3.bsc Maths Syllabus 664pr

B.Sc Mathematics

Curriculum and 201 Syllabus 5 SEMESTER-I

BAE111

BAE11 2

TAMIL - I

ENGLISH -I

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B.Sc Mathematics

Curriculum and 201 Syllabus 5

PROSE R.K.Narayan

-- The Engine’s Trouble

V.S.Srinivasa Sastri -- Mahatma Gandhi John Frazer

-- Mother Terasa

R.N.Roy

-- Martin Luther King

POETRY Wordsworth Byron

-- “Daffodils” -- “She Walks in Beauty”

Rob

FICTION: SHORT STORIES O. Henry

-- “Gift of the Magi”

Chekhov

-- “The Bet”

Rabindranath Tagore

-- “The Postmaster

GRAMMAR AND SPOKEN ENGLISH  Noun  Pronouns  Possessive forms  Articles & Nouns  Demonstratives  Some, any, no etc. (Response in one or two sentences) Greeting a person; Introducing oneself; Inviting somebody to attend a function; Expressing inability to attend; Requesting; Seeking permission: Refusing permission; Asking for advice; ing something; Expressing sympathy; Reminding others; Congratulating; Complaining; Apologizing; Making suggestions; Warning; Asking for information/direction; Expressing annoyance; Encouraging others; Expressing possibility/impossibility; Starting a conversation with a stranger; Ending a conversation; Asking for someone’s opinion; Expressing happiness; Expressing something unpleasant; Expressing gratitude. 2

B.Sc Mathematics


COMPOSITION AND VOCABULARY Composition (1)

Reading comprehension: 8 questions testing skills of locating direct information, associative comprehension, overall understanding, drawing inferences, evaluative comprehension and aspects of grammar and vocabulary.

(2)

Arranging jumbled sentences in a chronological order or a coherent paragraph.

(3)

Letter Writing (Personal letters).

Vocabulary One Word Substitutes: alimony, amateur, amnesty, anaesthesia, anarchist, anatomy, anonymous, archive, atheist, autobiography, cannibal, carcinogen, cardiologist, carnivorous, centenarian, contemporary, connoisseur, cosmopolitan, crew, detective, (21 – 40) emigrant, epitaph, extempore, fauna, feminist, fleet, flora, forgery, gymnasium, gynaecologist, herbivorous, hypocrisy, incorrigible, kleptomania, lexicographer, manuscript, mercenary, misanthrope, mortuary, novice, (41 – 60) obituary, omniscient, ophthalmologist, optimist, omnipotent, orphan, panacea, parasite, pedestrian, pessimist, philanthropy philatelist, polygamy, posthumous, post-mortem, secular, somnambulist , theology, unanimous, utopia.

TEXT BOOKS : Jegadisan, S. Portraits in Prose. Orient Black Swan, Chennai: 2009. Sadanand Kamalesh. & Punitha, Susheela. Spoken English: A Foundation Course. Part 2 Orient Black Swan, New Delhi, 2011

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B.Sc Mathematics

BMA101

Curriculum and 201 Syllabus 5 ALGEBRA

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UNIT I - MATRICES Rank of a matrix – Consistency of a system of linear equations, Characteristic equation – Eigen values and Eigen vectors – properties – problems - Cayley – Hamilton theorem (statement only) and its applications – Diagnolisation of Matrices – problems. UNIT II - THEORY OF EQUATIONS Descarte’s rule of signs –Polynomial equations – Imaginary and Irrational roots – relation between roots and coefficients of equations – Symmetric functions of roots in of coefficients of third degree equation - problems. UNIT III – RECIPROCAL EQUATIONS Sum of the powers of the roots of an equation – Newton’s Theorem on the sum of the powers of the roots – Transformation of equations – Roots with sign changed – Roots multiplied by a given number – Reciprocal equations – problems. UNIT IV – TRANSFORMATION OF EQUATIONS Increase or decrease the roots of a given equatioan by a given quantity. Removal of - Square of the roots – Transformations in general – problems. Unit V- SUMMATION OF SERIES Summation of series using Binomial, Exponential and Logarithmic series and approximations. TEXT BOOKS 1. T. K. Manickavasagam Pillay, Natarajan and Ganapathy, Algebra, Volume II, S.Viswanathan Pvt. Ltd., 2004. 2. S. Narayanan and T. K. Manickavachagam Pillay, Trigonometry, S. Viswanathan Printers & Publishers, (Reprint), 2012. REFERENCES 1. T.K.Manickavachagam Pillay, Matrices, S.Viswanathan Printers & Publishers, 2012. 2. S. Sudha, Algebra, Analytical Geometry (2D) and Trigonometry, Emerald publishers, 1998. 3. P. Duraipandian, Trigonometry, Emerald publishers, 2009. 4. A. Singaravelu, Algebra & Trigonometry, Vol. I & II, Meenakshi Agency, 2003. BPY701

ANCILLARY PHYSICS - I 4

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Unit – I Properties of matter Hooke’s law - Stress – strain diagram – Elastic Moduli - Relation between elastic constants- Surface tension- Definition and dimensions of surface tension- angle of , capillarity, coefficient of viscosity- Rate flow of liquid in a capillary tube Streamlined motion – Turbulent motion – Reynolds number- Poiseuille’s formula Determination of coefficient of viscosity of a liquid Unit – II Magnetism Magnetic properties of materials- relation between the three magnetic vectors -susceptibility and permeability - para, dia and ferro magnetism (qualitative ideas) magnetic hysterisis - super conductivity -persistent current and Meissner Effect. Unit III – Thermodynamics Thermodynamics – Introduction, first law of thermodynamics and its applications, isothermal, adiabatic, isochoric and isobaric processes, indicator diagrams, adiabatic relations for a perfect gas, reversible and irreversible processes, cyclic process. Work done by a perfect gas during isothermal and adiabatic process, Second law of thermodynamics – Clausius and Kelvin statements and their equivalence, Carnot’s theorem, entropy. Unit – IV Optics Fermat’s principle and its application to reflection and refraction in plane surfaces. Interference: Concept of spatial and temporal coherence, Young’s double slit experiment, intensity distribution, shapes of fringes and fringe width, Newton’s ring. Diffraction – Fresnel and Fraunhofer class, Fraunhofer diffraction, Single slit diffraction, plane transmission grating, Resolving power, Rayleigh’s criterion. Polarization – states of polarization, Brewster’s law, optical activity. Unit V – Light aser pumping, spontaneous and induced emissions, conditions for laser action, population inversion,Ruby Laser, Hologram construction and reconstruction process General ideas of optical fiber cable-Types of OFC- Applications References 1. 2. 3. 4.

Properties of matter – Brijlal and Subramanian Optics by A. Ghatak Heat and thermodynamics - D S Mathur, S Chand & Co., New Delhi Electricity and Magnetism K K Tiwari S Chand & Co 5

B.Sc Mathematics

BCS103


PROGRAMMING IN C

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UNIT-I History of C - Characteristics of C - C Program Structure - Data Types - Variables and Constants - Operators - Conditional Statements - Looping and Iteration UNIT-II Single Dimensional Array - Multi Dimensional Array - Types of functions - Functions and Arrays - String Functions - Recursive Functions UNIT-III Basics, Structures and functions - Arrays of structures - Pointers to structures - Self referential structures - Typedef - Union - Bitfields - Enum Data Types UNIT-IV Pointers introduction - declaration - ing function to pointers - pointers with arrays dynamic memory allocation. UNIT V File management and Console input and output – Functions for file management - Standard I/O, Formatted output - Formatted input - File access - Error handling TEXT BOOK: 1. E. Balagurusamy , Programming in Ansi C , 6th Edition, TMG - India 2012. REFERENCES: 1. Herbert Schildt, The Complete Reference C, 4th Edition, Tata Mc - Graw Hill, 2000. 2. Byron C Gottfried, Programming with C, Schaums’ outline series 2nd Edition, Tata Mc Graw Hill, 2006 6

B.Sc Mathematics

BPY 181


PHYSICS PRACTICAL – I

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1. Non-uniform bending – Pin and Microscope. 2. Uniform bending – Optic lever. 3. Surface tension – Capillary rise. 4. Sonometer –determination of AC frequency. 5. Melde’s Experiment – Transverse and longitudinal. 6. Compound pendulum – g and k. 7. Cantilever depression – scale and telescope. 8. Torsion Pendulum 9. Experiment to determine coefficient of viscosity of low viscous liquid by capillary Flow Method (Poiseuille’s method). 10. To determine the Elastic Constants of a Wire by Searle’s method. 11. Ultrosonic Interferometer – To find the velocity of sound in liquid 7

