 Pythagorean Triples

5.4 Assorted examples

(only simple problem should be asked)


Books for reference:

  1. Elementary theory of numbers, cy. Hsiung, Allied publishers, 1995.

  2. Elementary Number Theory, Allyn and Bacon Inc., Boston, 1980.

  3. Introduction to Analytic Number Theory, Tom. M. Apostol, Narosa Publishing House, New Delhi, 1989.



The Allied Subjects may be chosen from the following List.
List of Allied subjects.


  1. Physics – I

  2. Chemistry – I

  3. Calculus of finite differences and Numerical Analysis –I

  4. Mathematical Statistics – I

  5. Financial Accounting - I

  6. Physics – II (pre-requisite Physics – I)

  7. Chemistry – II (pre-requisite Chemistry – I)

  8. Calculus of finite differences and Numerical Analysis –II (pre-requisite Calculus of finite differences and Numerical Analysis –I )




  1. Mathematical Statistics – II (pre-requisite Mathematical Statistics – I)

  2. Financial Accounting – II (pre-requisite Financial Accounting – I)

  3. Cost Accounting

  4. Management Accounting

NOTE: Syllabus for Financial Accounting – I and II can be obtained from Board of Studies for Commerc



Calculus of finite differences and Numerical Analysis – I (5 Credits )

Solutions of algebraic and transcendental equations, Bisection method, Iteration method, Regulafalsi method, Newton-Raphsons method.


Solution of Simultaneous linear equations: Guass-elimination method, Guass-Jordan method, Guass-Siedel method, Crout’s method.
Finite differences: E operators and relation between them, Differences of a polynomial, factorial polynomials, differences of zero, summation series.
Interpolation with equal intervals: Newton’s forward and backward interpolation formulae. Central differences formulae-Gauss forward and backward formulae, Sterling’s formula and Bessel’s formula.
Interpolation with unequal intervals: Divided differences and Newton’s divided differences formula for interpolation and Lagrange’s formula for interpolation.

Inverse Interpolation – Lagrange’s method, Reversion of series method.


Reference Books:

  1. Calculus of finite differences and Numerical analysis by Gupta-Malik, Krishna Prakastan Mandir, Meerut.

  2. Numerical methods in Science and Engineering by M. K. Venkataraman, National publishing house, Chennai.

  3. Numerical Analysis by B. D. Gupta, Konark publishing.

  4. Calculus of finite differences and Numerical Analysis by Sexena, S. Chand & Co.




Calculus of finite differences and Numerical Analysis – II (5 Credits)
Numerical differentiation: Derivatives using Newton’s forward and backward difference formulae, Derivatives using Sterling’s formula, Derivative using divided difference formula, Maxima and Minima using the above formulae.
Numerical integration: General quadrature formula, Trapezoidal rule, Simpson’s one-third rule, Simpson’s three-eighth rule, Weddle’s rule, Euler-Maclaurin Summation formula, Sterling’s formula for n!.
Difference equations: Linear homogenous and nonhomogenous difference equation with constant coefficients, particular integrals for a^u x^m , x^m, sinkx, coskx.
Numerical solution of ordinary difference equations (I order only)
Taylor’s series method, Picard’s method, Euler’s method, Modified Euler’s method, Runge-kutta method fourth order only, Predictor-corrector method-Milne’s method and Adams-Bashforth method.
Reference Books:

  1. Calculus of finite differences and Numerical Analysis by Gupta-Malik, Krishna prakastan Mandir, Meerut.

  2. Numerical methods in Science and Engineering by M. K. Venkataraman, National publishing house, Chennai.

  3. Numerical Analysis by B. D. Gupta, Konark publishing.

  4. Calculus of finite differences and Numerical Analysis by Saxena, Chand & Co.


MATHEMATICAL STATISTICS – I (4 credits)

(Theory and Practicals)


UNIT – 1 : Statistics – Definition – functions – applications – complete enumeration – sampling methods – measures of central tendency – measures of dispersion – skew ness-kurtosis.
UNIT – 2 : Sample space – Events, Definition of probability (Classical, Statistical & Axiomatic ) – Addition and multiplication laws of probability – Independence – Conditional probability – Bayes theorem – simple problems.

