Dr.M.G.R. UNIVERSITY DEPARTMENT OF MATHEMATICS B.Sc ...

Dr.M.G.R. EDUCATIONAL AND RESEARCH INSTITUTE

UNIVERSITY (Decl. U/S 3 of the UGC Act 1956)

DEPARTMENT OF MATHEMATICS

B.Sc - Mathematics - 2013 Regulations

B.Sc Mathematics (Full Time) Curriculum and Syllabus

2013 Regulation

I SEMESTER

S.No Sub. Code Title of Subject L T P C

1

HBTA13001/

HBHI13001/

HBFR13001

Language – Paper I 3 0 0 3

2 HBEN14001 English – Paper I 3 0 0 3

3 HBMA13001 Algebra & Trigonometry 3 1 0 4

4 HBMA13002 Calculus 3 1 0 4

5 HBPY13A01 Allied I – Applied Physics I 3 1 0 4

TOTAL 15 3 0 18

II SEMESTER


1

HBTA13002/

HBHI13002/

HBFR13002

Language – Paper II 3 0 0 3

2 HBEN14002 English – Paper II 3 0 0 3

3 HBMA13003 Differential Equations, Laplace Transforms & Fourier Series 3 1 0 4

4 HBMA13004 Differential Geometry & Analytical Geometry of Three

Dimensions 3 1 0 4

5 HBPY13A02 Allied I – Applied Physics II 3 1 0 4

TOTAL 15 3 0 18





III SEMESTER


1 HBMA13005 Algebraic Structures 3 1 0 4

2 HBMA13006 Multivariate Calculus & Theory of Numbers 3 1 0 4

3 HBMA13007 Mathematical Statistics 3 1 0 4

4 HBCH13A01 Allied II – Allied Chemistry I 4 0 0 4

5 HBMG13L01 Soft Skills I 2 0 0 2

6 HBMG13001 Environmental Studies 3 0 0 3

TOTAL 18 3 0 21

IV SEMESTER


1 HBMA13008 Linear Algebra 3 1 0 4

2 HBMA13009 Advanced Calculus 3 1 0 4

3 HBMA13010 Numerical Methods 3 1 0 4

4 HBCH13A02 Allied II – Allied Chemistry II 4 0 0 4

5 HBMG13L02 Soft Skills II 2 0 0 2

6 HBMG13G01 Entrepreneurship Development 3 0 0 3

TOTAL 18 3 0 21





V SEMESTER


1 HBMA13011 Real Analysis 3 1 0 4

2 HBMA13012 Mechanics 3 1 0 4

3 HBMA13013 Discrete Mathematics I 3 1 0 4

4 Elective I 3 1 0 4

5 Elective II 3 1 0 4

6 Elective III 3 1 0 4

TOTAL 18 6 0 24

VI SEMESTER


1 HBMA13014 Complex Analysis 3 1 0 4

2 HBMA13015 Linear Programming 3 1 0 4

3 HBMA13016 Discrete Mathematics II 3 1 0 4

4 HBMA13017 Fuzzy set theory 3 1 0 4

5 Elective IV 3 1 0 4

6 Elective V 3 1 0 4

7 Elective VI 3 1 0 4

TOTAL 21 7 0 28

List of Electives


1 HBMA13E01 Financial Mathematics 3 1 0 4

2 HBMA13E02 Fluid Dynamics 3 1 0 4

3 HBMA13E03 Mathematical Modeling 3 1 0 4

4 HBMA13E04 Formal Languages & Graph theory 3 1 0 4

5 HBMA13E05 Mathematical Physics 3 1 0 4

6 HBMA13E06 Introduction to Mathematica 3 0 1 4





HBTA13001 TAMIL-I 3 0 0 3

Ø

Ø

Ø

Ø





Total no of Hrs: 45





HBHI13001 HINDI – I 3 0 0 3

OBJECTIVES:

Ø Special emphasis on creative writing with phrases and quotes. Ø Essays of eminent authors have been selected Ø Administrative terms prescribed by official language department is taught

Prose, Administrative Hindi and Grammer.

UNIT I 9 Hrs

1. Sabhyata kaa rahasya – lesson and annotations ,Questions & answers,

2. Administrative terms ( Prayojan mulak Hindi)

UNIT II 9 Hrs

1. Mitratha ka rahasya - lesson and annotations questions and answers

2. Patra lekhan, definitions, correspondence in hindi

UNIT III 9 Hrs

1. Paramanu oorja evam and kadhya sanrakshan (lesson ) annotations and answers,

2. Technical terms and words, letter writing

UNIT IV 9 Hrs

1. Yuvavon se (lesson), annotations, essay and questions and answers

2. Types of official correspondence, technical terms

3. Grammer(Change of voice, correcting the sentences)

UNIT V 9 Hrs

1. Yogyata aur vyavasay ka chunav (Lesson) essay, questions and answers

2. Letter writing

3. grammer & technical terms

Total no of Hrs: 45

REFERENCES

1. Dr. Syed Rahmatullah & Poornima Prakashan, Hindi gadhya maala

2. Dr. Syed Rahmatullah & Poornima Prakashan, Prayojanmulak Hindi

3. Dakshin Bharat Hindi Prachara Sabha, T.Nagar, Saral Hindi Vyakaran-2





HBFR13001 FRENCH I 3 0 0 3

UNITS : 1-6 (Module A et B)

UNITÉ 1

Décrouvrir le langue francaise

UNITÉ 2

Faire connaissance

UNITÉ 3

Organizer son temps

UNITÉ 4

Découvrir son environment

UNITÉ 5

S’ informer, Se faire plaisir

Authors : Jacky Girardet, Jacques Pécheur

Available at : Goyal Publishers Pvt Ltd 86, University Block Jawahar Nagar

New Delhi – 110007. Tel : 011 – 23858362 / 23858983





HBEN14001 ENGLISH – I 3 0 0 3

OBJECTIVES: · To make students improve their vocabulary and its usage .

· To inculcate in them the pleasure of reading stories, plays and dramas.

· To promote their skill of writing essays,paragraph etc.

· To make them learn grammar in an informal way.

· To improve their speaking skill.

· To fecilitate the learners in enhancing their LSRW skills.

UNIT I PROSE 12 Hrs Textures of English (Cambridge University Press India Pvt. Limited)

Headache - R.K Narayan

A Little Bit of What You Fancy - Desmond Morris

My Early Days - Abdul Kalam

How to Escape from Intellectual Rubbish - Russell

Town by the Sea - Amitav Ghosh

UNIT II POETRYVerse (Macmillam Publishers India Limited) 8 Hrs Written in Early Spring - Wordsworth

When I have Fears - John Keats

Ulysses - Tennyson

The Unknown Citizen - Auden

For Elkana - Ezekiel

Unit III Short Stories 8 Hrs Vignettes: A Collection of Short Stories Ed.Dr.P.N.Ramani

(New Century Book House(p)Limited) Upper Division Love - Manohar Malgonkar

The Doll’s House - Katherine Mansfield

Marriage is a Private Affair - Chinua Achebe

The Man Who Knew Too Much - Alexander Baron

The Ransom of Red Chief - O Henry

Unit IV Functional English & Soft Skills 8 Hrs Synonym, Antonym, Prefix-Suffix, Word Formation, Tense, Auxilliaries (Primary and Modal), Types of Sentences,

Voice, Interogatives (Yes or No, Wh questions), Tag questions, Adjectives, Degrees of Comparison, Adverb,

Conditional Sentences, Sentenoes Expressing Cause and Effect, Purpose, Concord or subject-verb agreement,

Common errors

Letter Writing –seeking permission, requests, comprehension, note-making.

Soft Skill: Spring Board to Success, Sharda Kaushik. Etal Orient Black Swan – 2014.

Part I – Speech Sounds in English Language

Part II – Group Talk

Unit V One Act Plays 5 Hrs Six One Act Plays Ed;Dr.Nafeesa Kaleem – (Anu Chitra Publications) The Dear Departed - Stanley Houghton

The Discovery - Herman Ould

The Shirt - Francis Dillon

The Pie and the Tait - Hugh Chesterton

Refund - Fritz Karinthy

Test and Written Exercises: 4 Hrs Total no. of Hrs :45 REFERENCES

v English Pronunciation in Use-Marks Hancock Cambridge Univ – 2003.

v Sharda Kaushik etal Orient Black Swan ( 2014) Spring Board to Success.