B.Sc Mathematics

BCS182


PROGRAMMING IN C LABORATORY

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. To demonstrate use of data types, simple operators (expressions) 2. To demonstrate decision making statements (if and if-else, nested structures) 3. To demonstrate decision making statements (switch case) 4. To demonstrate use of simple loops 5. To demonstrate use of nested loops 6. To demonstrate menu driven programs and use of standard library functions. 7. To demonstrate writing C programs in modular way ( use of defined functions) 8. To demonstrate recursive functions. 9. To demonstrate use of arrays (1-d arrays) and functions 10. To demonstrate use of multidimensional array (2-d arrays ) and functions 11. To demonstrate use of pointers 12. To demonstrate concept of strings (strings and pointers) 13. To demonstrate array of strings. 14. To demonstrate structures (using array and functions) 15. To demonstrate nested structures and Unions 16. To demonstrate file handling (text files) 8

B.Sc Mathematics

Curriculum and 201 Syllabus 5 SEMESTER-II

BAE121

TAMIL - II

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B.Sc Mathematics

Curriculum and 201 Syllabus 5 L

BAE12 2

ENGLISH - II

PROSE D.H.Lawrence

-- The Rocking Horse Winner

Anton Chekov

-- The Bet

Somerset Maugham -- Princess September

POETRY William Wordsworth

-- “Lucy”

W.B.Yeats

-- “The Wild Swans”

D.H.Lawrence

-- “The Best of School”

T.S.Eliot

-- “To the Indians who Died in Africa”

Philip Larkin

-- “That Whitsun”

FICTION – SHORT STORIES William Somerset Maugham

-- The Verger

R.K.Narayan

-- An Astrologer’s Day

Bhabani Bhattacharya

-- Glory at Twilight

GRAMMAR AND SPOKEN ENGLISH Grammar: 1. Tenses 10

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2. Active and ive Spoken English (Responses in one or two sentences) Making assertions; Describing persons and objects; Taking a vow; Commenting on situations; Exclamations; Giving yourself time to think; Asking for someone’s opinion; Asking about preferences; Asking whether someone knows; Saying you know; Checking if someone has understood; Asking if someone agrees; Asking someone to repeat; Leaving someone for a short time; Asking if someone is able to do something; Saying you are unable to do something; Changing the subject; Avoiding giving an opinion; Ordering food at a restaurant; Talking about weather and season; Asking about daily activities; Making polite requests using, “Would (Will) you . . . . Please?”, etc.; Discussing Television Programme.

COMPOSITION & VOCABULARY (1)

Letter Writing (Official) and Preparation of curriculum vitae.

(2)

Developing hints into a story/general essay; Simple topics to be chosen for essay.

(3)

Note making.

Vocabulary Homophones: beer – bier; berth – birth; deer – dear; desert – dessert; diseased – deceased; feat – feet; heard – herd; cast – caste; check – cheque; draught – draft; hangar – hanger; hear – here; knight – night; loan –lone; mane – main; Meet – meat; meter – metre; pair – pear; peal – peel; personal – personnel; piece – peace -- peas; pray – prey; root – route; sent -- scent – cent; cite -- site – sight; sow – sew; stationary – stationery; steal – steel; story – storey; wait – weight. BOOKS PRESCRIBED: Board of Editors. Journey through Words. Orient Longman, Hyderabad: 2007. Mukherjee, Meenakshi. Let’s Go Home and Other Stories. Orient Black Swan, Chennai: 2009 11

B.Sc Mathematics

BMA102


CALCULUS

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Unit I : Differential Calculus Rolle’s theorem - 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 : Differential Calculus Maxima and minima of functions of 2 variables – Lagrange’s method of undetermined multipliers – simple problems. Unit III: Integral Calculus Definition of the Riemann integral - Introduction to integration - Methods of integration – Integration by parts - Bernoulli’s formula. Unit IV : Integral Calculus Properties of definite integrals – reduction formulae for standard integrals. Unit V : Geometrical Applications of Integration Areas in polar coordinates - Length of the curve (Cartesian and polar coordinates) – Area of surface of revolution (Cartesian and polar coordinates). Text Book: 1. Calculus, Vol.I, S. Narayanan and T K ManicavachagomPillay,S. ViswanathanPrinters and Publishers Pvt. Ltd., 2010. 2. CalculusVol. II, S. Narayanan and T K ManicavachagomPillay,S. ViswanathanPrinters and Publishers Pvt. Ltd., 2010.

BPY702

ANCILLARY PHYSICS - II 12

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B.Sc Mathematics

Curriculum and 201 Syllabus 5 4

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Unit – I Special Theory of Relativity Postulates of Special Theory of Relativity. Lorentz transformation equations and its geometrical interpretation. Group properties of Lorentz transformations. Relativistic Kinematics - composition of parallel velocities. Length contraction. Time dilation. Transformation equations for components of velocity and acceleration of a particle. Variation of mass with velocity. Equivalence of mass and energy. Relativistic energy momentum relation, longitudinal and transversal mass. Unit – II Electrostatics Coulomb’s Law – Gauss Theorem, its application Field due to an infinite long plane, Sphere and Cylinder – Mechanical force on the surface of a charged conductor – Electrostatics Energy in the Medium – Formation of Cloud on charged particles. Capacitors – Principles of a Capacitor – Capacity of a capacitor – Capacity of an isolated Sphere and Cylinder – Energy of a charged Capacitor – Sharing of charges and loss of energy.

Unit – III Photoelectric effect and Wave mechanics

Photo electric effect – Einstein’s photo electric equation –verification of Einstein’s photo electric equation by Millican’s experiment – photo electriccells – applications De Broglie matter waves – calculation of De Broglie wave length– Experimental study of De Broglie matter wave by G.P.Thomson experiment.

Unit – IV Nuclear Physics Particle accelerators – cyclotron, particle detectors – GM Counter Artificial Transmutation – Rutherford’s Experiment – The Q value equation for nuclear reaction – Threshold energy – Nuclear Reactions. Conservation Laws: Conservation of Charge – 13

B.Sc Mathematics


Conservation of Nucleons – Conservation of Mass – Energy – Conservation of Parity – Quantities conserved and quantities not conserved in a nuclear reaction. Biological effects of radiation – control of radiation hazards.

Unit – V Electronics Diode, – Characteristics, Zener diode– Voltage regulation using zener diode –Transistors – some basic concepts LED – uses of LED. Digital Electronics : AND, OR, NOT, NAND and NOR gates – NAND and NOR as universal building blocks – Fabrication of a Integrated circuit by monolithic technology – Advantages and limitations of an integrated circuit – LSI, MSI and VLSI.

References

1. Resnick, R., Introduction to Special Relativity 2. Modern Physics – R. Murugesan 3. Electricity and magnetism -- Brijlal subramaniam 4. Electronic Principles and Applications – A.B. Bhattacharya,

BCE103

ENVIRONMENTAL SCIENCE

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UNIT-I SCOPE OF ENVIRONMENTAL STUDIES AND NATURAL RESOURCES Scope and importance of environmental sciences - Natural resources: Forest resources, Water resources, Mineral resources, Energy resources, Land resources-Role of individual in conservation of natural resources.

UNIT-II ECOSYSTEM AND BIODIVERSITY Ecosystem –Definition, Structure and function of an ecosystem - Food chains, food webs and ecological pyramids - Ecological succession. Biodiversity – Definition, value of biodiversityThreats to biodiversity -· Endangered and endemic species of India - Conservation of biodiversity: In-situ and Ex-situ conservation of biodiversity.

UNIT-III ENVIRONMENTAL POLLUTION Types, sources, consequences and control measures of water pollution- Sources, effects and control measures of Air pollution, Soil pollution, Marine pollution, Noise pollution, Thermal pollution and Nuclear pollution.

UNIT-IV MANAGEMENT OF ENVIRONMENTAL POLLUTION Causes, effects, treatments methods and control measures of solid waste, municipal waste, hazardous waste and biomedical waste - Waste minimization techniques - Cleaner TechnologyGreen Chemistry: Principles and its role in controlling environmental pollution-Disaster management: earthquake, cyclone , and Tsunami.

