2006-2009 Batch(CU5MA).doc

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI 620 002

PAGE 7

(SHIFT I)

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI 620 002.

DEPARTMENT OF MATHEMATICS

CURRICULUM STRUCTURE (CAFETERIA)

B.SC., MATHEMATICS

( 2005 2008) (2006-2009)

1. Foundation Courses F

2. Major Compulsory and Optional courses M

3. Allied Compulsory and Optional courses A

4. Interdisciplinary Courses ID

5. Extra Projects and Placements.

SemCom

ponentCode NoCourseSubject TitleHrs/

WeekCredits

1F1CU5T:01Language 1

Paper 155

F2CU5E:01Language II

Paper 166

F3RESCAPESCapacity Building11

F4Life Oriented

Education1

M1CU5MA:OM1Major CoreCalculus and Fourier Series77

M2CU5MA:OM2Major CoreClassical Algebra &Trigonometry66

A1CU5MA:OA1AAllied Compulsory-Paper 1Mathematical Statistics-I 55

TOTAL3031

IIF1CU5T:E2Language 1

Paper II55

F2CU5E:E2Language II

Paper II66

F3RESCAPESEnvironmental Studies4

F4Life Oriented Education11

M3CU5MA:EM3Major CoreAnalytical Geometry of Three Dimensions and Vector Calculus77

M4CU5MA:EM4Major CoreSequences and Series66

A2CU5MA:EA2AAllied Compulsory Paper IIMathematical Statistics -II55

TOTAL3034

IIIF1CU5T:O3Language I -

Paper III55

F2CU5E:O3Language II

Paper III66

F3RESCAPESEnvironmental Sustenance Project --1


M5CU5MA:OM5Major CoreStatics44

M6CU5MA:OM6AMajor CoreDifferential Equations and Laplace Transforms55

A3CU5MA:OA3AAllied Compulsory Paper IIIMathematical

Statistics -III55

ID1Inter Disciplinary Course44

TOTAL3031

IVF1CU5T:E4Language I

Paper IV55


Paper IV66

F3RESCAPES Environmental Sustenance Project1


M7CU5MA:EM7Major CoreDynamics44

M8CU5MA:EM8AMajor CoreAlgebra55

A4 Allied Optional

Paper I 55


TOTAL3031

VF3RESCAPESImpact Study1


M9CU5MA:OM9Major CoreReal Analysis55

M10CU5MA:OM10AMajor OptionalOptimization

Techniques -155

M11CU5MA:OM11AMajor OptionalProgramming in C For Numerical Methods55

M12CU5MA:OM12AMajor OptionalNumerical Methods 55

A5 Allied Optional

Paper II55


TOTAL3031

VIF3RESCAPES Project (optional)

F4Life Oriented Education 11

M13CU5MA:EM13Major CoreTheory of Functions of a Complex Variable55

M14CU5MA:EM14AMajor OptionalOptimization

Techniques - II55

M15CU5MA:EM15AMajor OptionalIntroduction to Fuzzy Mathematics 55

M16CU5MA:EM16AMajor OptionalGraph Theory55

A6Allied Optional

Paper III55


TOTAL3030

SEMESTER WISE CREDIT DISTRIBUTION

ISEMESTER

31

IISEMESTER

34

IIISEMESTER

31

IVSEMESTER

31

VSEMESTER

31

VISEMESTER

30

-------

188



B.Sc., MATHEMATICS

SEMESTER I

MAJOR (CORE) CALCULUS AND FOURIER SERIES

No. of Hours: 7

Max. Marks:100

No. of Credits: 7

CODE:CU5MA:OM1

UNIT I:

Successive differentiation Leibnitz theorem (with proof) Curvature radius of curvature centre of curvature circle of curvature (both in Cartesian and polar coordinates) and evolute.

UNIT II:

Partial differentiation Total differential coefficient Homogeneous functions-Partial derivatives of a function of two functions Jacobian of two and three variables-Maxima and minima of functions of two variables.

UNIT III:

Reduction formulae: 0 (/2 sinn x dx, 0 (/2 cosn x dx, 0 (/2 sinn x cosn x dx

Multiple integrals Evaluation of double integrals in cartesian and polar co-ordinates. Triple integrals (evaluation in Cartesian Co-ordinates only) - Change of order of Integration.

UNIT IV:

Beta and gamma functions Definition, recurrence formula of gamma functions Properties of Beta functions-Relations between Beta and Gamma functions Evaluation of simple integrals.

UNIT V:

Fourier cosine and sine series Half range Cosine and Sine series.