HBMA13001 ALGEBRA AND TRIGONOMETRY 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Theory of Equations and the methods of solving them. Ø To understand the basic concepts in Summation of Series and Trigonometric Identities.

UNIT I (12 hrs) Theory of Equations: Introduction to polynomials - Roots of polynomial equations – Imaginary and irrational roots –

Relation between roots and coefficients – Symmetric function of the roots.

UNIT II (12 hrs) Transformation of equations – Reciprocal equations - Descartes’ rule of signs – Solution by Newton’s and Horner’s

method, Cardon’s method of solution of a cubic polynomial equation with real coefficients.

UNIT III (12 hrs) Series: Summation of series using Binomial, Exponential and Logarithmic series and approximations. UNIT IV (12 hrs) Expansion of cosnx, sin nx, tan nx, cosnx, sin nx –Expansion of sin x, cos x, tan x in terms of x –Hyperbolic

functions.

UNIT V (12 hrs) Logarithms of complex quantities – Sums of sines and cosines of n angles which are in Arithmetic Progression -

Summation of trigonometric series using complex quantities.

Total no. of hrs: 60 TEXT BOOKS:

1) Manicavachagom Pillay,T.K. Natarajan, T. Ganapathy, K.S (2004) Algebra, Volume – I ,S. Viswanathan

Publishers.

2) Kandasamy, P Thilagavathy, K. (2004) Mathematics, Volume – I (First Edition), S. Chand & Co,.

3) Narayanan, S. Manicavachagom Pillay T.K (2010) Trigonometry, S.Viswanathan Publishers.

REFERENCE BOOKS: 1) Vittal, P.R. Malini, V. (2001) Algebra, Analytical Geometry and Trigonometry - I Year – Paper I,

Margham Publications, Chennai.





HBMA13002 CALCULUS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Differential and Integral Calculus. UNIT I (12 hrs) Introduction to differentiation - Successive differentiation - nth derivative – Leibnitz formula for nth derivative of a

product – Partial differentiation – total differential Coefficient– Homogeneous functions – Euler’s theorem.

UNIT II (12 hrs) Maxima and minima of functions of 2 variables – Lagrange’s method of undetermined multipliers – simple

problems.

UNIT III (12 hrs) Introduction to integration - Methods of integration – Integration by parts - Bernoulli’s formula.

UNIT IV (12 hrs) Properties of definite integrals – reduction formulae for standard integrals.

UNIT V (12 hrs) Areas in polar coordinates - Length of the curve (Cartesian and polar coordinates) – Area of surface of revolution

(Cartesian and polar coordinates).


1) Narayanan, S. Manicavachagom Pillay T.K (2010) Calculus Vol. I, S.Viswanathan Publishers.

2) Narayanan, S. Manicavachagom Pillay T.K (2010) Calculus Vol. II, S.Viswanathan Publishers.

REFERENCE BOOKS:

1) Kandasamy, P Thilagavathy, K. (2004) Mathematics, Volume – I, S. Chand & Co,.





HBPY13A01 APPLIED PHYSICS I 3 1 0 4 UNIT I (12 hrs) Heat and Sound: Conduction of Heat – Thermal conductivity – Thermal Conductivity of bad conductor – Lee’s Disc

method- Radial flow of Heat – Thermal conductivity of glass and rubber. Ultrasonics – Production of Ultrasonics –

Piezo electric method – Magnetostriction method – Properties - Applications.

UNIT II (12 hrs) Fiber Optics: Introduction – Total internal reflection – Acceptance Angle and Numerical Aperture – Classification

of Optical Fibers – Step index Fiber and Graded index Fiber – Optical Fiber communication. Laser: Spontaneous

and Stimulated emission – Population Inversion – He-Ne Laser, CO2 Laser – Semiconductor Laser – Applications.

UNIT III (12 hrs) Electrostatics, Electricity & Magnetism: Capacitor – Energy of a charged capacitor – Capacity of a cylindrical

capacitor – Loss of energy due to sharing of charges – Magnetic field due to a current carrying conductor. – DC &

AC motors – Transformer – Construction and principle of operation – Eddy current.

UNIT IV (12 hrs) DC circuits: Introduction to electrical circuits, ohm’s law, Kirchhoff’s law, method of solving circuits by

Kirchhoff’s laws, series and parallel connections – problems. AC circuits: peak, average and RMS values of AC

current and voltage – LR circuits, CR circuits, LCR circuits, Resonance frequency – Power factor and current values

in an AC circuit.

UNIT V (12 hrs) Nano materials: Definition – classification – properties – Types of synthesis method – Sol-gel method – Gas

condensation method – chemical method their applications. Non-Destructive Method: Definition – Liquid Penetrant

method – Ultrasonic Flaw detection method – Applications.


1) Thangaraj, K. Jeyaraman, D Allied Physics, Popular Book Depot..

2) Rajendran, V. Marikani, A. Applied Physics for Engineers, Tata-Mcgraw Hill.

3) Khare, N.S. Srivastava, S.S. (1983) Electricity and Magnetism, Atma Ram & Sons.

REFERENCE BOOKS:

1) Resnick, Halliday Fundamentals of Physics.

2) Jeyaraman, D. Engineering Physics.

3) Arumugam, M. Materials Science, Anuratha publications.





HBTA13002 TAMIL II 3 0 0 3

Ø

Ø

Ø

Ø





HBHI13002 HINDI II 3 0 0 3 OBJECTIVES:

Ø Famous ancient and modern poets from the Hindi literature are prescribed

Ø Navrasas and meters are taught

Ø To keep with latest trends in modern Hindi, Computer applications in Hindi, provisions of official language

Act etc are included

UNIT I (Poetry, Hindi computing ,alankar) 9 Hrs

1. Poetry Manu Ki chintha – kavi parichay, annotation, summary, Madhushala and kabirdhas , two padhya

only

2. 2. Alankaar anupras, and upma only

UNIT II 9 Hrs

1.Poetry Surdas (two padh only), kavi parichay, annotation , Kaikeyi ka paschatap

2. Utpreksha alankar

UNIT III 9 Hrs

1. Meerabai only only one padya

2. Kaamkaji hindi, concept of official language, and hindi computing theory

UNIT IV 9 Hrs

1. Jugnu ,summary & meaning annotation

2. Hin di software packages,

UNIT V 9 Hrs

1. Kavi parichay

2. Kabirdas, Meerabai Mythili saran gupta

3. Jaishankar Prasad

4. Slesha alankar.

Total No of Hrs :45

REFERENCES

1. Dakshin Bharat hindi prachara sabha, Kavya Kusum- 3

2. Murali Manohar & vidhya nilaya, Ras Chand Alankar

3. Hareesh vishwavidyalay prakashan, agra, Kaam kaji hindi and hindi computing





HBFR13002 FRENCH II 3 0 0 3

UNITS : 1(Module C et D)

UNITÉ 2 Cultiver

ses relations

UNITÉ 3 9 Hrs

Découvrir le passé

UNITÉ 4 9 Hrs

Entreprendre

UNITÉ 5 9 Hrs

Prendre des décisions

UNITÉ 11 9 Hrs

Faire face aux problémes

UNITÉ 12 9 Hrs

S’ evader

Total No of Hrs :45

Authors : Jacky Girardet, Jacques Pécheur

Available at : Goyal Publishers Pvt Ltd 86, University Block Jawahar Nagar

New Delhi – 110007. Tel : 011 – 23858362 / 23858983





HBEN14002 ENGLISH – II 3 0 0 3

OBJECTIVES:

· To make students improve their vocabulary and its usage .

· To inculcate in them the pleasure of reading stories, plays and dramas.

· To promote their skill of writing essays,paragraph etc.

· To make them learn grammar in an informal way.

· To improve their speaking skill.

· To fecilitate the learners in enhancing their LSRW skills.