UNIT-V SOCIAL ISSUES AND THE ENVIRONMENT Water conservation, rain water harvesting, Resettlement and rehabilitation of peopleEnvironmental impact assessment, Precautionary and polluters pay principle, environment protection act – air (prevention and control of pollution) act – water (prevention and control of pollution) act – wildlife protection act – forest conservation act. Population explosion , Family Welfare Programmes , Human Rights .

REFERENCE BOOKS 15

B.Sc Mathematics


1. S.K.Dhameja, Environmental engineering and Management, S.K. Kataria and sons, New Delhi, 1st edition 2004. 2. Gilbert M.Masters, “Introduction to Environmental Engineering and Science”, pearson education Pvt., Ltd., second edition, ISBN 81-297-0277-0, 2004. 3. C.Townsend., J.Harper and Michael Begon, “Essentials of Ecology”, Blackwell science, 2003. 4.

C.N.Sawyer, P.L.McCarty and G.F.Parkin., Chemistry for Environmental Engineering, McGraw-Hill, Inc., New York, 1994.

5. T.G.Miller Jr.,Environmental science, wadsworth Publishing Co. USA, 2nd edition 2004. 6. Bharucha Erach, “The Biodiversity of India”, mapin publishing Pvt. Ltd., Ahmedabad India, 1st Edition, 2001. 7. R.K.Trivedi, “Handbook of Environmental Laws”, Rules, Guidelines, Compliances and Standards, Vol. I and II, Enviro media, New Delhi, 2nd Edition, 2004. 8. Cunningham, W.P.Cooper, T.H.Gorhani, “Environmental Encyclopedia”, Jaico Publ., House, Mumbai, 2001. 9.

K.D.Wager, “Environmental Management”, W.B. Saunders Co., Philadelphia, USA, 1998.

10. R.K.Trivedi. and P.K.Goel, “ An Introduction to Air Pollution”, BS publications, 2005.

BPY182

PHYSICS PRACTICAL – II

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1. Ballistic Galvanometer – Figure of merit. 2. B.G. – Absolute capacity of condenser 3.

To determine the Mutual Inductance of Two Coils by Absolute method using a B.G.

4. To determine the Dielectric Constant of a Dielectric placed inside a parallel plate capacitor using a B.G. 5. Anderson’s bridge – AC self inductance of a coil. 6.

To determine a unknown Resistance by Carey Foster’s Bridge.

7. Charging and discharging in R.C. and R.C.L. circuits. 8. To determine Self Inductance of a Coil by Anderson’s Bridge using AC 9. To determine Self Inductance of a Coil by Rayleigh’s Method. 10. Potentiometer - Calibration of high range voltmeter 11. Potentiometer - resistance and specific resistance of a wire. 12. To determine High Resistance by Leakage of a Capacitor. 13. To determine the Ratio of Two Capacitances by de Sauty’s Bridge. 14. Thermo e.m.f. – spot galvanometer

BAE307

HUMAN RIGHTS AND HUMAN VALUES

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UNIT I Introduction to Human Rights and Theories of Human Rights Human Rights, Introduction, Definition, Historical Background, Bases and Sources, Idea and Ethos; The UN and its Charter, International Bill of Human Rights, Perspectives on Human Rights and Human Duties, State Responsibility in International Law, Indian Perspectives on Human Rights, UN Perceptions, Emerging Dimensions in Human Rights. UNIT II Culture, Wisdom, Religion, International Relations and Human Rights Human Rights and Cultural Relativism, Religion and Human Rights, Theological Perspectives, Impacts of the New World Order, UN and the Challenge of Human Rights and Cultural Diversity. UNIT III State of Human Rights in India Genesis of Human Rights in India, Human Rights in Ancient India, Human Rights in Islamic Era, Human Rights in British India, Human Rights after Independence, Right to Equality, Civil Rights, Political Rights, Rights relating to Person. UNIT IV Human Values in Literary and Holy Texts Sources from where Values Come in, Core Values in Family, Building Values in Personal Life, Values, Morals and Ethics, Integrity, Work Ethics, Honesty, Courage, Empathy, SelfConfidence. UNIT V Human Values in Professional Life Professional Life and ability, Creating a Safe Social Environment, a Safe Natural Environment, Avoid Harming others, Avoiding Unnecessary Expenditure of Resources, Being Honest in all Enterprises, Being Fair—Values of Equality, Tolerance, Respect for Others, Principles of Equal Justice.

BAE 181

COMMUNICATIVE ENGLISH LABORATORY

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B.Sc Mathematics


Module-1: (Phonetics Theory & Practice) Module-2: (Communicative English-Interactive) Module-3: (Situational Conversation-Listen) Module-4: (Situational Conversation-Listen) Module-5: (Situational Conversation-Listen) Module-6: (Global Communication-Listen) Module-7: (Global Communication-Listen) Module-8: (Monologues with exercise) Module-9: (Comprehension) Module-10: (Biographies) Module-11: (Errors in Spoken English) Module-12: (Essential English Grammar) Module-13: (Vocabulary) Module-14: (Learning Through Cartoons) Module-15: (Learning Through Fun) Module-16: (Learning Through Games) Module-17: (Learning Through Music) Module-18: (Learning Through Stories) Module-19: (Learning Through Situations) Module-20: (Learning Through Activities) Module-21: (Learning Through Discussion) Module-22: (Learning Through Interview) SEMESTER-III

BAE211

TAMIL - III

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B.Sc Mathematics


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B.Sc Mathematics

BAE 212

Unit – 1

Unit – II

Unit – III

Unit – IV


ENGLISH - III

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Short Stories Mulk Raj Anand

--The Terrorist

Shama Futehally

-- Photographs

Arun Joshi

-- The Homecoming

Poetry Emily Dickinson

– “Some Keep the Sabbath Going to Church”

Willam Blake

– “Poison Tree”

Wole Soyinka

– “Telephonic Conversation”

Tagore

– “Gitanjali Songs No: 35,36

Drama

(One-Act Plays)

Erisa Kironde

- The Trick

M.Sajitha

-- Matsyaganddhi

Grammar and Spoken English

Grammar    

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B.Sc Mathematics

 


Reported Speech Infinitive forms

Spoken English Conversation in situations – dialogues a) b) c) d) e)

A father and his son talk about higher education. A house owner and a tenant. A Customer at a medical shop. Two friends about the latest film. A Salesman and a prospective buyer of a car

Unit – V

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Composition and Vocabulary

Composition 1. Précis Writing 2.Email 3.ment 4. Notices, Agenda, Minutes; 5.Writing descriptive and narrative ages

Vocabulary Phrases: in accordance with; on of’; to for; to aim at; apart from; to approve of; on behalf of; to carry on; in front of; in order to; to call off; to call upon; to consist of; contrary to; to depend on; to drop in; due to; in the face of; to get used to; be good at; in keeping with; in the light of; to look down on; to look up to; to look into; to refer to; in the long run; to look forward to; to make an attempt to make fun of; to opt out of; to persist in; to put an end to; with regard to; as a result of; to result in; to root out; to run into; to see through; in spite of; to take for granted; to turn against; in view of; to wipe out; be worthy of;

References: 1. K.Sujatha. On the Stage One-act Plays. Orient Black Swan, Chennai: 2011. 2. Mukherjee, Meenakshi. Let’s Go Home and Other Stories. Orient Black Swan, Chennai: 2009

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B.Sc Mathematics

BMA201


SEQUENCE AND SERIES

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Unit I: Sequence (definition) – Limits – Convergence of a sequence – cauchy’s general principle of convergence – cauchy’s first theorem on Limits – Bounded sequences – monotonic sequence always tends to a limit, finite, or infinite – Limit superior and Limit inferior. Unit II: Infinite series – Definition of convergence, Divergence and Oscillation – Necessary condition for convergence – convergence of Geometric series. Unit III: Convergence of series - Comparison test, D’Alembert’s ratio test , Raabe’s test. Simple problems. Unit IV: Cauchy’s condensation test , Cauchy’s root test - simple problems – Alternate series – simple problems. Unit V: General summation of series including successive difference and recurring series. Text Book: 1. S. Arumugam, A. Thangapandi Issac, Sequences and Series and Fourier series, New Gamma Publishing House, Aug 2006. Reference Books: 1. T.K. Manicavachagam pillay, T. Natarajan, K. S. Ganapathy, Algebra Vol 1, S. Viswanathan Pvt. Ltd, Chennai, 2004 2. M.K. Singal & Asha Rani Singal, A First course in Real Analysis, Chand & Co, 1999.