TREATMENT as in

CALCULUS (Vol I) by S. Narayanan and T.K. Manicavachagom Pillay for units

I and II.

Unit I Chapter III, Chapter X Sec2 (from 2.1 to 2.6)

Unit II- Chapter VIII (Sec 1 and Sec.4)

CALCULUS (Vol II) by S. Narayanan and T.K. Manicavachagam Pillay for units III and IV

Unit III- Chapter V Sections 1 to 4

Unit IV Chapter VII Sections 2,3,4,5

Engineering Mathematics Third year (Part B), 11th Edition by Dr. M.K. Venkatraman for unit V.

Unit V Chapter I (Section 1 to 6, Section 8, Section 10)

REFERENCES:

Schaums Outline series Theory and problems of Advanced Calculus.

Differential and Integral Calculus by N. PISKUNOV Mir Publishers.

Advanced Calculus David V. Widder Prentice Hall of India

(II Edition)

Calculus and Analytic Geometry Thomas/Finney Narosa Publishing House.

Calculus with Computer Applications:- Ransom V. Lynch,

Donald R. Ostberg & Robert G. Kuller.

Xerox College Publishing.

Schaums Outline series Theory and Problems of Laplace Transforms.

********************************


B.Sc., MATHEMATICS

SEMESTER I

MAJOR (CORE) CLASSICAL ALGEBRA AND TRIGONOMETRY

No. of Hours: 6

Max. Marks:100

No. of Credits: 6

CODE:CU5MA:OM2

CLASSICAL ALGEBRA

UNIT I:

Theory of Equations:

Relation between roots and coefficients symmetric functions of roots in terms of the coefficients Sum of the powers of the roots of an equation-Newtons Theorem on the sum of the powers of the roots - Transformation of equations Reciprocal equations To increase or Decrease the roots by a given quantity Removal of terms To form an equation whose roots are any power of the roots of a given equation - Descartes rule of signs.

UNIT II:

Theory of Numbers:

Introduction Divisors of a given number N Eulers function (N) highest power of a prime p contained in n! congruences numbers in arithmetical progression Fermats theorem-Wilsons theorem Lagranges theorem.

TRIGONOMETRY

UNIT III:

Expansions of Cosn, Sinn, tann where n is a positive integer (excluding formation of equations); Expansions of Cosn, Sinn in a series of sines and cosines of multiples of , ( in radians) and expansion of Cos, Sin, tan in a series of powers of approximations.

UNIT IV:

Hyperbolic functions in verse hyperbolic functions, separation into real and imaginary parts. Logarithm of complex numbers x+iy general value of logarithm.

UNIT V:

Summation of trigonometric series-method of differences sum of sines of n angles in A.P. sum of cosines of n angles in A.P. summation of series using complex quantities.

TREATMENT as in:

UNIT I: Algebra Vol I by T.K. Manicavachagom Pillay, T. Natarajan and K.S. Ganapathy

Chapter 6 Sec: 11 to 21,24.

UNIT II: Algebra Vol II by T.K. Manicavachagom Pillay, T. Natarajan and K.S. Ganapathy

Chapter 5 fully.

TREATMENT as in Trigonometry by Narayanan and Manicavachagom Pillay for UNIT III,

IV & V.

UNIT III: Chapter III (Formation of Equations Excluded)

UNIT IV: Chaper IV and in Chapter V (Sec 5 only)

UNIT V: Chapter VI (Sec. 1 to Sec.3)

REFERENCES:

1. Set Theory, Number System and Theory of Equations by Arumugam and

Thangapandi Issac, New Gamma Publishing House.

2. Trigonometry by P.R. Vittal, Margham Publisher.

3. Trigonometry by P.P. Gupta, Oxford University Press.

4. Trigonometry by P. Duraipandian, Emerald Publications.

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B.Sc., MATHEMATICS

SEMESTER II

MAJOR (CORE) ANALYTICAL GEOMETRY OF THREE DIMENSIONS AND VECTOR CALCULUS

No. of Hours: 7

Max. Marks:100

No. of Credits: 7

CODE:CU5MA:EM3

UNIT I:

Cartesian coordinates- Distance between points Direction Cosines Direction ratios angle between two lines. The plane the general equation of the plane standard forms of equations of planes Equation of the plane in the form P+ P = Bisector planes.

UNIT II:

Different forms of equations of a straight line the plane and the straight line coplanar lines the shortest distance between two skew lines equations of two skew lines.

UNIT III:

Equation of a sphere Length of the tangent from a point Tangent planes. The plane section of a sphere - Intersection of two spheres.