UNIT I PROSE 12 Hrs

Textures of English (Cambridge University Press India Pvt. Limited)

History of Chess - Barbara Mack

To Know When to Say, “It’s None of Your Business -McCormck

The India of My Dreams -Indira Gandhi

The Second Crucifixion -Collins and Lapiere

How to Avoid Argument -Sam Horn

UNIT II POETRY Verse (Macmillam Publishers India Limited) 8 Hrs

Lcave this Chanting -Tagore

The Stonc -Gibson

Mending Wall -Frost

The Ballad of Father Gilligan -W.B.Yeats

The Listeners -De La Mare

UNIT III BIOGRAPHICAL SKETCHES 8 Hrs

Portraits in Prose-An Anthology of Biographical Sketches

Ed:S.Jagadisan, Orient Blackswan Private Limited

Socrates -Sir Richard Livingstone

Leo Tolstoy -Ronald Seth

Alexander Fleming -Philip Cane

Mother Teresa -John Frazer

Martin Luther King -R.N.Roy

UNIT IV FUNCTIONAL ENGLISH & SOFT SKILLS 8 Hrs

Prepositions, Reported Speech, Editing, Phrasal Verbs and Idioms, Gerunds Infinitives, Beginning Senternces with

‘It’, Common Errors,Use in sentence words as different word classes – (Text based) Writing CV, Completing a

dialogue, Expansion of hints

Soft Skill: Spring Board to Success, Sharda Kaushik. Etal Orient Black Swan – 2014.

Part III English Usage





Part IV Listening Skills

Part V Face to Face Interaction

Unit V Scenes from Shakespeare – Emerald Pulblication 5 Hrs

Test and Written Exercies 4 Hrs

Total No of Hrs: 45

REFERENCES v English Pronunciation in Use-Marks Hancock Cambridge Univ – 2003.

v Sharda Kaushik etal Orient Black Swan(2014) Spring Board to Success





HBMA13003 DIFFERENTIAL EQUATIONS, LAPLACE TRANSFORMS & FOURIER SERIES 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Ordinary and Partial Differential Equations. Ø To understand the basic concepts in Laplace Transforms and Fourier Series.

UNIT I (12 hrs) Ordinary Differential Equations:Introduction to ordinary differential equations - First order but of higher degree

equations – solvable for p, solvable for x, solvable for y – Clairaut’s form – simple problems. Second order equation

with constant coefficient with particular integrals for eax

xm, e

axsin mx, e

axcos mx.

UNIT II (12 hrs) Second order differential equation with variable coefficients ax

2 d

2y/dx

2 + bx dy/dx + cy = g(x) – method of

variation of parameters.

UNIT III (12 hrs) Laplace Transforms: Introduction - Laplace transforms – inverse transform -Application of Laplace to solution of

first and second order linear differential equation with constant coefficients.

UNIT IV (12 hrs) Partial Differential Equations: Introduction to partial differential equations (PDE) - Formation of PDE by

eliminating arbitrary constants and arbitrary functions – complete integral – singular integral – general integral -

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 equation

Pp+Qq = R . (Simple Problems)

UNIT V (12 hrs) Fourier Series: Introduction to Fourier series - Definition – Examples of Fourier series – Even or odd functions –

Fourier series for even and odd functions – Half range expansions. (Simple problems)


1) Narayanan, S. Manicavachagom Pillay T.K (2010) Calculus Vol. III, S.Viswanathan Publishers.

REFERENCE BOOKS: 1) Venkataraman, M.K (2001) Engineering Mathematics Volume III, The National Publishing Company.





HBMA13004 DIFFERENTIAL & ANALYTICAL GEOMETRY OF THREE DIMENSIONS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Differential & Analytical Geometry. UNIT I (12 hrs) Curvature – Cartesian formula for radius of curvature - The coordinates of the centre of curvature – Evolute and

involute.

UNIT II (12 hrs) Radius of curvature in polar coordinates – p-r equation – Envelopes (definitions and problems only) – Linear

asymptotes (definitions and simple problems only).

UNIT III (12 hrs) The plane – the general equation – several forms of the equations of a plane – angle between planes – length of

perpendicular – equation of the planes bisecting the angle between the planes.

UNIT IV (12 hrs) The Straight Line – symmetrical form – plane and straight line – coplanar lines – shortest distance between two

lines.

UNIT V (12 hrs) The Sphere – standard form – plane section – equation of sphere passing through a given circle – intersection of two

spheres – tangent plane to a sphere.


1) Narayanan, S. Manicavachagom Pillay T.K (2010) Calculus Vol. I, S.Viswanathan Publishers.

2) Narayanan, S. Manicavachagom Pillay T.K (2007) Calculus A text book of Analytical Geometry – part II

(Three Dimensions), S.Viswanathan Publishers.

REFERENCE BOOKS: 1) Jain, P.K Khalil Ahmed (1986) Text book of Analytical Geometry of Three Dimensions, Wiley Eastern

Ltd.

2) Arumugam, S Thangapandi Isaac, A. Analytical Geometry (3D) and Vector Calculus, New Gamma

Publishing House, Palayamkottai.





HBPY13A02 APPLIED PHYSICS II 3 1 0 4 UNIT I (12 hrs) Crystal Physics: Space lattice – Unit cells – Bravais space lattices – Lattice planes – Miller indices – Calculation of

number of atoms per unit cell – Atomic radius – Coordination number and Packing factor for SC, BCC, FCC, HCP

structures.

UNIT II (12 hrs) Semiconductor Diodes: P-type and N-type semiconductors – Junction diode and Zener Diode – Junction Diode &

Zener Diode characteristics – Junction Diode as a rectifier – Zener diode as a voltage regulator – Transistor:

Characteristics – Transistor as an amplifier.

UNIT III (12 hrs) Electronic Devices: Rectifiers – Half wave and Full wave rectifier – Efficiency – Capacitive Filter – Ripple factor –

Field Effect Transistor: Types – Junction field effect Transistor, Metal Oxide – Semiconductor field effect

Transistor – Characteristics – Silicon Control Rectifier – Characteristics.

UNIT IV (12 hrs) Digital Electronics: Number system – Binary system, Decimal to Binary, Octal system, Hexadecimal system, Binary

– Addition, Subtraction, Multiplication and Division. Logic Gates: OR, AND, NOT, Exclusive-OR, NOR, NAND

gates, simple combinational - logic circuits – half adder, full adder, BCD adder.

UNIT V (12 hrs) Operational Amplifier: OP-Amp–Voltage amplifier, OP-Amp-Adder, Subtractor, OP-Amp-Comparator, OP-Amp-

Intrgrators.


1) Mehta, V.K. Principles of Electronics, S.Chand & Co.

2) Sedha, R.S. A Text book of Applied Electronics, S.Chand & Co.

3) Theraja, B.L. Fundamentals of Electrical Engineering & Electronics, S.Chand & Co.

4) Rajendran, V. Marikani, A. Applied Physics for Engineers, Tata-Mcgraw Hill.





HBMA13005 ALGEBRAIC STRUCTURES 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Group & Ring theory. UNIT I (12 hrs) Group Theory: Groups – Subgroups – Counting Principle – Normal Subgroups.

UNIT II (12 hrs) Homomorphisms – Automorphisms – Cayley’s theorem – Permutation groups.

UNIT III (12 hrs) Ring Theory: Definition and examples of Rings – Some special classes of rings – Homomorphisms.

UNIT IV (12 hrs) Ideals and Quotient rings: More ideals and Quotient ideals – field of quotients of an integral domain.

UNIT V (12 hrs) Euclidean rings: A particular Euclidean ring – Polynomial Rings – Polynomials over the rational field.


1) Herstein, I.N (2009) Topics in Algebra, Second Edition,Wiley Student edition.

REFERENCE BOOKS: 1) Santiago, M.L (2001) Modern Algebra, Tata McGraw-Hill Publishing Co. Ltd.





HBMA13006 MULTIVARIATE CALCULUS & THEORY OF NUMBERS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Multiple Integrals & Vector Calculus. Ø To understand the basic concepts in Theory of Numbers.

UNIT I (12 hrs) Multiple Integral: Double integral – Polar and Cartesian coordinates – Change of order of

integration – Jacobian – Application to area.