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BMA202


ANALYTICAL GEOMETRY

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UNIT-I: Two Dimensional Analytical Geometry: Pair of Straight lines -Conics - Parabola, Ellipse, Hyperbola- Chord in of middle points Pole, Polar. UNIT-II: Two Dimensional Analytical Geometry Conjugate Hyperbola, Conjugate Diameter for Ellipse and Hyperbola UNIT-III: Three Dimensional Analytical Geometry Direction cosines, Direction ratios, Planes – angle between two planes – perpendicular distance from a point to the plane –coplanar planes- Straight lines – symmetric form – coplanar lines – skew lines – shortest distance and its equation between two skew lines. UNIT-IV: Three Dimensional Analytical Geometry: Sphere – touching of spheres - Section of a Sphere by a Plane- Tangent Plane, Orthogonal Spheres UNIT-V: Three Dimensional Analytical Geometry: Cone and Cylinder -Equation of a Cone - Cone whose vertex is at the origin - Quadric Cone with the vertex at the origin - Right Circular Cone - Cylinder- Right Circular Cylinder- Equation of a Cylinder Text Books:

1. S. Arumugam, A. Thngapandi Issac, “Analytical Geometry 3D, Vector Calculus & Trigonometry, New Gamma Publishing House, Jan 2006. 2. T.K.Manickavachagom Pillay & others. (2004) Analytical Geometry (Two & Three Dimensions) S.Viswanathan Printers & Publishers Pvt. Ltd. Chennai. Reference Books: 1. P.Duraipandian and Laxmi Duraipandian (1965) Analytical Geometry-2D, Asia Publishing company, Bombay 2. P.Duraipandian and Laxmi Duriapandian (1975) Analytical Geometry-3 D, Emerald Publishers, Chennai. 3. G.B.Thomas and R.L.Finney.(1998) Calculus and Analytic Geometry, Addison Wesley (9th Edn.), Mass. (Indian Print). 4. P.R.Vittal (2003) Coordinate Geometry. Margham Publishers, Chennai

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B.Sc Mathematics

BMA203


Differential Equations and Laplace Transform

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Differential Equations and Laplace Transform UNIT-I: Ordinary Linear Differential Equations Bernoulli Equation – Exact Differential Equations – Equations Reducible to Exact Equations – Equations of First order and Higher degree: Equations solvable for p, Equation solvable for x and Equations Solvable for y – Clairaut’s Equation. UNIT-II: Ordinary Linear Differential Equations 2nd order Differential Equations with Constant Coefficients for finding the P.I’s of the form eax V, where V is sin(mx) or cos(mx) and xn – Equations reducible to Linear equations with constant coefficients – Cauchy’s homogeneous Linear Equations – Legendre’s Linear Equations – Method of Variation of Parameters – Linear Dependence of Solutions – Simultaneous Equations with Constant Coefficients. UNIT-III: Differential Equations of Other Types Equations of form d2y/dx2 = f(x) – Equations of the form d2y/dx2=f(y) – Equations which do not contain y – Equations which do not contain x – Total Differential Equations Simultaneous Total Differential Equations – Equations of the form dx/P = dy/Q = dz/R – Method of Grouping. UNIT-IV: Partial Differential Equations Formation of PDF – Complete Integral – Particular Integral – Singular Integral – equations Solvable by direct Integration – Linear Equations of the first order – Non-linear Equations of the first Order–Non-linear Equations of the first Order: Types: f[p,q]=0, f[x,p,q]=0, f[y, p, q]=0, f(z, p, q]=0, f[x, q]= f[y, p], z= px+qy + f[p, q] UNIT-V: Laplace Transform Transform-Inverse Transform – Properties – Application of Laplace Transform to solution of first and second order Linear Differential equations [with constant coefficients]. Recommended Texts 1. B.S.Grewal , Higher Engineering Mathematics, Khanna Publishers, New Delhi, 2002

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B.Sc Mathematics


Reference Books 1. M.K.Venkataraman [1998] Higher Engineering Mathematics, III-B, National Publishing Co., Chennai. 2. P.R.Vittal [2004] Differential Equations and Laplace Transform, Margham Publications, Chennai. 3. P.Kandasamy, K.Thilagarathy [2004] Mathematics for B.Sc. Vol. III S.Chand & Co., Ltd., New Delhi-55. 4. S.Narayanan & T.K.Manicavachagam Pillay, Calculus, S.Viswanathan Printers & Publishers Pvt. Ltd., Chennai, 2004.

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B.Sc Mathematics

BMA701


ALLIED STATISTICS-I

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UNIT-I Random variables- discrete and continuous random variables –distribution function- propertiesprobability mass function, probability density function-mathematical expectation – addition and multiplication theorems on expectations UNIT II Moment generating and cumulative generating & characteristic functions and their properties.t probability distributions-marginal and conditional probability distributionsindependence of random variables-transformation of variables (one & two dimensional only).Tchebychev’s inequality, weak law of large numbers and central limit theorem UNIT III Probability distributions: Binomial, Poisson and Normal distributions and their properties and fitting of distributions - Chi-square, t and F Statistics, their probability functions and their properties. UNIT IV Curve fitting : principle of least squares - fitting of : straight line, second degree parabola, power curve and exponential curves Unit V Correlation – rank correlation - regression analysis. Text Book: 1. Guptha, S.C &Kapoor, V.K , Fundamentals of Mathematical statistics, S.Chand & Co, 2010. Reference Books: 1. Introduction to Statistical methods by Guptha ,C.B and Vijay Guptha (1988) 2. Statistics by Dr.S.Arumugam Publications: SciTech,2006.

28

B.Sc Mathematics

BMA781


STATISTICS LAB -I

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1.Construction of univariate frequency distribution – Diagrammatic and Graphical representation of Statistical data 2.Computation of measures of central Tendency – Calculation of measures of Dispersion – Coefficient of variation 3.Fitting of Y= a + bX, Y=a+bX+cX², Y=ae , y=ab and y=ax by the method of least squares. bx

X

b

4.Fitting of Binomial, Poisson distribution – Test for goodness of fit using Chi – Square test 5.Computation of correlation co-efficient and Rank correlation - Regression equation (2 Variables Only)

BHS201

PROFESSIONAL ETHICS

29

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B.Sc Mathematics


UNIT - I: Human values – Types - Morals – Ethics – Integrity – Work ethics – Service learning – Virtues – Respect for others – Honesty – Courage - Commitment – Empathy – Challenges in the workplace – Character – Spirituality – Corporate excellence UNIT- II: Variety of moral issues – Types of inquiry – Moral dilemmas – moral autonomy – Kohlberg’s theory – Gilligan’s theory – Consensus and Controversy – Models of professional roles – Theories about right action UNIT - III: Self interest – Customs and religion – Use of ethical theories – Valuing time – Cooperation Codes of ethics – Outlook on law – The challenger case study UNIT - IV: Safety and risk – Assessment – Responsibility and rights - Risk benefit analysis – reducing risk – The Three Mile Island and Chernobyl case studies UNIT - V: Global issues – Multinational corporations – Environmental ethics – Computer ethics – Weapons development and ethics – Moral leadership

References: 1. Naagarazan. R.S., A textbook on Professional Ethics and Human values, New Age International, New Delhi, 2006. 2. Mike Martin, Ethics in engineering, McGraw Hill, New York, 1996.

SEMESTER-IV

30

B.Sc Mathematics


BAE221

TAMIL - IV

BAE222

ENGLISH -IV

31

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B.Sc Mathematics


Unit I: Poetry 1. William Shakespeare

“All the World’s a Stage”

2. Percy Bysshe Shelley

“Ode to the West Wind”

3. Lord Alfred Tennyson

“Ulysses”

Unit II: Poetry 1. William Butler Yeats

“A Prayer for My Daughter”

2. W.H.Auden

“The Unknown Citizen”

3. Kamala Das

“Punishment in Kindergarten”

Unit III: Short Stories 1. Saki

The Open Window

2. Chinua Achebe

Marriage is a Private Affair

3. R.K.Laxman

The Gold Frame

Unit IV: One-act Plays 1. Anton Chekhov

The Swan Song

2. Eugene O’Neill

Before Breakfast

Unit V: Composition 1. 2. 3. 4. 5.