VECTOR CALCULUS

UNIT IV:

Differentiation:

Derivatives of vector functions velocity and acceleration differential operators directional derivatives, gradient, divergence and curl solenoidal and irrotational vectors vector identities.

UNIT V:

Integration:

Integration of vector functions velocity and acceleration Line integrals work done by a force conservative field surface integral and its applications volume integral and its applications Integral theorems (without proof ) - Gauss divergence theorem, Greens theorem, Stokes theorem and their applications.

Treatment as in A Text Book of Analytical Geometry (Part II Three Dimensions) By

T.K. Manicavachagom Pillay and T. Natarajan. Revised Edition 1996, Reprint July 2000.

UNIT I: Chapters I and II

UNIT II: Chapter III (excluding sections 9,10 & 11)

UNIT III: Chapter IV for the Sphere

Reference:

Analytical Geometry (3 Dimensional) by P.Duraipandian,Laxmi Duraipandian & D.Mahilan Emerald Publishers(1990)

For Vector calculus, Treatment as in Vector Calculus By K. Viswanathan and S. Selvaraj Emerald Publishers)

UNIT IV: Chapters 1 and 2

UNIT V: Chapters 3 and 4.

Reference:

Vector Analysis by P.Duraipandian ,Laxmi Duraipandian Emerald Publishers (1998)

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B.Sc., MATHEMATICS

SEMESTER II

MAJOR (CORE) SEQUENCES AND SERIES

No. of Hours: 6

Max. Marks:100

No. of Credits: 6

Code: CU5MA:EM4

UNIT I:

Sequences sets Sequences Limit of a sequence bounded sequences Cauchys general principle of convergence monotonic sequence.

UNIT II:

Infinite Series- definition of convergence, divergence and oscillation some general theorems convergence of 1/ np and Geometric Series.

Tests of convergence. Comparison tests

1. Cauchys condensation test

2. DAlemberts Ratio Test

3. Cauchys Root test

4. Raabes test (simple problems only)

UNIT III:

Alternating Series : Absolute convergence conditional convergence Leibnitzs test and simple problems.

Binomial theorem for rational index summation of series and approximations:

UNIT IV:

Exponential and Logarithmic Series summation and approximations.

UNIT V:

General summation of series Application of partial fractions summation by difference series recurring series.

TREATMENT as in Algebra volume I by Manicavachagom Pillay, Natrarajan & Ganapathy.

UNIT I: Chapter 2 Section 4, Section 6, Section 7.

UNIT II: Chapter 2 Section 8 to Section 20.

UNIT III: Chapter 2 Section 21 to Section 24.

Chapter 3 Section 5,10 & 14.

UNIT IV: Chapter 4

UNIT V: Chapter 5

REFERENCES:

1. A first course in Real Analysis by M.K. Singal and Asha Rani Singal,

R. Chand & Co, New Delhi.

2. Sequences and Series by Dr. Arumugam.

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HOLY CROSS COLLEGE ( AUTONOMOUS) TIRUCHIRAPPALLI 620 002.

B.SC., MATHEMATICS

SEMESTER III

MAJOR (CORE) : STATICS

No. of Hours: 4

Max.Marks:100.

No. of Credits:4

Code:CU5MA: OM5.

Unit : I

Force Types of Forces Equilibrium Forces acting at a point Parallelogram of forces Triangle of forces Ploygon of forces - Lamis theorem Resolution of a force Composition of forces Resultant Conditions of equilibrium.

Unit: II

Parallel Forces Like and Unlike parallel forces Resultants Moment of a force about a point - Varignons Theorem on Moments Principle of Moments Moment of a force about an axis Couples Equilibrium of two couples Equivalence of two couples Couples in Parallel Planes Resultant of Coplanar Couples Resultant of a couple and a force.

Unit : III

Equilibrium of Three Forces acting on a rigid body Three coplanar forces conditions of Equilibrium Two trigonometrical theorems useful in the solution of statical problems Problem solving.

Unit : IV

Friction Laws of friction angle of friction cone of friction equilibrium of a body on a rough inclined plane Problems involving the force of friction.

Unit : V

Equilibrium of strings Common catenary equations tension at any point geometrical properties Parabolic catenary Suspension Bridge.

Treatment as in Statics by Dr. M.K. Venkataraman, Agasthiar Publications, Trichy (1996).

Unit: I - Chapters 1 & 2

Unit: II Chapters 3 & 4

Unit: III Chapter 5

Unit: IV Chapter 7

Unit: V Chapter 11

BOOKS FOR REFERENCE

1.Statics by A.V. Dharmapadam

2.Mechanics by P. Durai Pandian & Others.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPALLI - 2.