UNIT II (12 hrs) Triple integral – Volume under triple integral – Surface area - Special functions: Beta and Gamma Functions, their

properties and simple problems.

UNIT III (12 hrs) Vector Calculus: Introduction–Gradient – Divergent – Curl – Formulae involving Ñ–Invariance.

UNIT IV (12 hrs) Line, Surface and Volume integrals – Theorems of Gauss, Stokes and Green’s (Statements only)

– simple problems.

UNIT V (12 hrs) Prime and Composite numbers – The sieve of Eratosthenes-Divisors of a given number N – Euler’s function –

Integral part of a real number- The highest power of a prime p contained in n! – the product of r consecutive integers

is divisible by r! – Congruences – Numbers in arithmetic progressions – Fermat’s Theorem- (statement only) -

Wilson’s theorem – (statement only) – Simple Problems.

Total no. of hrs: 60 Text Books:

1) Narayanan, S. Manicavachagom Pillay T.K (2007) Calculus Vol. II, S.Viswanathan Publishers.

2) Spiegel, Seymour Lipschutz, Dennis Spellman (2009) Vector Analysis, Schaum’s outline series, Second

Edition, McGraw Hill Book Company.

3) Manicavachagom Pillay,T.K. Natarajan, T. Ganapathy, K.S (2006) Algebra, Volume – II ,S. Viswanathan

Publishers.





HBMA13007 MATHEMATICAL STATISTICS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Discrete & Continuous probability distributions. Ø To understand the basic concepts in Sampling theory.

UNIT I (12 hrs) Discrete and Continuous Probability Distributions: Random variables – Probability distributions – Discrete and

Continuous, Mathematical expectation, moments, moment generating function, characteristic function.

UNIT II (12 hrs) Special Discrete and Continuous Distributions: Introduction – Binomial, Poisson distributions – Normal distribution.

UNIT III (12 hrs) Correlation and Regression: Correlation coefficient, linear regression – equations of lines of regression.

UNIT IV (12 hrs) Tests of Significance – Large Samples: Introduction – Types of Sampling – Large samples – Testing the

significance for a single proportion - Testing of significance for difference of proportions – Sampling of values of a

variable – Sampling distribution of the mean – Confidence limits - Testing the significance of difference between

standard deviations of two large samples.

UNIT V (12 hrs) Tests of Significance – Small Samples: Introduction – Chi – square distribution – Student’s t – distribution –

Snedecor’s F distribution (Definitions only) – Properties (Statements only) - Tests of significance based on t, F -

distributions, Chi square test : Goodness of fit, test of independence.

Total no. of hrs: 60 Text Books:

1) Kapur, J.N. Saxena, H.C (2010) Mathematical Statistics, 20th Edition, S. Chand & Co. Ltd., New Delhi.

Reference Books: 1) Gupta, S.C. Kapoor, V.K (1994) Fundamental of Mathematical Statistics, 9th Edition, Sultan Chand &

Sons, New Delhi.

2) Vittal P.R. (2002) Mathematical Statistics, Margham Publications.





HBCH13A01 ALLIED CHEMISTRY I 3 1 0 4 UNIT I (12 hrs) Atomic structure: electronic configuration - Aufbau principle - Pauli's exclusion principle- Hund's rule.

Bonding: electrovalent, covalent, hydrogen bonds-orbital overlap - s-s, s-p - hybridization, and VESPR theory -

CH4, C2H4, C2H2- BeCl2, BF3, NH3, H2O, PCl5, IF5, IF7.

UNIT II (12 hrs) Metallurgy : General principles - ores and minerals - ore dressing - extraction methods-purification of crude metal

(electrolytic refining only)- ferrous alloys only- heat treatment of steel. Solid state: crystalline and amorphous

solids-structure and properties- laws of crystallography- Miller indices simple cube, body centered cube and face

centered cube structure of NaCl and CsCl, diamond and graphite.

UNIT III (12 hrs) Coordination Chemistry: IUPAC nomenclature -Werner, Sidgwick and Pauling theories of metal-ligand bonding-

stability-chelates applications of complexes in qualitative and volumetric analyses- geometrical and volumetric

analyses- geometrical isomerism of four coordinated complexes. Principles of qualitative analysis and volumetric

analysis: concept of solubility product, common ion effect, its application in qualitative and volumetric analyses-

principles of acid-base and redox titrations.

UNIT IV (12 hrs) Fuel gases: composition-natural-water-semi water- carbonated water, producer, oil and gobar gases.

Fertilizers - preparation of urea, ammonium sulphate, ammonium nitrate, potassium nitrate-triple super phosphate-

NPK ratio. Cement and glass: Portland cement-manufacture only. Manufacture of glass types and uses borosilicate -

photochromic and safety glass.

UNIT V (12 hrs) Aromaticity: Concept (reference to benzene only) heterocyclic chemistry - preparation and properties of

pyrrole,furan,thiophene and pyridine. Types of reagents and reactions: Electrophile, nucleophile and free radicals -

substitution -elimination-addition- oxidation-reduction-rearrangement: Pinacol-pinacolone, benzidine, ortho Claisen

and Beckmann rearrangements. Stereochemistry: optical isomerism of tartaric acid, geometrical isomerism of

maleic and fumaric acids.

Total no. of hrs: 60 Reference Books: 1. R.Gopalan, R. .Sundaram , S. Allied Chemistry 2. Ramachandra Shastri Ancillary Chemistry





HBMG13L01 SOFT SKILLS I 2 0 0 2

Carrier & Confidence Building

OBJECTIVES: To improve

Ø Value system

Ø Interpersonal skills

Ø Behaving in corporate culture

Ø Self awareness/confidence

Ø Communication skill

UNIT I 6 Hrs

Creation of awareness of the top companies / different verticals / courses for improving skill set matrix, Industry

expectations to enable them to prepare for their carrer – Development of positive frame of mind – Avoiding

inhibitions – Creation of self awareness – Overcoming of inferiority / superiority complex.

UNIT II 6 Hrs

Selection of appropriate field vis-à-vis personality / interest to create awareness of existing industries, Preparation

of Curriculum Vitae – Objectives, Profiles vis-à-vis companies.

UNIT III 6 Hrs

Group discussions: Do’s and Don’ts – handling of group discussions – What evaluators look for Interpersonal

relationships – with colleagues – clients – understanding one’s own behavior – perception by others, How to work

with persons whose background, culture, language / work style different from one’s, behavior pattern in multi-

national offices.

UNIT IV 6 Hrs

Interview – awareness of facing questions – Do’s and Don’ts of personal interview / group interview, Enabling

students prepare for different Procedures / levels to enter into any company – books / websites to help for further

preparation, Technical interview – how to prepare to face it. Undergoing employability skills test.

UNIT V 6 Hrs

Entrepreneurship development – preparation for tests prior to the interview – Qualities and pre-requisites for

launching a firm.

Total No of Hrs : 30

REFERENCES

1. Aggarwal R,S (1989) Quantitative Aptitude, S.Chand,

2. Shalini Verma(2009) Soft Skills Pearson.

3. Shalini verma (2012) Enhancing employability @ SOFT SKILLS, Pearson.

4. Kiranmai Dutt,P & Geetha Rajeevan(2010) A Couse in Communication Skills, Foundation Books.

5. Nira konar (2011) English Language Laboratories, PHI Learning. 6. Anandamurugan, S (2011) Placement Interviews, Tata McGraw Hill Education.





HBMG13001 ENVIRONMENTAL STUDIES 3 0 0 3

OBJECTIVES:

Ø Understanding of the human and natural environment

Ø Demonstrate in-depth understanding of the environment.

Ø Demonstrate an ability to integrate the many disciplines and fields that intersect with environmental

concerns

UNIT I 9 Hrs

INTRODUTION TO ENVIRONMENTAL STUDIES : Definition, Scope and importance – Need for Public

awareness – Types of resources – Utilization of forest resources, water resources, Mineral resources, food resources,

energy resources and land resources- Dams and their effects on forest and tribal people-conflicts over water-

equitable use of resources for sustainable life styles.