Letter-Writing (Formal & Informal) Interviews Group Discussion General Essays Word Power

References: 1. Sasikumar, V. Fantasy: A Collection of Short Stories. Orient Black Swan, Mumbai: 2011 2. Sujatha, K. On the Stage One-act Plays. Orient Black Swan, Chennai,2011

L 32

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BMA204


VECTOR CALCULUS AND TRIGONOMETRY

4

1

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Unit I Vector differentiation: Limit of a vector function – continuity and derivative of vector function - Geometrical and Physical significance of vector differentiation - Partial derivative of vector ffunction – gradient and directional derivative of scalar point functions – Equations of tangent plane and normal line to a level surface. Unit II Vector point function: Divergence and curl of a vector point function – solenoidal and irrotional functions – physical interpretation of divergence and curl of a vector point function. Unit III Integration of vector functions – Line , surface and volume intergrals. Guass - Divergence Theorem – Green’sTheorem – Stoke’s Theorem (Statements only). Verification of theorems and simple problems using the theorems. Unit IV Expansion of cosnx, sin nx, tan nx –Expansion of sin x, cos x, tan x in of x –Hyperbolic functions Unit V Logarithm of complex quantities – Sums of sines and cosines of n angles which are in Arithmetic Progression - Summation of trigonometric series using complex quantities. Text Book: 1. S. Arumugam, A. Thngapandi Issac, “Analytical Geometry 3D, Vector Calculus & Trigonometry, New Gamma Publishing House, Jan 2006. Reference Books: 1. T.K. Manicavachagam Pillay, Vector Analysis, Vijay Nochole Imprints Pvt. Ltd, 2004 2. P. Duraipandian, Vector Analysis, S. Viswanathan & Co, 1984. 3. Harikrishnan, Trigonometry, Atlantic, 2005.

BMA205

Basic Graph theory

33

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B.Sc Mathematics


Unit I Introduction – Definition – Examples – Degrees – subgraphs – Isomorphism of graphs Operations on Graphs - problems. Unit II Walks , Trails and paths – Connectedness and components – cut vertex –Distance –– Bridge – Blocks – Connectivity. Unit III Eulerian Graphs - Konigsberg Bridge Problem – Fleury’s Algorithm – Hamiltonian Graphs – simple theorems – Dirac Theorem on Hamiltonian graphs – closure of a graph Unit IV Characterization of Trees – Center of a Tree – simple results. Unit V Digraphs – Definition – Examples- Paths and connections – Digraphs and Matrices. Text Book: 1. S. Arumugam, S. Ramachandran, Invitation to Graph Theory, Scitech Publications (India) Pvt. Ltd, 2008 Reference book: 1. S.A.Choudam, First Course in Graph Theory ,Macmillian India Ltd-new Delhi, 2000 2.

John Clark,Derek Allan Holton ,A First Look at Graph Thoery World Scientific Publishing Company ,1991.

BMA206

MODERN ALGEBRA -I

Unit I 34

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B.Sc Mathematics


Group – Definition – Examples – Some Preliminary lemmas – Problems – Subgroups – definition – lemmas – cosets – definition – theorems – Lagrange’s Theorem – order of an element – Euler Theorem – Fermat Theorem. Unit II A Counting Principle – Normal Sub Groups – Definition – Properties – Problems – Quotient groups – Definitions – Lemma. Unit III Homomorphism – Definition – Examples - Lemmas - Kernal of a homomorphism – Fundamental theorem – Automorphism – Definition – Inner Automorphism – Lemmas – Examples – Cayley’s Theorem. Unit IV Ring – Definition – Examples – some special classes of Rings – Zero Divisor – Integral Domain. Unit V Field - Definition –Examples-Ideals – Quotient Rings – Maximal ideal. Text Book: 1. S. Arumugam, E. Franklin John, A.Thangapandi Issac, Modern Algebra, Gamma Publications, 2010 Reference Books: 1. A.R. Vasistha, A first course in Modern Algebra, Krishna Prekasan Mandhir, 1983 2. M.L.Santiago, Modern Algebra, Tata McGraw Hill, 1994.

BMA702

Allied Statistics-II

35

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B.Sc Mathematics


UNIT-I Concept of population, sample, statistics, parameter-point estimation-concept of point estimation -consistency, unbiased ness, efficiency- sufficiency-Neyman factorization theoremCramer Rao inequality -Rao-Blackwell theorem. UNIT-II Methods of estimation-maximum likelihood, moments and minimum chi-square –properties – interval estimation –confidence interval-derivation of confidence intervals based on normal, t, and chi-square and F. UNIT-III: Sampling from finite population-simple random sampling, stratified random sampling and systematic sampling-Test of hypothesis: Type-I error and II errors-power test –Neyman-Pearson Lemma-likelihood ratio tests-concept of most powerful test (statements and results only). Test of significance-standard error-large sample tests with respect to mean, standard deviaton, proportion, difference between means, standard deviations and proportions Unit- IV: Estimation of mean, total and their standard standard errors. Sampling and non sampling errors (concepts only).Small sample test - Tests based on t,chi-square and F distributions. UNIT-V Analysis of variance: one way, two classifications –fundamental principles of experimentationCRD, RBD and LSD. Text Book: 1. Guptha, S.C &Kapoor, V.K , Fundamentals of Mathematical statistics, S.Chand & Co, 2010. 2. T.Veerarajan, Probability ,Statistics and Random Process,Tata McGraw-Hill Publishing Company Limited ,2006. Reference Books: 1. Fundamentals of Applied statistics by Guptha, S.C& Kapoor, V.K 2.Statistics by Dr.S.Arumugam,Thangapandi Isaac

BMA782

STATISTICS LAB -II

36

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B.Sc Mathematics


Software : Any Statistical software (1) Formation of discrete and continuous frequency distributions - descriptive statistics. (2) Graphs and diagrams: Pie, bar, line and scatter diagrams-Histogram and Normal probability plot (3) Correlation coefficient rank correlation, partial and multiple correlations. (4) Regression : Simple and multiple linear regression. (5) Curve estimation. (6) Compare means: Independent sample test and paired t- test. (7) Cross tabulation and Chi-square test. (8) One way and two way ANOVA Factorial designs.

BHS202

SOFT SKILL

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UNIT-I: Resume/Report Preparation/Letter Writing Structuring the resume/reportLetter writing/E-mail communication-Samples 37

B.Sc Mathematics


UNIT-II: Presentation Skills Elements of an effective presentation - Structure of presentation - Presentation tools - Voice Modulation - Audience analysis - Body Language - Video Samples.

UNIT-III: Time Management Time Management - Articulateness - Assertiveness Psychometrics - Innovation and Creativity - Stress Management & Poise - Video Samples.

UNIT-IV: Group Discussion Why is GD part of selection process?- Structure of GD -led and other GDs - Strategies in GD - Team work - Body Language Mock GD - Video Samples.

UNIT-V: Interview Skills Kinds of Interviews - Required Key Skills - Corporate culture - Mock Interview - Video Samples. References: 1. Lewis, Norman, 1991. Word Power Made Easy. Pocket Books. 2. Hewings, Martin. 1999. Advanced English Grammer. A Self-Study Reference and Practice Book for South Asian Students. Cambridge University Press. New Delhi 3. Sets, Paul.W.1983. the Art of Talking So That People Will Listen: Getting Through to Family, Friends and Business Associated. Prentice Hall Press. New York 4. Sasikumar.V and P.V. Dhamija. 1993. Spokem English:m A Self-Learning Guide to Conversation Practice. 3 Tata MCGraw-Hill. New Delhi.

SEMESTER-V

38

B.Sc Mathematics

BMA301


MODERN ALGEBRA -II

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Unit I Vector Spaces – Definition – Simple properties – Examples – Homomorphism –Sub space – Quotient spaces – Internal direct sum – External direct sum. Unit II Linear Independence – Dimension of a Vector space – Bases - Dimension of Quotient spaces – related theorems. Unit III Inner product spaces – Definition – Examples – Applications – Orthogonal complement of a sub space – Orthonormal & Orthonormal Basis - Gram Schmidt Orthogonalization process . Unit IV Linear Transformation – The Algebra of linear transformations - Characteristic roots . Unit V Matrices – Canonical forms – Triangular forms. Text Book: 1. S. Arumugam, E. Franklin John, A.Thangapandi Issac, Modern Algebra, Gamma Publications, 2010 Reference Book: 1. A.R. Vasistha, A first course in Modern Algebra, Krishna Prekasan Mandhir, 1983 2. M.L.Santiago, Modern Algebra, Tata McGraw Hill, 1994.