B.SC. MATHEMATICS

SEMESTER III

MAJOR (CORE ) : DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS

No.of.Hours: 5

Max.Marks: 100

No.of Credits:5 Code:CU5MA:OM6A

UNIT I :

ORDINARY DIFFERENTIAL EQUATIONS

Linear homogeneous equations with variable coefficients. Equations reducible to the linear homogeneous equation. Method of variation of parameters.

UNIT II :

PARTIAL DIFFERENTIAL EQUATIONS

Formation of partial differential equations by eliminating arbitrary constant and functions - solutions - General, particular and complete integrals - solutions to first order equations in four standard forms F(p, q) = 0, F(z,p,q) = 0, F(x,p,q) = 0,F(y,p,q) = 0, F1 (x,p) = F2 (y,q),

z = px+qy+f (p,q), Lagranges method of solving linear equation Pp + Qq = R.

UNIT III :

LAPLACE TRANSFORMS

Definition - Laplace transforms of functions eat, Cosat, Sinat, tn (n is a +ve integer), eat cosbt,

eat sinbt, f'(t), f''(t), fn(t), tn f(t), f(t)/ t

UNIT IV :

INVERSE TRANSFORMS

Inverse transforms relating to the above standard functions - application to solution of ordinary differential equations with constant coefficients.

UNIT V :

Second order linear partial differential equation with constant coefficients - Particular integrals for functions of the type e ax + by, Sin (ax + by), Cos (ax + by), xrysApplication of partial differential equations - Solution to heat and wave equations by method of separation of variables (No derivation of equations)

Treatment as in Differential Equations by Narayanan & Manicavachagom Pillay for Units I, II & III

UNIT:I Chapter V - Section 5 & 6 and Chapter VII - Section 4

UNIT:II Chapter XII ( Omit from Section 5.5)

UNIT:III Chapter IX Sections 1 to 5

UNIT:IV Chapter IX Sections 6 to 9

Treatment as in ENGINEERING MATHEMATICS Part B by Dr.M.K.Venkatraman for Unit V.

UNIT:V Chapter 2 ( Section 13 to Section 19 ) & Chapter 3 ( Omit from Section 10 )

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HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2

B.SC. MATHEMATICS

SEMESTER : IV

MAJOR ( CORE ) : DYNAMICS

No. Of. Hrs: 4 Max. Marks:100

No. of Credits:4

CODE: CU5MA:EM7

UNIT: I

Momentum Newtons Laws of Motion Absolute units of forces Conservation of linear momentum Motion of a particle on planes Motion of connected particles.

UNIT : II

Projectiles Path of a projectile Characteristics of the motion of a projectile Greatest height - Time of flight - Horizontal range Maximum horizontal range Directions of projection Velocity of the projectile Simple problems.

UNIT : III

Motion of a projectile on an inclined plane Range on an inclined plane Time of flight Greatest distance from the inclined plane Maximum range on an inclined plane Directions of projection on an inclined plane Enveloping parabola Simple problems.

UNIT : IV

Impulsive forces Impact of two bodies Motion of a shot and gun Collision of elastic bodies Fundamental laws of inpact Impact of a smooth sphere on a fixed plane Direct impact Oblique impact Simple problems.

UNIT : V

Simple harmonic motion in a straight line Definitions General solution of a simple harmonic motion equation Composition of two simple harmonic motions Simple problems.

Treatment as in A Text Book of Dynamics by Dr. M.K. Venkatraman Agasthiar Publications, Tiruchy-2.

Eleventh Edition February 2004.

Unit: I Chapter IV 4.1 to 4.18, 4.2 to 4.23

Unit:II- Chapter VI 6.1 to 6.11

Unit:III Chapter VI 6.12 to 6.17

Unit:IV Chapter VII 7.1 to 7.5, Chapter VIII - 8.1 to 8.8

Unit:V Chapter X 10.1 to 10.3, 10.6, 10.7

BOOKS FOR REFERENCE:

1.Dynamics by Prof. M.L. Khanna - Jai Prakash Nathan & Company, Meerut 10th Edition 1975.

2.Principles of Dynamics by Greenwood, Donald T-Prentice Hall of India-New Delhi 1988.

3.Dynamics K.Viswanatha Naik & M.S. Kasi Emerald Publishers, Egmore, Chennai-2001.

4.Golden Dynamics by N.P. Bali Laxmi Publishers, New Delhi 1986.