UNIT II 9 Hrs

ECOSYSTEMS AND BIODIVERRSITY : Kinds of ecosystems- Structure and functions of an ecosystems- Energy

flow within the ecosystem –Productivity- food chains and Trophic Levels- Ecological Pyramids- value of

biodiversity – Biodiversity at global, National & local levels – Hot spots of Biodiversity –Threats to biodiversity –

Endangered and Endemic species of India – Conservation of Biodiversity.

UNIT III 9 Hrs

ENVIRONMENTAL POLLUTION : Environmental Pollution, sources, effects-control measures for air pollution,

water pollution, Noise pollution, Land pollution, Marine pollution, e-waste pollution,Solid Waste Management-

Disaster Management.

UNIT IV 9 Hrs

ENVIRONMENTAL MANAGEMENT Introduction - Environmental Management – climate change -

population growth – Nuclear Accidents and Holocaust- Human Health and Human Rights- Environmental Ethics-

Environmental Legislation- public awareness – Role of information Technology in Environmental & human health

UNIT V 9 Hrs

CASE STUDIES Visit to a local area to document environmental assets River/forest/grassland/hill/mountain) -

Study of common plants, insects, birds- Study of simple ecosystems-pond, river, hill slopes – Visit to a local

polluted site (Urban/Rural/ Industrial/ Agricultural)- e-waste hazardous –case study.Total No of Hrs : 45

TEXT BOOK

1. Meenambal,T(2009) Environmental Science and Engineering, MJP Publishers, Chennai.

REFERENCES 1. Iftikaruddin,(2006) Principles of Environmental science and Engineering’, Sooraj Publication.

2. Masters,G(2006) Environmental Engineering, New Centurion Book House, New Delhi.

3. Rajagopal, Environmental Engineering, Oxford University Press, New Delhi.

4. Biny Joseph(2006) Environmental Engineering, Tata McGraw Hills.

5. Rana(2003) Essentials of Ecology and Environmental Science, Prentice – Hall of India Private Limited,

New Delhi.





HBMA13008 LINEAR ALGEBRA 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Vector spaces & Linear Transformations. UNIT I (12 hrs) Vector Spaces: Definitions, examples – Subspaces and Quotient Spaces – Sums and Direct Sums – Linear

Independence.

UNIT II (12 hrs) Basis and Dimensions – Homomorphisms – Dual Spaces – Inner Product Spaces.

UNIT III (12 hrs) Linear Transformations and Matrices: Algebra of Linear Transformations – Eigen values and Eigenvectors.

UNIT IV (12 hrs) Matrix Algebra – Trace and Transpose of a Matrix – Rank of Matrix.

UNIT V (12 hrs) Determinants – Hermitian and Unitary Transformations.


1) \Santiago, M.L (2001) Modern Algebra, Tata McGraw-Hill Publishing Co. Ltd,.

REFERENCE BOOKS: 1) Herstein, I.N (2009) Topics in Algebra, Second Edition, Wiley Student edition.





HBMA13009 ADVANCED CALCULUS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Set theory, Sequences & Series. Ø To understand the basic concepts in Fourier Transforms.

UNIT I (12 hrs) Sets and Functions : Sets and elements – Operations on sets – Functions – Real valued functions – Equivalence –

Countability – Real numbers – Least upper bounds.

UNIT II (12 hrs) 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.

UNIT III (12 hrs) 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.

UNIT IV (12 hrs) Tests for absolute convergence; Series whose terms form a non-increasing sequence.

Limits and metric spaces: Limit of a function on a real line; Metric spaces; Limits in metric spaces.

UNIT V (12 hrs) Fourier Transform: Complex form of Fourier integral formula, Properties of Fourier transform, Fourier Cosine and

Fourier Sine Transforms, Properties, Convolution, Parseval’s identity.


1) Richard Goldberg Methods of Real Analysis, Oxford and IBH Publishing Co.

2) Narayanan, S. Manicavachagom Pillay T.K (2010) Calculus Vol. III, S.Viswanathan Publishers.

REFERENCE BOOKS: 1) Walter Rudin (1976) Principles of Real analysis, Third edition, Mc-Graw Hill international edition.

2) Arumugam, Issac, S. (1993) Sequence and Series, New Gamma Publishing House.





HBMA13010 NUMERICAL METHODS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Solving Algebraic & Transcendental equations. Ø To understand the basic concepts in Interpolation, Numerical Differentiation & Integration.

UNIT I (12 hrs) Algebraic and Transcendental Equations: Introduction, Errors in numerical computation, Iterative method, Bisection

method, Regula-Falsi method, Newton-Raphson method.

UNIT II (12 hrs) Finite Differences: Difference operators, other difference operators, Error propagation in a difference table,

Summation of series.

UNIT III (12 hrs) Interpolation: Introduction, Newton’s interpolation formulae, Bessels’s and Stirling’s formula, Lagrange’s

interpolation formulae, Divided differences, Newton’s divided differences formula, Inverse interpolation.

UNIT IV (12 hrs) Numerical Differentiation and Integration: Introduction, Derivatives using Newton’s forward difference formula,

Derivatives using Newton’s backward difference formula, Numerical integration – Trapezoidal rule, Simpson’s one

– third, three – eighth rule, Weddle’s rule.

UNIT V (12 hrs) Numerical Solutions of Ordinary Differential Equations: Introduction, Taylor’s series method, Picard’s method,

Euler method, Runge-Kutta methods, Predictor-Corrector methods – Milne’s method, Adam- Bashforth method.


1) Arumugam, S. Thangapandi Isaac, A. Somasundaram, A. (2001) Numerical Methods, Scitech Publications

Pvt. Ltd.

REFERENCE BOOKS: 1) B.D.Gupta,B.D. (2003) Numerical Analysis, Konark Publishers Pvt Ltd.

2) Kandaswamy, P. Thilagavathy, Gunavathi (1997) Numerical Methods, First Edition, S.Chand & Company

Ltd.





HBCH13A02 ALLIED CHEMISTRY II 3 1 0 4 UNIT I (12 hrs) Polymer chemistry: types of polymerisation addition and condensationthermosetting and thermoplastics rubber

natural and synthetic fibers nylon-6 and 66, polyesters, PE , PVC, Poylvinyl acetate.

Amino acids, polypeptides and proteins: Classification and sources of amino acids, preparation and properties of

glycine, zwitterion structure, isoelectric point, peptides synthesis of a dipeptide, end group analysis, proteins

classification and general characteristics. UNIT II (12 hrs) Sulpha drugs: Preparation and uses of sulphanilamide, sulphaguanidine and sulphathiozole. Source and uses of

penicillin, chloromycetin and streptomycin (structural elucidation not needed)

Carbohydrates: Occurrence, classification, reactions and constitution of glucose and fructose-elucidation of

structures (only open chain structure) disaccharides sucrose and maltose (reactions only).

Vitamins: Sources, deficiencies and uses.

UNIT III (12 hrs) Air pollution: Pollution due to automobile fuels - green house effect - SO2 emission and acid rain - depletion of

ozone and its consequences. Water pollution: Characteristics, BOD-COD treatment of domestic waste water.

Agricultural pollution: Pesticides-biomagnification and consequences. Noise pollution: Pollution measurement and

control. Food pollution: Natural toxins and food additives. Environmental pollution by plastics. Radiation

pollutants: sources and examples.

UNIT IV (12 hrs) Chemical kinetics: Order and molecularity , zero, first and second order reactions differential and integrated forms,

experimental methods for determination of order of a reaction, activation energy, evaluation and significance, simple

numerical problems. Photochemistry: Laws, Grothus-Draper, Beer-Lambert, Stark- Einstein, examples of

photochemical reactions, chlorination of methane, quantum yield photolysis of acetaldehyde and

photopolymerisation of polythene, photosensitisation fluorescence, phosphorescence and chemiluminescence.

UNIT V (12 hrs) Electrochemistry: Specific and molar conductances, Kohlrausch's law - measurement of dissociation constant.

Conductometric titration.

Galvanic cells: Standard electrode potential, electrochemical series - electroplating. pH, buffer solutions -

significance of pH and buffer solution in biological system - acid base theories and simple numerical calculations.