39

B.Sc Mathematics


40

B.Sc Mathematics

BMA302


REAL ANALYSIS

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Unit I: Countable and uncountable sets-Holder’s and Minkowski’s inequalities-Metric spaceDefinition and examples –Open sets and closed sets (Definitions and examples only).

Unit II: Completeness-Definitions and examples – Cantors’s intersection theorem and Baire’s category theorem. Unit III : Continuity – Definitions and examples-Homeomorphism-Uniform Continuity Unit IV: Connectedness – Definitions and examples-Connected subsets of R- Connectedness and continuity- Intermediate value theorem. Unit V: Compactness-Definition and examples – Compact subsets of R – Equivalent Characterization of Compactness. Text Book: S.Arumugam, A. Thangapandi Issac, ModernAnalysis, New Gamma Publications, 2008. Reference Books: Methods of Real Analysis, Richard R Goldberg, Oxford & IBH Publishing company New Delhi 1970.

BMA303

LINEAR PROGRAMMING

41

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B.Sc Mathematics


UNIT-I Linear programming problem - Mathematical formulation of the problem - Graphical solution method - simplex method (Simple problems) UNIT-II Duality - primal and dual relation – revised simplex method ( simple Problems). UNIT-III Transportation problem - Degeneracy in transportation problem. UNIT-IV The Assignment problem – Travelling salesman problem. UNIT-V Game theory - two persons zero sum game - the maximin minimax principle - saddle points games without saddle points. Text Book: 1. Kanti Swaroop, Gupta P.K. and Manmohan, (2002) Problems in Operation Research, Sultan Chand & Sons. Reference Books : 1.Gupta P.K.and Hira D.S., (2000) Problems in Operations Research, S.Chand & Co. Delhi 2. Taha H.A. (2003) Operations Research, Macmillan Publishing Company, New York. 3. V.K.Kapoor [1989] Operations Research, Sultan Chand & sons.

BMA381

LINEAR PROGRAMMING LAB 42

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B.Sc Mathematics


Software: Excel Solver, QM, and TORA Topics to be covered:         

Modeling with Graphical solution of Linear Programming problems Simplex Method Revised simplex method Two Phas method Big-M Method Dual Problems Sensitivity Analysis and Duality Transportation and Assignment problems Network Models

BET301

ENTREPRENEURSHIP

43

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B.Sc Mathematics


Unit-I Business Plan : a. Meaning and Definition b. Importance of business plan c. Content of business plan d. Preparation of business plan. Unit-II Financial Management : a. Meaning and definitions. b. Importance of financial management. c. Techniques of managing finance. d. Management of working capital Unit-III Books of : a. Importance of ing assessment. b. Different books and its relevance. c. stationary and its use. d. Operating mechanism. Unit-IV Marketing Management : a. Marketing for small business. b. Methods of Sales Promotion. c. Pricing Policies and Methods. Unit-V Visit to small-scale industries to understand problems and issues involved in launching and managing an enterprise. Interaction with Entrepreneurs to understand the real life situations of entrepreneurs. Suggested Readings : 1. Ziemmeser & Scalorough : Entrepreneurship Development and Small Enterprise Management PHI, New Delhi. 2. C.B.Gupta & S.S.Kanka : Entrepreneurship & Small Business Management, Sultan Chand & Sons, New Delhi. 3. C.B. Gupta & : Entrepreneurial Devemopment, Sultan Chand & N.P. Srinivasan Sons, New Delhi. 4. Renu Arora : Fundamentals of Entrepreneurship & Small Business, S.K.Sood Kalyani Publishers, New Delhi. 5. Greene : Entrepreneurship Ideas in Action, Thomson Asia PTE Ltd. New Delhi. 6. Dr. G.K. Warshroy : Fundamentals of Entrepreneurship, Sahitya Bhavan, Agra.

SEMESTER-VI

BMA 304

Complex Analysis 44

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B.Sc Mathematics


Unit I Fundamental Theorems Line Integrals – Rectifiable arcs – Line integrals as Functions of Arcs – Cauchy’s Theorem for Rectangle – Cauchy’s Theorem in a Disk. Unit II Cauchy’s Integral Formula The index of a point with respect to a closed curve – The integral formula – Higher Derivatives – Removable Singularities – Taylor’s Theorem – Zeroes and Poles. Unit III Calculus of Residues The Local mapping – The Maximum principle – The Residue theorem – The argument principle – Evaluation of Definite Integrals. Unit IV Harmonics Functions Definitions and Basic Properties – The Mean Value Property- Poisson’s Formula – Schwarz’s Theorem – The Reflection principle. Unit V Power Series Expansion Weierstrass’s Theorem – The Taylor series – The Laurent series – Partial Fractions – Infinite products. Text Book: Complex Analysis : An introduction to the Theory of Analytic Functions of One Complex Variable, Lars V. Ahlfors, Third Edition, McGraw Hill Book Company, New York, 1979. References Book 1. Functions of one Complex variable, John B. Conway, second Edition, Springer Graduate Texts in Mathematics, New York, 1978 2. Foundations of Complex Analysis S. Ponnusamy, Second Edition, Narosa Publishing House, India, 2005.

BMA305

NUMERICAL METHODS

45

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B.Sc Mathematics


Unit I: SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS Review of open end methods, bracketed end methods - The intermediate theorem (excluding proof) - Iterative method - False position method - Newton – Raphson method for single variable and for simultaneous equations with two variables - Solutions of a linear system by Gaussian, Gauss-Jordan, Jacobi and Gauss – Seidel methods. Unit II: INTERPOLATION Newton forward and backward difference formulae - Newton’s divided difference formulae Lagrange’s polynomials - Stirling’s Central difference formulae. Unit III: NUMERICAL DIFFERENTIATION AND INTEGRATION Numerical differentiation with interpolation polynomials - Numerical integration by Trapezoidal and Simpson’s (both 1/3rd and 3/8th) rules - Two and Three point Gaussian quadrature formulae - Double integrals using Trapezoidal and Simpson’s rule. Unit IV: INITIAL VALUE PROBLEMS Single step Methods – Taylor Series, Euler and Modified Euler, Runge – Kutta method of order four for first and second order differential equations - Multistep Methods-Milne’s predictor and corrector method. Unit V: BOUNDARY VALUE PROBLEMS Finite difference solution for the second order ordinary differential equations - Finite difference solution for one dimensional heat equation (both implicit and explicit) , One-dimensional wave equation and two-dimensional Laplace and Poisson equations.

TEXT BOOK 1. S. Arumugam, A. Thangapandi Issac, A. Somasundaram, Numerical Methods for Engineers, Scitech Pubcations Pvt. Ltd, Nov – 2006. Reference Books: 1. Kreyszig, E., Advanced Engineering Mathematics, John Wiley and Sons (Asia) Limited, Singapore, 8th Edn. , 2001. 46

B.Sc Mathematics


2. Jain, M.K., Iyengar, S.R.K., Jain, R.K., Numerical Methods for Scientific and Engineering Computation, New Age International (P) Ltd., New Delhi, 4th Edn., 2003.

BMA382

NUMERICAL METHODS LAB

Software: C / C++/ Python EXPERIMENTS 47

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B.Sc Mathematics


1. To find the roots of non-linear equation using bisection method 2. to find the roots of non-linear equation using newton’s method 3. to solve the system of linear equations using gauss - elimination method. 4. To solve the system of linear equations using gauss – seidal iteration method 5. To solve the system of linear equations using gauss - jorden method. 6. Integrate numerically using trapezoidal rule. 7. Integrate numerically using simpson’s rules. 8. To find numerical solution of ordinary differential equations by euler’s method. 9. to find numerical solution of ordinary differential equations by runge- kutta method. 10.To find numerical solution of ordinary differential equations by milne’s method. 11.To find the numerical solution of laplace equation 12.To find the numerical solution of wave equation 13.To find the numerical solution of heat equation.