UNIT – 3 : Random Variables (Discrete and continuous), Distribution function – Expected values & moments – Moment generating function – probability generating function – Examples. Characteristic function – Uniqueness and inversion theorems (Statements and applications only) – Cumulants, Chebychev’s inequality – Simple problems.
UNIT – 4 : Concepts of bivariate distribution – Correlation : Rank correlation coefficient – Concepts of partial and multiple correlation coefficients – Regression : Method of Least squares for fitting Linear, Quadratic and exponential curves - simple problems.
UNIT – 5 : Standard distributions – Binomial, Hyper geometric, Poission, Normal and Uniform distributions – Geometric, Exponential, Gamma and Beta distributions, Inter-relationship among distributions.
Books for study and reference:

  1. Hogg R. V. & Craig A. T. 1988) : Introduction to Mathematical Statistics, Mcmillan.

  2. Mood A. M & Graybill F. A & Boes D. G (1974) : Introduction to theory of Statistics, Mcgraw Hill.

  3. Snedecor G. W. & Cochran W. G (1967) : Statistical Methods, Oxford and
    IBH.

MATHEMATICAL STATISTICS – II (4 credits)
(Theory and Practicals)

UNIT – 1 : Sampling Theory – sampling distributions – concept of standard error-sampling distribution based on Normal distribution : t, chi-square and F distribution.
UNIT – 2 : Point estimation-concepts of unbiasedness, consistency, efficiency and sufficiency-Cramer Rao inequality-methods of estimation : Maximum likelihood, moments and minimum chi-square and their properties. (Statement only)
UNIT – 3 : Test of Significance-standard error-large sample tests. Exact tests based on Normal, t, chi-square and F distributions with respect to population mean/means, proportion/proportions variances and correlation co-efficient. Theory of attributes – tests of independence of attributes based on contingency tables – goodness of fit tests based on Chi-square.
UNIT – 4 : Analysis of variance : One way, two-way classification – Concepts and problems, interval estimation – confidence intervals for population mean/means, proportion/proportions and variances based on Normal, t, chi-square and F.
UNIT – 5 : Tests of hypothesis : Type I and Type II errors – power of test-Neyman Pearson Lemma – Likelihood ratio tests – concepts of most powerful test – (statements and results only) simple problems

.

Books for study and reference:




  1. Hogg R. V. & Craig A. T (1998) : Introduction to Mathematical Statistics, Mcmillan.

  2. Mood A. M & Graybill F. A & Boes D. G (1974) : Introduction to theory of Statistics.

  3. Snedecor G. W & Cochran W. G : Statistical Methods, Oxford and IBH.

  4. Hoel P. G. (1971) : Introduction to Mathematical Statistics, Wiley.

  5. Wilks S. S : Elementary Statistical Analysis, Oxford and IBH.



Practicals Based on Mathematical Statistics I and II (credits)


  1. Construction of univariate and bivariate frequency distributions with

samples of size not exceeding 200.

  1. Diagramatic and Graphical Representation of data and frequency

distribution.

  1. Cumulative frequency distribution-Ogives-Lorenz curve.

  2. Measure of location and dispersion(absolute and relative), Skewness and

Kurtosis.

  1. Numerical Problem involving derivation of marginal and conditional

distributions and related measures of Moments.

  1. Fitting of Binomial, Poisson and Normal distributions and tests of

goodness of fit.

  1. Curve fitting by the method of least squares.

(i) y=ax+b ;(ii) y=ax^2 +bx+c ;(iii) y=ae^bx ;(iv) y=ax^b

  1. Computation of correlation coefficients and regression lines for raw and

grouped data. Rank correlation coefficient.

  1. Asymptotic and exact test of significance with regard to population

mean, proportion, variance and coefficient of correlation.

  1. Test for independence of attributes based on contingency table.

  2. Confidence Interval based on Normal,t,Chi-square statistics.


NOTE:

Use of scientific calculator may be permitted for Mathematical Statistics Practical Examination.

Statistical and Mathematical tables are to be provided to students at the examination hall.
12. B.Sc. DEGREE COURSE IN MICROBIOLOGY
SYLLABUS

SEMESTER - III
PAPER V - MOLECULAR BIOLOGY

UNIT I

DNA structure, various forms (A, B, Z & H), Stability of nucleic acid structures; prokaryotic and eukaryotic genome organizations.


UNIT II

DNA replication, repair and recombination: Unit of replication, enzymes involved, replication origin and replication fork, fidelity of replication, extrachromosomal replicons, DNA damage and repair mechanisms.

UNIT III

RNA synthesis and processing: Transcription factors and machinery, formation of initiation complex, transcription activators and repressors, RNA polymerases, capping, elongation and termination, RNA processing, RNA editing, splicing, polyadenylation, structure and function of different types of RNA, RNA transport.
UNIT IV

Protein synthesis and processing: Ribosome, formation of initiation complex, initiation factors and their regulation, elongation and elongation factors, termination, genetic code, aminoacylation of tRNA, tRNA-identity, aminoacyl tRNA synthetase, translational proof-reading, translational inhibitors, post-translational modification of proteins.
UNIT V

Control of gene expression at transcription and translation level: Regulation of phages, viruses, prokaryotic and eukaryotic gene expression, role of chromatinin regulating gene expression and gene silencing.
PAPER VI - MAJOR PRACTICAL III

UNIT I

Estimation of DNA by diphenylamine method. Estimation of RNA by orcinol method.


UNIT II

Isolation of Plasmid DNA by Alkalysis method.