Total no. of hrs: 60

REFERENCE BOOKS: 1. R.Gopalan and S.Sundaram - Allied Chemistry 2. A.Ramachandra Shastri - Ancillary Chemistry





HBMG13L02 SOFT SKILLS II 2 0 0 2

To be organized by the Placement & Training department with the assistance of external agencies.

OBJECTIVES:

The purpose of this is to build confidence and inculcate various Soft skills and to help students to identify and

achieve their personal potential

At the end of this training program the participant will be able to,

Explain the concept problem solving

Ø Outline the basic steps in problem solving

Ø List out the key elements

Ø Explain the use of tools and techniques in problem solving

Ø Discuss the personality types and problem in solving techniques

Ø By adapting different thinking styles in group and lean environment

Ø Recognizing and removing barriers to thinking in challenging situations

Ø Make better decision through critical thinking and creative problem solving

Methodology

The entire program is designed in such a way that every student will participate in the class room activities. The

activities are planned to bring out the skills and talent of the students which they will be employing during various in

their life.

1. Group activities + individual activities

2. Collaborative learning

3. Interactive sessions

4. Ensure participation

5. Empirical learning

UNIT I 6 Hrs

Self Introduction – Narration – Current news update – Current Tech update – GD

UNIT II 6 Hrs

Verbal Aptitude Test I – odd man out series – GD I – Mock Interview I

UNIT III 6 Hrs

Verbal Aptitude Test II – Resume Writing- Mock Interview II – reading comprehension

UNIT IV 6 Hrs

GD III – Numbers – Height and distance – directions – permutation and combination – odd man out – problem on

ages.





UNIT V 6 Hrs

1. Mock Interview III – ratio and proportion – clocks – HCF and LCM – Time and work – profit and loss –

partnership.


REFERENCES

1. Pushpalata a& Sanjay kumar (2007) Communicate or Collpase: A Handbook of Effective Public Speaking,

Group Discussions and Interviews. Prentice-Hall, Delhi.

2. Thorpe & Edgar(2003) Course in Mental Ability and Quantitative Aptitude, Tata MCGraw-Hil.

3. Thorpe & Edgar(2003) Test of Reasoning, Tata MCGraw-Hill.

4. Prasad, H.M,(2001) How to prepare for Group Discussion and Interview, Tata MCGraw-Hill.

5. Agarwal, R.S(2004) A Modern Approach to verbal non-Verbal Reasoning, S.Chand & Co.

Mishra Sunita & Muralikrishna, Communication Skills for Engineers(1st ed.) , Pearson Education.





HBMG13G01 ENTREPRENEURSHIP DEVELOPMENT 3 0 0 3

OBJECTIVES:

Ø Understand the process and procedure involved in setting up a small enterprise.

Ø Acquire the necessary managerial skills required to run a small-scale industry.

Ø Know the pros and cons in becoming an entrepreneur.

UNIT I 9 Hrs

Entrepreneur –Meaning – Definition – Characteristics – Functions – Role of Entrepreneurs in the economic

development – Classification of entrepreneurs – Factors affecting entrepreneurial growth.

UNIT II 9 Hrs

Entrepreneurship – Concept – Distinction between Entrepreneur and Entrepreneurship - Entrepreneurship

Development Programmes – Objectives - Stages in EDP- Pre-training Stage – Training phase – Post Training –

Evaluation and Feedback of EDP.

UNIT III 9 Hrs

Project Identification - Sources of ideas – Preliminary evaluation and testing of ideas – Constraints - Project

formulation – Stages- Feasibility study and Feasibility Report – Selection Criteria.

UNIT IV 9 Hrs

Project Report - Project Appraisal – Technical – commercial appraisal –Financial appraisal– Sources of finance –

Steps to star an industrial unit.

UNIT V 9 Hrs

Incentives and subsidies of State and Central Govt. – Aims – Backward areas – Industrial Estates –Role of

DIC,SISI, TCO in entrepreneurial growth.


TEXT BOOKS:

1. Singh,P,N(1986) Developing Entrepreneurship for Economic Growth.

REFERENCES:

1. Guide to Entrepreneurs – Industrial Development – Govt. of Tamil Nadu – SIPCOT





HBMA13011 REAL ANALYSIS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Metric spaces, Connectedness, Completeness and compactness. Ø To understand the basic concepts in Sequences and Series of Functions.

UNIT I (12 hrs) 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.

UNIT II (12 hrs) Connectedness Completeness and compactness: More about open sets, Connected sets, Bounded sets and totally

bounded sets, Complete metric spaces, Compact metric spaces.

UNIT III (12 hrs) Continuous functions on a compact metric space, Continuity of inverse functions, Uniform continuity. Sets of

measure zero, Definition of the Riemann integral, Existence of the Riemann integral (Statement of theorem 7.3a

only) –Properties of Riemann integral.

UNIT IV (12 hrs) Calculus: Derivatives, Rolle’s theorem, Law of mean, Fundamental theorems of calculus, Taylor’s theorem.

UNIT V (12 hrs) Sequences and Series of Functions: Point wise convergence of sequences of functions – Uniform convergence of

sequences of functions – Consequences of uniform convergence – Convergence and uniform convergence of series

of functions – Integration and differentiation of series of functions.


1) Richard Goldberg Methods of Real Analysis, Oxford and IBH Publishing Co.

REFERENCE BOOKS: 1) Chandrasekhara Rao, K. Narayan, K.S (2008) Real analysis, Volume II, S.ViswanathanPrinters &

Publishers Pvt. Ltd.

2) Shanti Narayan, Raisinghania (2011) Elements of Real Analysis, S.Chand & Company Ltd.





HBMA13012 MECHANICS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Statics, Friction & Projectiles. UNIT I (12 hrs) Statics: Concurrent system of forces: Triangle law of forces, Lami’s Theorem, Polygon law of forces, Moment of a

force, Varignon’s Theorem.

UNIT II (12 hrs) Friction: Laws of friction, Angle of friction, Ladder problems - Dynamics - Energy: Kinetic energy, Conservation of

energy, Conservation forces.

UNIT III (12 hrs) Projectiles: Trajectory, Horizontal and inclined planes.S.H.M: General solution, Elastic strings, Composition of two

S.H.M, Simple Pendulum, Seconds Pendulum.

UNIT IV (12 hrs) Motion of a particle along a curve: Conical Pendulum, Motion on a curved track, Circular track, Banked up track,

Vertical curve, Motion on the outside of a smooth vertical circle, inside a vertical circle.

UNIT V (12 hrs) Central Orbits: Central forces, Differential equation of a central orbit, Pedal equation, Apse, p-r equation, Inverse

square law.


1) Viswanatha Naik, Kasi (1992) Statics, Emerald Publishers. 2) Viswanatha Naik, Kasi (1992) Dynamics, Emerald Publishers.

REFERENCE BOOKS: 1) Duraipandian, Laxmi Duraipandian, Muthamizh Jayapragasam (2010) Dynamics, S.Chand & Company

Ltd.

2) Venkataraman, M.K (1994) A text book of Statics, M.K Agasthiar Publications.

3) Venkataraman, M.K (1994) A text book of Dynamics, M.K Agasthiar Publications.





HBMA13013 DISCRETE MATHEMATICS I 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Combinatroics. UNIT I (12 hrs) Basic Combinatorial Numbers – Stirling Numbers of the First Kind – Stirling Numbers of the Second Kind.

UNIT II (12 hrs) Generating Functions and Recurrence Relations – Symmetric Functions.

UNIT III (12 hrs) Multinomials – Multinomial Theorem – Inclusion and Exclusion Principle.

UNIT IV (12 hrs) Euler Function – Permutations with Forbidden Positions – The ‘Menage’ Problem – Problem of Fibonacci.

UNIT V (12 hrs) Polya Theory – Necklace Problem and Burnside’s Lemma – Cycle Index of a Permutation Group – Polya’s

theorems and their Immediate Applications.


1) Krishnamurthy, V. (1989) Combinatorics Theory and Applications, East –West Press.