ELECTIVE – I

BMA331

COMBINATORICS

Unit I 48

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B.Sc Mathematics


Basic Combinatorial Numbers – Stirling Numbers of the First Kind – Stirling Numbers of the Second Kind. Unit II Generating Functions and Recurrence Relations – Symmetric Functions. Unit III Multinomials – Multinomial Theorem – Inclusion and Exclusion Principle. Unit IV Euler Function – Permutations with Forbidden Positions – The ‘Menage’ Problem – Problem of Fibonacci. Unit V Polya Theory – Necklace Problem and Burnside’s Lemma – Cycle Index of a Permutation Group – Polya’s theorems and their Immediate Applications. Text Book: 1. Kenneth P. Boggart, Introductory Combinatorics, Pitman Books Ltd, 1983. Reference Books: 1. V. Krishnamurthy, Combinatorics Theory and Applications, East –West Press, 1989. 2. V.K. Balakrishnan, Theory and Problems of combinatorics, Schaums outline series – McGraw Hill, 1994. 3. Ian Anderson, Combinatorics of finite sets, Oxford Science Publication, 2011.

BMA332

MATHEMATICAL MODELLING

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UNIT I Mathematical Modeling through Ordinary Differential Equations of First order: Linear Growth and Decay Models – Non-Linear Growth and DecayModels – Compartment Models – Dynamic problems – Geometrical problems. 49

B.Sc Mathematics


UNIT II 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 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 Mathematical Modeling through Difference Equations: Simple Models – BasicTheory of Linear Difference Equations with Constant Coefficients – Economics and Finance – Population Dynamics and Genetics – Probability Theory. UNIT V Mathematical Modeling through Graphs: Solutions that can be Modelled Through Graphs – Mathematical Modeling in of Directed Graphs, SignedGraphs, Weighted Digraphs and Unoriented Graphs. Text Book: 1. Mathematical Modeling, J.N. Kapur, Wiley Eastern Limited, New Delhi, 1988. Reference: 1. J.N. Kapur, Mathematical Models in biology and Medicine, EWP, New Delhi,1985.

BMA333

FOURIER SERIES AND INTEGRAL TRANSFORM

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UNIT - I: Fourier series : Fourier series, Theorems, Dirichlet's conditions – Fourier Series for the interval (0,2π), (-π, π) Fourier series for even and odd functions - Half range Fourier series. UNIT - II: 50

B.Sc Mathematics


Fourier series for the interval (c, c+2l) – Parseval’s identity – Complex form of Fourier series – Harmonic Analysis UNIT - III: Integral transform – definition – simple problems – Fourier integral formula , Fourier sine and cosine integrals – Fourier transforms - Dirichlet's conditions , (without proof), Fourier transform, Inverse Theorem for Fourier transform – related problems UNIT - IV: Fourier sine and cosine transforms and their inversion formulae. Linearity property of Fourier transforms, Change of scale property, Shifting theorem, Modulation theorem, Convolution theorem of Fourier transforms, Parseval's identity UNIT – V Finite Fourier sine transform -Inversion formula for sine transform, Finite Fourier cosine transform, Inversion formula for cosine transform - Applications of Fourier transforms to initial and boundary value problems. Text Book: 1. T.K. Manicavachagam Pillay, S. Narayanan, Calculus – Vol 3, S. Vishwanathan Publications, 2010 2. A.R. Vasistha , Integral transforms, Gupta Published by Krishna Prakashan Media Pvt. Ltd., Meerut. Reference Book: 1. R.V. Chuchil, Operational Mathematics, McGraw Hill Company

BMA334

NUMBER THEORY

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Unit I The Division Algorithm – The g.c.d. – The Euclidean Algorithm – The Diophantine Equation ax + by = c. Unit II The Fundamental theorem of arithmetic , The sieve of Eratesthenes – The Goldbach conjecture – basic properties of congruence. 51

B.Sc Mathematics


Unit III Special Divisibility tests – Linear congruences – The Little Fermat’s theorem – Wilson’s theorem. Unit IV The functions μ and σ – The Mobius inversion formula – The greatest integer function. Unit V Euler’s Phi – function – Euler’s theorem – Some properties of the Phi – function. Text Book: David M Burton, Elementary Number Theory, Universal Book stall, 2001 Reference Book: Kumaravelu and Suseela Kumaravelu, Number Theory, S. Kumaravelu, Muruga Bhavanam, Chidambaram, 2001

BMA335

FUZZY LOGIC AND ITS APPLICATIONS

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UNIT I Introduction- Fuzzy subsets-Lattices and Boolean Algebras- L fuzzy sets-operations on fuzzy sets – level sets – properties of fuzzy subsets. UNIT II

52

B.Sc Mathematics


Algebraic product and sum of two fuzzy subsets-properties satisfied by Addition and product-cartesian product of fuzzy subsets. UNIT III Algebra of fuzzy relations-logic-connectives. UNIT IV Some more connectives-Introduction-fuzzy subgroup-homomorphic image and Preimage of subgroupoid. UNIT V Fuzzy invariant subgroups-fuzzy subrings. TEXT BOOK S. Nanda and N. R. Das Fuzzy Mathematical concepts, Narosa Publishing House, New Delhi, 2010. REFERENCES 1. M.Ganesh, Introduction to Fuzzy Sets & Fuzzy Logic, Prentice Hall of India Pvt. Ltd., 2006. 2. John N.Mordeson and Premchand S.Nair, Fuzzy Mathematics, Springer- verlog, 2001.

ELECTIVE PAPERS-II

BMA341

DISCRETE MATHEMATICS

53

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B.Sc Mathematics


UNIT I: PROPOSITIONAL CALCULUS Propositions – Logical connectives – Compound propositions – Conditional and biconditional propositions – Truth tables – Tautologies and contradictions – Contra positive – Logical equivalences and implications – DeMorgan’s Laws - Normal forms – Principal conjunctive and disjunctive normal forms – Rules of inference – Arguments - Validity of arguments. UNIT II: PREDICATE CALCULUS Predicates – Statement function – Variables – Free and bound variables – Quantifiers – Universe of discourse – Logical equivalences and implications for quantified statements – Theory of inference – The rules of universal specification and generalization – Validity of arguments. UNIT III: SET THEORY AND FUNCTIONS. Basic concepts – Notation – Subset – Algebra of sets – The power set – Ordered pairs and Cartesian product – Relations on sets –Types of relations and their properties – Relational matrix and the graph of a relation – Partitions – Equivalence relations – Partial ordering – Poset – Hash diagram – Lattices and their properties – Sublattices – Boolean algebra – Homomorphism. Definitions of functions – Classification of functions –Type of functions - Examples – Composition of functions – Inverse functions – Binary and n-ary operations – Characteristic function of a set – Hashing functions – Recursive functions – Permutation functions. UNIT IV: GROUPS Algebraic systems – Definitions – Examples – Properties – Semigroups – Monoids – Homomorphism – Sub semigroups and Submonoids - Cosets and Lagrange’s theorem – Normal subgroups – Normal algebraic system with two binary operations - Codes and group codes – Basic notions of error correction - Error recovery in group codes.

UNIT V: GRAPH THEORY Introduction of graphs - paths, cycles, and trails, vertex degrees and counting. Directed graphs - trees and distance basic properties - Spanning trees, enumeration, optimization and trees.

TEXT BOOKS 54

B.Sc Mathematics


1. Tremblay, J.P., Manohar, R., Discrete Mathematical Structures with applications to Computer Science, Tata McGraw–Hill Pub. Co. Ltd, New Delhi, 1st Edn., Reprint 2003, 1997. REFERENCES 1. Rosen, K.H., Discrete Mathematics and its applications, Tata McGraw-Hill Publishing Company Limited, New Delhi, 4th Edn., 1999. 2. Grimaldi, R.P., Discrete and Combinatorial Mathematics An Applied Introduction, Pearson Education Asia, Delhi,Fourth Edn, 2002.

BMA342

MECHANICS

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Unit I Statics: Concurrent system of forces: Triangle law of forces, Lami’s Theorem, Polygon law of forces, Moment of a force, Varignon’s Theorem. 55

B.Sc Mathematics


Unit II Friction: Laws of friction, Angle of friction, Ladder problems. Dynamics : Energy: Kinetic energy, Conservation of energy, Conservation forces. Unit III 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 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 Central Orbits: Central forces, Differential equation of a central orbit, Pedal equation, Apse, p-r equation, Inverse square law. Text Books: 1. A text book of Statics, Dr.M.K.Venkataraman, Agasthiar Publications, 1994. 2. A text book of Dynamics, Dr.M.K.Venkataraman, Agasthiar Publications ,1994. References: 1. Dynamics, K.Viswanatha Naik, M.S. Kasi, Emerald Publishers, 1992. 2. Mechanics, P.Duraipandian, Laxmi Duraipandian, Muthamizh Jayapragasam,S.Chand & Company Ltd publications, 2010.