Isolation of Chromosomal DNA from Eukaryotic cells. Eg. Leaves, Human Lymphocytes.
UNIT III

Isolation of RNA from yeast.

Isolation of antibiotic resistant auxotrophic mutants.

UNIT IV

Preparation of competent cells.


UNIT V

Transformation of E.coli.


ALLIED SUBJECT II

PAPER I - BIOCHEMISTRY
UNIT I

Organization of life. Importance of water, Cell structure and organelles. Composition, Structure and function of biomolecules: Carbohydrates, Lipids, Proteins and Nucleic acids and Vitamins.
UNIT II

Principles and applications of Gel-filtration, Ion - Exchange and Affinity Chromatography; Thin Layer and Gas Chromatography; High Pressure Liquid (HPLC) Chromatography; Electrophoresis and Electrofocussing; Ultracentrifugation (velocity and buoyant density). Spectroscopic methods: UV- visible and fluorescence.


UNIT III

Proteins structure, folding and function. Myoglobin, Hemoglobin, Lysozme, Ribonuclease A, Carboxypeptidase and Chymotrypsin. Principles of catalysis, enzymes and enzyme kinetics, enzyme regulation, mechanism of enzyme catalysis, isozymes.


UNIT IV

Metabolism and bioenergitics. Generation and utilization of ATP. Photo synthesis. Major metabolic pathways and their regulation.


UNIT V

Biological membrances. Transport across membranes. Signal transduction hormones and neurotransmitters.



ALLIED SUBJECT II

PAPER II - BIOCHEMISTRY PRACTICAL
UNIT I

Estimation of monosaccharides- Glucose(Benedict’s) fructose, mannose. Estimation of disaccharides- lactose, sucrose.


UNIT II

Qualitative analysis of starch. Qualitative analysis of arginine, cystenine, trytophan, tyrosine.


UNIT III

Estimation of chloride by Mohr’s method. Estimation of glycine by formal titration method.




UNIT IV

Estimation of iron using potassium permanganate as link solution and ferrous ammonium sulphate as standard.


UNIT V

Estimation of ascoribic acid using 2,6-dichlorophenol indophenol as link solution Estimation of protein by Biuret method.


Semester - IV

paper VII - Soil AND AGRICULTURAL MICROBIOLOGY
UNIT I

Soil microbiology - quantitative and qualitative micro flora of different soils-role of microbes in soil fertility-tests for soil fertility-soil structure, soil formation-characterization of soil types and importance.


UNIT II

Biogeochemical cycles-role of micro organisms in carbon, phosphorus. sulphur and iron cycles. Methods of studying ecology of soil micro organisms-microbial gas metabolism-carbon dioxide, hydrogen, and methane and hydrogen sulphide.


UNIT III

Microbial interactions between microorganisms, plant and soil. Rhizoplane, rhizosphere, phyllosphere, spermosphere, mycorrhizae. Microbial association with insects-gut micro flora - symbiosis between microbes and insects; organic matter decomposition.



UNIT IV

Nitrogen cycle; ammonification- nitrification- de-nitrification- nitrogen fixation- Bio-fertilizers (bacterial, cyanobacteria and azolla) and crop response-bio-pesticides (bacterial, viral and fungal) saprophytes for pathogen suppression.


UNIT V

Principles of plant infection and defense mechanisms. Symptoms, Etiology, Epidemiology and Management of the following plant diseases: Mosaic disease of tobacco; Bunchy top of banana; Leaf roll of potato; Bacterial blight of paddy; Angular leaf spot of cotton, Late blight of potato; Damping off of tobacco, downy mildew of bajra; Powdery mildew of cucurbits; Head smut of sorghum; Leaf rust of coffee; Blight of maize/sorghum; Leafspot of paddy, Grassy shoot of sugar cane; Root knot of mulberry.


Paper VIII - MAJOR PRACTICAL IV

UNIT I

Methods to study soil microorganisms - Isolation and enumeration of Bacteria, Fungi, Bacterio-phages, Algae, Protozoa etc., Microbiological test for fertility - Bacterial and Fungal


UNIT II

Microbiological demonstration of soil enzymes – Amylase, Protease, Lipase, Gelatinase etc.,


UNIT III

Isolation and identification of root nodule bacteria- Rhizobium(symbiotic), demonstration of rhizobium in the root nodule(CS of root nodule) Isolation and identification of Azotobacter (Asymbiotic).




UNIT IV

Isolation and identification of nitrogen fixing Cyanobacteria-Anabaena, Nostoc etc., Demonstration of Azolla Demonstration of antagonistic activity –bacterial and fungal.


UNIT V

Study of the following discases: Tobacco mosaic; Bacterial blight of paddy; Downy mildew of bajra; Powdery mildew of cucurbits; Head smut of sorghum; Leaf rust of coffee; Leaf spot of paddy, Red rot of sugar cane, Root knot of mulberry.


ALLIED SUBJECT II

PAPER III - BIOSTATISTICS

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