REFERENCE BOOKS: 1) Balakrishnan, V.K (1994) Theory and Problems of combinatorics, Schaums outline series – Mcgraw Hill.





HBMA13014 COMPLEX ANALYSIS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Analytic functions & Conformal mapping. Ø To understand the basic concepts in Complex Integration.

UNIT I (12 hrs) Analytic functions: Functions of a Complex variable, Mappings, limits, Theorem on limits, Continuity, derivatives,

differentiation formulas, Cauchy Riemann equations, sufficient conditions, Polar coordinates, Analytic functions,

Harmonic functions.

UNIT II (12 hrs) Conformal mapping – preservation of angles, Linear fractional transformations, an implicit form, mappings of the

upper half plane, special linear fractional transformations, w = z2, w = e

z.

UNIT III (12 hrs) Integrals: Contours, Contour integrals, upper bounds for moduli of contour integrals, Anti derivatives, Cauchy

Goursat theorem, Proof of the Cauchy Goursat theorem, Simply and Multiply connected domains,– Cauchy integral

formula – Derivatives of Analytical functions. Liouville’s theorem and Fundamental theorem of Algebra.–

Maximum modulus principle.

UNIT IV (12 hrs) Convergence of sequence, Convergence of series, Taylor’s series , Laurent series, Absolute and uniform

convergence of power Series, Continuity of sums of power series ,Integration and differentiation of power series.

Uniqueness of series representation.

UNIT V (12 hrs) Residues –Cauchy Residue theorem, Using a single residue, The three types of isolated singular points, Residues at

poles, Zeros of analytical functions, Zeros and poles, Evaluation of real improper integrals, improper integrals from

Fourier Analysis, Jordans lemma, Definite integrals involving sines and cosines.


1) James Brown, Churchill (2003) Complex variables and application, Seventh Edition, Mc-Graw Hill Book

Co.

REFERENCE BOOKS: 1) Arumugam, Thangapandi Isaac, Somasundaram (2010) Complex Analysis, Scitech publications (India) Pvt.

Ltd.

2) Venkatachalapathy, S.G (2009) Complex Analysis, Margham Publication.





HBMA13015 LINEAR PROGRAMMING 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Linear Programming and Duality in Linear Programming. Ø To understand the basic concepts in Transportation & Assignment problems.

UNIT I (12 hrs) Mathematical Formulation-Graphical Solution and Extension: Introduction- Linear Programming Problem –

Mathematical formulation of L.P.P – Illustration on Mathematical formulation of L.P.P. Graphical Solution Method

– Some Exceptional Cases – General Linear Programming Problem –Canonical and Standard Forms of L.P.P.

UNIT II (12 hrs) Simplex Method: Introduction-Fundamental Properties of Solutions (Theorems-Statement only)-The Computational

Procedure-Use of Artificial Variables (only Big-M Method or Method of Penalties)-Degeneracy in Linear

Programming.

UNIT III (12 hrs) Duality in Linear Programming: Introduction –General Primal-Dual Pair-Formulating a Dual Problem- Primal-Dual

Pair in Matrix Form-Duality Theorems-Complementary Slackness Theorem- Duality and Simplex Method.

UNIT IV (12 hrs) Transportation Problem: Introduction –LP formulation of the transportation Problem –

Existence of solutions in T.P-Duality in Transportation Problem-The Transportation table-Loops

in Transportation tables-Triangular Basis in a T.P-Solution of a Transportation Problem –Finding

an Initial Basic Feasible Solution –Test for Optimality - Degeneracy in Transportation Problem - Transportation

Algorithm (Modi Method)-Stepping Stone Solution Method.

UNIT V (12 hrs) Assignment Problem: Introduction- Mathematical Formulation of the problem-Solution

Methods of Assignment Problems –Special Cases in Assignment Problem.

Sequencing Problem: Introduction-Problem of Sequencing-Basic terms Used in Sequencing-

Processing n jobs through Two Machines.


1) Kanti Swarup, Gupta, Man Mohan (2010) Operations Research, Sultan Chand and Sons Ltd.

REFERENCE BOOKS: 1) Prem Kumar Gupta, Hira, D.S (2007) Operations Research, S. Chand &Company Ltd.





HBMA13016 DISCRETE MATHEMATICS II 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Mathematical Logic & Lattices. Ø To understand the basic concepts in Boolean Algebra.

UNIT I (12 hrs) Mathematical Induction, Recurrence Relations and Generating Functions

Techniques of Proof – Mathematical Induction – Recurrence – Polynomials and their Evaluations – Recurrence

Relations – Generating Functions – Some Common Recurrence Relations – Primitive Recursive Functions –

Recursive and Partial Recursive Functions.

UNIT II (12 hrs) Mathematical Logic: TF Statements – Connectives – Atomic and Compound Statements – Well-Formed Statement

Formulae –Parsing – Truth Table of a Formula – Tautology – Tautological Implications and Equivalence of

Formulae.

UNIT III (12 hrs) Replacement Process – Functionally Complete sets of connectives and Duality law – Normal Forms – Principal

Normal Forms.

UNIT IV (12 hrs) Lattices: Lattices – Some properties of Lattices – New Lattices – Modular and Distributive Lattices.

UNIT V (12 hrs) Boolean Algebra:Boolean Algebra – Boolean Polynomials – Karnaugh Maps.


1) Venkataraman, Sridharan, Chandrasekaran (2003) Discrete Mathematics, The National Publishing

Company.

REFERENCE BOOKS: 1) Johnson baugh, R.(2001) Discrete Mathematics, 5th Edn., Pearson Education, Asia.





HBMA13017 FUZZY SET THEORY 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Fuzzy sets & Possibility theory. Ø To understand the basic concepts in Fuzzy Decision making.

UNIT I (12 hrs) Fuzzy sets – Basic concepts – set theoretic operations on fuzzy sets – Fuzzy relations.

UNIT II (12 hrs) Fuzzy Measures Possibility Theory – Possibility distributions – Possibility and necessity measures – Possibility and

Probability – Relationship among class of Fuzzy measures.

UNIT III (12 hrs) Linguistic variables, Fuzzy logic, Fuzzy Languages, Approximate Reasoning, Expert systems, Uncertainty modeling

in expert system.

UNIT IV (12 hrs) Fuzzy control, Pattern recognition, Fuzzy clustering, Modeling the diagnostic process, Applications in Management.

UNIT V (12 hrs) Fuzzy decisions, Fuzzy linear programming, Fuzzy Dynamic Programming.


1) George Kir, Tina Folger (2000) Fuzzy sets, Uncertainty and Information, Prentice Hall of India.

2) Zimmerman, H.J (2000) Fuzzy set Theory and its Applications, Allied Publishers Ltd.

REFERENCE BOOKS: 1) Klir, Yuan (2000) Fuzzy sets and Fuzzy logic – Theory and Applications, Prentice Hall of India.





HBMA13E01 FINANCIAL MATHEMATICS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Simple Interest & Compound Interest. Ø To understand the basic concepts in Bonds & Capital Budgeting.

UNIT I (12 hrs) Simple Interest and Compound Interest: Simple interest, Equations of value, Partial payments, Simple discount,

Compound Interest, Accumulated value, Discounted value, Finding the rate, Finding the time, Equations of value,

Compound Discount.

UNIT II (12 hrs) Simple Annuities: Simple Annuities, Accumulated value and discounted value of ordinary simple annuity, Finding

term and interest rate, General annuities, Perpetuities.

UNIT III (12 hrs) Amortization and Sinking Funds: Amortization of a debt, Outstanding funds, Mortgages, Sinking funds,

Comparison of amortization and sinking fund methods.

UNIT IV (12 hrs) Bonds: Callable bonds, Premium and discount, Price of a bond between bond interest dates, Finding the yield rate,

Other type of bonds.

UNIT V (12 hrs) Capital Budgeting and Depreciation: Net present value, Internal rate of return, Capitalized cost and capital

budgeting, Depreciation.


1) Petra Zima, Robert Brown (2005) Mathematics of Finance, Second edition, Schaum’s Outlines Tata

McGraw-Hill.

REFERENCE BOOKS: 1) Vittal, P.R (2005) Business Mathematics, Margham Publications.