BMA343

PARTIAL DIFFERENTIAL EQUATIONS

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UNIT-I Partial differential equations: Formation, order and degree, Linear and Non-Linear Partial differential equations of the first order: Complete solution, singular solution, General solution, Solution of Lagrange’s linear equations, Charpit’s general method of solution. Compatible 56

B.Sc Mathematics


systems of first order equations, Jacobi’s method. UNIT-II Linear partial differential equations of second and higher orders, Linear and non-linear homogenious and non-homogeneous equations with constant co-efficient, Partial differential eqution with variable co-efficient reducible to equations with constant coefficients, their complimentary functions and particular Integrals, Equations reducible to linear equations with constant co-efficients. UNIT-III Classification of linear partial differential equations of second order, Hyperbolic, parabolic and elliptic types, Reduction of second order linear partial differential equations to Canonical (Normal) forms and their solutions, Solution of linear hyperbolic equations, Monge’s method for partial differential equations of second order. UNIT-IV Cauchy’s problem for second order partial differential equations, Characteristic equations and characteristic curves of second order partial differential equation. Unit V Method of separation of variables: Solution of Laplace’s equation, Wave equation (one and two dimensions), Diffusion (Heat) equation (one and two dimension) in Cartesian Coordinate system. Text Books: 1. D.A. Murray: Introductory Course on Differential Equations, Orient Longman, (India), 1967 2. 4. J.N. Sharma & Kehar Singh: Partial Differential Equations for Engineers and Scientists, Alpha Science International. Reference Books: 1. Erwin Kreyszing, Advanced Engineering Mathematics,John Wiley & Sons, Inc., New York, 1999 2. A.R. Forsyth, A Treatise on Differential Equations, Macmillan and Co. Ltd. 3. B.S. Garewal: Higher engineering mathematics, Khanna publications.

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4 1 0 3 Unit I Introduction – Big – M method – Definitions of Big – M method , surplus variables and artificial variables – Procedure of solving an LPP by Big – M method – Pseudo optimal solution – Problems – Two – Phase Simplex method – Procedure of solving an LPP by two – phase simplex method – problems. 57

B.Sc Mathematics


Unit II Introduction – Balanced and unbalanced T.P , Feasible solution – Basic feasible solution – Optimum solution – Degeneracy in a T.P. – Mathematical formulation – North – West Corner rule – Vogell’s approximation method (unit penalty method) - Method of Matrix minima (Least cost Method) – problems – Algorithm of Optimality test (Modi Method) – Problems . Unit III Assignment problem – Definition – Mathematical formulation of the Assignment problem – Test for optimality by using Hungarian method - Unbalanced Assignment problem – Degeneracy in Assignment problem - Maximization case in Assignment problem – Restrictions on Assignment problem – Variations in Assignment problem –problems . 31 Unit IV Introduction – Definition – Basic assumptions – n jobs to be operated on two machines – problems – n jobs to be operated on three machines – problems – n jobs to be operated on m machines – problems – Two jobs to be operated on ‘m’ machines (graphical method) – problems. Unit V Elements of queueing system – waiting time – idle time – Kendall’s Notation – Queueing models:Poisson arrival and exponential service (M/M/1):(FCFS/  /  ); (M/M/1):(FCFS/n/M); (M/M/c):(FCFS/n/M). Recommended Text Gupta P.K.and Hira D.S., (2000) Problems in Operations Research, S.Chand & Co. Delhi Reference Books 1. Kanti Swaroop, Gupta P.K. and Manmohan, (2002) Problems in Operation Research, Sultan Chand & Sons. 2. Taha H.A. (2003) Operations Research, Macmillan Publishing Company, New York. 3. V.K.Kapoor [1989] Operations Research, Sultan Chand & sons. 4. P.R.Vittal (2003) Operations Research, Margham Publications, Chennai. 5. J.K.Sharma, (2001) Operations Research: Theory And Applications Macmillan, Delhi 6. S.J.Venkatesan, Operations Research, J.S. Publishes, Cheyyar-604 407. BMA703

ALLIED MATHEMATICS-I

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[ For B.Sc.(Physics) and B.Sc.(Chemistry)] Unit I Introduction to Partial Differentiation - Total differential co-efficient - Euler’s Theorem – Maxima and Minima of functions of two variables – Lagrange’s method of undetermined multipliers- Jacobian - Definition and simple problems. 58

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Unit II Introduction - Integration of irrational functions - Methods of integration of the following types only: dx ( px  q) 2 2  ax 2  bx  c ,  ax 2  bx  c dx,  ax  bx  c dx, ( px  q) ax  bx  c dx,

 (x  k)

dx ax  bx  c 2

and

 (ax

dx 2

 b) cx 2  d

Properties of Definite integrals - Integration by parts - Bernoulli’s formula. Unit III Second order linear differential equations with constants co-efficients – Methods of finding particular integral of the functions of eax, sin ax or cos ax, eaxv(x), xm. Fourier series – Even and odd functions – Half range Fourier series. Unit IV Analytical geometry of three dimensions: Direction Cosines – direction ratios. The plane: Three forms of an equation of a plane (without derivations) – Angle between the two planes – Length of the perpendicular from a point to the plane (simple problems only) – The straight line. Unit V Theory of equations: Nature of roots – Relation between the coefficients and the roots of an algebraic equation – Transformation of equations – Reciprocal equation. Matrices: Rank of a matrix – Eigen values and Eigen vectors – Cayley Hamilton theorem. Text Books: 1. S. Arumugam, Ancillary Mathematics, Gamma Publications, Reprint 2006. 2. T. K. ManicavachagomPillay, T. Natarajan, K.S. Ganapathy S., Algebra Vol – I and Vol II, Viswanathan Printers and Publishers Pvt. Ltd., 2004. 3. Calculus – Vol- I, II, III by S. Narayanan and T. K. ManicavachagomPillay, S. Viswanathan Printers & Publishers Pvt. Ltd., 2009. References 1. P.R. Vittal, Allied Mathematics (in single volume) , Margham Publications, Reprint 2005. 2. A. Singaravelu, Allied Mathematics (For Physics, Chemistry and Computer Science Major Courses of Madras University), Meenakshi Traders, 2001. L T P C BMA704 ALLIED MATHEMATICS-II 4 1 0 3 Unit I: Partial Differential Equations Introduction to Partial Differential Equations - Order and derivation of Partial Differential Equations, Different integrals of Partial Differential Equations, Solution of Partial Differential Equations in some simple cases, Standard types of first order Partial Differential Equations (standard types I to IV). Unit II: Multiple Integrals 59

B.Sc Mathematics


Introduction - Definition of double integral, evaluation of double integral(including changing the order of integration), triple integrals, application of multiple integrals (area enclosed between curves), volume as a triple integral. Unit III:Vector Calculus Gradient, Divergence and curl, Vector identities, Line integral, Surface integral, Volume integral. Unit IV:Vector Integration Statement of Gauss divergence theorem, Green’s Theorem, Stokes theorem (without proof) and Applications. Unit V: Groups Binary operation, Definition of groups, Abelian group, Infinite group, properties of groups, Composition table for finite sets, Addition modulo m, Multiplication modulo m, Permutation and order of an element, cyclic permutation, Integral powers of an element of a group, Isomorphism of groups, Cayley’s theorem, cyclic group, Properties of cyclic groups. Text Books Books: 1. S. Arumugam, Ancillary Mathematics Paper IV, Gamma Publications, Reprint 2006. 2. T. K. ManicavachagomPillay, T. Natarajan, K.S. Ganapathy S., Algebra Vol – I and Vol II, Viswanathan Printers and Publishers Pvt. Ltd., 2004. 3. Calculus – Vol- I, II, III by S. Narayanan and T. K. ManicavachagomPillay, S. Viswanathan Printers & Publishers Pvt. Ltd., 2009. References 1. P.R. Vittal, Allied Mathematics (in single volume) , Margham Publications, Reprint 2005. 2. A. Singaravelu, Allied Mathematics (For Physics, Chemistry and Computer Science Major Courses of Madras University), Meenakshi Traders, 2001. 3. P. Kandasamy and K. Thilagavathy, Allied Mathematics – Paper II – Second Semester , S. Chand & Co., Reprint 2010. 4. T.K. Manicavachagam pillay, S. Narayanan, Ancillary Mathematics Book I and III, S. Viswanathan Publishers, 1999.

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