HBMA13E02 FLUID DYNAMICS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Kinematics. Ø To understand the basic concepts in Two & Three Dimensional flows.

UNIT I (12 hrs) Kinematics of fluids in motion: Real fluids and ideal fluids – velocity of a fluid at a point – stream lines and path

lines; steady and unsteady flows – the velocity potential – the vorticity vector – local and particle rates of change –

the Equations of continuity – worked examples – Acceleration of fluid – Conditions at a rigid boundary – general

analysis of fluid motion.

UNIT II (12 hrs) Equations of motions of a fluid: Pressure at a point in a fluid at rest – Pressure at a point in moving fluid –

Conditions at a boundary of two inviscid immiscible fluids – Euler’s equation of motion, Bernoulli’s equation –

worked examples.

UNIT III (12 hrs) Discussion of the case of steady motion under conservative body forces – some flows involving axial symmetry –

some special two dimensional flows – Impulsive motion – some further aspects of Vortex motion.

UNIT IV (12 hrs) Some Three dimensional flows: Introduction – Sources, sinks and doublets – Images in a rigid infinite plane –

Images in solid spheres – Axisymmetric flows; Stoke’s stream function.

UNIT V (12 hrs) Some Two-dimensional flows: Meaning of two dimensional flow – use of cylindrical polar coordinates – stream

function – the complex potential for two dimensional, irrotational, incompressible flow – the complex velocity

potentials for standard two dimensional flows – some worked examples – Two dimensional image systems – Milne

Thompson circle Theorem – The Theorem of Blasius.


1) Chorlton, F. (1985) Text book of Fluid Dynamics, CBS Publishers.

REFERENCE BOOKS: 1) Walther Kaufmann (1963) Fluid Dynamics, Tata McGraw-Hill.





HBMA13E03 MATHEMATICAL MODELING 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Mathematical Modeling through Ordinary Differential Equations. Ø To understand the basic concepts in Mathematical Modeling through Difference Equations & Graphs.

UNIT I (12 hrs) Mathematical Modeling through Ordinary Differential Equations of First order: Linear Growth and Decay Models –

Non-Linear Growth and Decay Models – Compartment Models – Dynamic problems – Geometrical problems.

UNIT II (12 hrs) Mathematical Modeling through Systems of Ordinary Differential Equations of First Order: Population Dynamics –

Epidemics – Compartment Models –Economics – Medicine, Arms Race, Battles and International Trade –

Dynamics.

UNIT III (12 hrs) Mathematical Modeling through Ordinary Differential Equations of Second Order: Planetary Motions – Circular

Motion and Motion of Satellites –Mathematical Modeling through Linear Differential Equations of Second Order –

Miscellaneous Mathematical Models.

UNIT IV (12 hrs) Mathematical Modeling through Difference Equations: Simple Models – Basic Theory of Linear Difference

Equations with Constant Coefficients – Economics and Finance – Population Dynamics and Genetics – Probability

Theory.

UNIT V (12 hrs) Mathematical Modeling through Graphs: Solutions that can be Modelled Through Graphs – Mathematical Modeling

in Terms of Directed Graphs, Signed Graphs, Weighted Digraphs and Unoriented Graphs.


1) Kapur, J.N (1988) Mathematical Modeling, Wiley Eastern Limited.

REFERENCE BOOKS: 1) Kapur, J.N (1985) Mathematical Models in biology and Medicine, EWP, New Delhi.





HBMA13E04 FORMAL LANUGAGES AND GRAPH THEORY 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Finite State Automata, Graphs & Trees. UNIT I (12 hrs) Phrase-Structure languages, Closure properties:Four types of grammars, Chomskian hierarchy, Closure operations,

Derivation trees, Ambiguity.

UNIT II (12 hrs) Normal form of CFG, Property of CFL:Auxiliary lemmas, Chomsky Normal form, u-v theorem.

UNIT III (12 hrs) Finite State Automata: Finite Automaton, Non-Deterministic Finite Automaton, Finite Automata and Regular sets,

Closure properties of Regular sets, Charaterisation of the family of Regular sets.

UNIT IV (12 hrs) Introduction, Paths and Circuits: Graphs, Incidence and degree of a vertex, Walks, Paths and Circuits, Euler graphs,

Operations on graphs, Hamiltonian paths and circuits, Travelling Salesman Problem.

UNIT V (12 hrs) Trees, Fundamental Circuits, Cut-sets and Cut-vertices:Trees, Properties of trees, On counting trees, Spanning trees,

Fundamental circuits, Cut-sets, Properties of cut-sets, Connectivity and separability.


1) Rani Siromoney (1984) Formal Languages and Automata, CLS.

2) Narsingh Deo (2005) Graph Theory with Applications to Engineering and Computer Science, Prentice Hall

of India Pvt. Ltd..

.

REFERENCE BOOKS: 1) Arumugam, S. Ramachandran, S. (2002) Invitation to Graph Theory, Scitech Publications (India) Pvt. Ltd.





HBMA13E05 MATHEMATICAL PHYSICS 3 1 0 4 OBJECTIVES:

Ø To understand the basic concepts in Lagrange’s equations, Wave & Heat equations. Ø To understand the basic concepts in Bessel’s functions.

UNIT I (12 hrs) Introduction – Formation of Partial Differential Equations by Elimination of Arbitrary Functions

– Formation of Partial Differential Equations by Elimination of Arbitrary Functions – Types of

Solutions of Partial Differential Equations – Solutions by Direct Integration – First Order Partial

Differential Equations – Solutions by Direct Integration – First Order Partial Differential

Equations

UNIT II (12 hrs) Lagrange’s Equation – Partial Differential Equations of Higher Order – Non-homogeneous

Linear Equations with Constant Coefficient.

UNIT III (12 hrs) Derivation of One Dimensional Wave Equation – Solution of One Dimensional Wave Equation – One Dimensional

Heat Flow – Solution of One Dimensional Heat Equation

UNIT IV (12 hrs) Two Dimensional Heat equation – Cartesian Form – Temperature Distribution in a Rectangular

Plate – Temperature Distribution in an Infinite Plate – Temperature Distribution In Rectangular

Plate with Insulated Sides

UNIT V (12 hrs) Introduction – Bessel Functions (Omit Series Solution) - Legendre’s Equation


TEXT BOOKS:

1) Arumugam, Thangapandi Isaac, Somasundaram Engineering Mahematics Volume – III Second Edition,

Scitech Publications (India) Pvt. Ltd.

REFERENCE BOOKS: 1) Gupta, B.D (2004) Mathematical Physics, Second Revised Edition, Vikas Publising House Pvt. Ltd.





HBMA13E06 INTRODUCTION TO MATHEMATICA 3 0 1 4 OBJECTIVES:

Ø To understand the basic concepts in the programming with Mathematica. UNIT I (12 hrs) Simplification of algebraic expression, simplification of expressions involving special functions, builtin functions

for transformations on trigonometric expressions, definite and indefinite symbolic integration, symbolic sums and

products, symbolic solution of ordinary and partial differential equations, symbolic linear algebra, equations solving,

calculus, polynomial functions, matrix operations.

UNIT II (12 hrs) Special functions, inverse error function, gamma and beta function, hyper-geometric function,

elliptic function, Mathieu function.

UNIT III (12 hrs) Numerical solution of differential equations, numerical solution of initial and boundary value

problems, numerical integration, numerical differentiation, matrix manipulations and optimization techniques.

UNIT IV (12 hrs) Two and Three dimensional plots, parametric plots, contours, typesetting capabilities for labels and text in plots,

direct control of final graphics size, resolution etc.

UNIT V (12 hrs) Algebra, linear algebra, calculus, discrete math, geometry, graphics, number theory, vector analysis, Laplace and

Fourier transforms, statistics.


TEXT BOOKS:

1) Stephen Wolfram (2003) The Mathematica book, Wolfram Research Inc.

REFERENCE BOOKS: 1) Wellin, Gaylord, Kamin (2005) An introduction to programming with Mathematica, 3rd ed, Cambridge.

Dr.M.G.R. UNIVERSITY DEPARTMENT OF MATHEMATICS B.Sc ...

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