B.SC. MATHEMATICS - SEMESTER IV / VI

MAJOR (CORE) : ALGEBRA

No. of. Hours : 5 Max.Marks : 100

No.of Credits: 5

Code: CU5MA:EM8A / CU5MA:EM15B

UNIT I:

Groups

Cosets and Lagrange's theorem - Normal subgroups and quotient groups - Finite groups and Cayley tables - isomorphism and homomorphism.

UNIT II:

Rings:

Definition and examples - elementary properties of rings - ismorphism -types of rings - Characteristic of a ring - subrings-ideals - quotient rings - homomorphism of rings

UNIT III:

Vector spaces

Definition and examples - subspaces - Linear transformation - span of a set - Linear independence and Linear dependence.

UNIT IV:

Vector spaces ( Contn)

Basis and dimension Maximal Linearly Independent set, Minimal Generating set, Isomorphism of vector spaces - Rank and nullity - matrix of a linear transformation.

UNIT V:

Inner Product spaces

Definition and examples of inner product spaces, Orthonormal set, Gram Schmidt Orthogronalisation Process - Orthogonality - Orthogonal complement.

Treatment as in Modern Algebra by N. Arumugam and A. Thangapandi Isaac June 1997 - Edition

UNIT I: ( Chapter 3 - Sec.3.8 to 3.12)

UNIT II: ( Chapter 4 - Sec.4.1 to 4.8 & 4.10)

UNIT III: (Chapter 5 - Sec 5.1 to 5.5)

UNIT IV: ( Chapter 5 - Sec 5.6 to 5.8)

UNIT V: ( Chapter 6 - Sec 6.1 to 6.3)


1. A text book of Modern Abstract Algebra by Shanti Narayanan.

2. Modern Algebra by K. Sivasubramanian.

3. A text book of Modern Algebra byR. Balakrishnan & N. Ramabadran.

HOLY CROSS COLLEGE (AUTONOMOUS)TIRUCHIRAPALLI - 2.

B.SC. MATHEMATICS

SEMESTER V

MAJOR (CORE) REAL ANALYSIS

No.of.Hours : 5 Max.Marks: 100

No.of Credits:5 Code:CU5MA:OM9

UNIT I : REAL NUMBERS

Introduction to Real Number system - the field axioms and theorems - Order in R - Absolute value - Completeness - Some important subsets of R - Representation of real numbers as points on a straight line - Intervals - Countable and uncountable sets.

UNIT II : NEIGHBOURHOOD AND LIMIT POINTS

Neighbourhoods - Open sets - Closed sets - Limit points of a set - Closure of a set - Interior of a set - Compactness and connectedness.

UNIT III : LIMITS AND CONTINUITY

Limits - Continuous functions - Types of discontinuities - Algebra and boundedness of continuous functions - Intermediate value theorem - Inverse function theorem - Uniform continuity.

UNIT IV : DERIVATIVES

Introduction - Derivability and continuity - Algebra of derivatives - Inverse function theorem for derivatives - Darboux's theorem.

MEAN VALUE THEOREMS

Rolle's theorem - Mean value theorems on derivatives (Lagrange's and Cauchy's) - Taylor's theorem with remainder - Taylor's series - power series expansions of some standard functions: e , Sin x, Cos x, (1+x) and log(1+x)

UNIT V : RIEMANN INTEGRATION

Introduction - Riemann integrability and integral of bounded functions over bounded intervals - Properties of Darboux sums - Darboux's theorems I and II - Equivalent definition of integrability and integral - Conditions for integrability - Particular classes of bounded integrable functions - Properties of integrable functions - Integrability of sum, difference, product, quotient and modulus of integrable functions - Continuity and derivability of the integral function - fundamental theorem of integral calculus.

Treatment as in 'A First Course in Real Analysis' by M.K.Singal and Asha Rani Singal - R.Chand & Co. New Delhi. 20TH Edition,1998

UNIT I : CHAPTER 1

UNIT II : CHAPTER 2

UNIT III : CHAPTER 5

UNIT IV : CHAPTER 6 (Omit from section 6) and Chapter 8 ( Omit sections 7 and 8)

UNIT V : Treatement as in "Elements of Real Analysis" by Shanti Narayan.

Chapter 9 (Omit Sec 9.12, 9.13, 9.16 and 9.17)


1. 'A Course of Mathematical Analysis' by Shanthi Narayan.

3. "Real Analysis" by Arumugam and others.

HOLY CROSS COLLEGE (AUTONOMOUS)TIRUCHIRAPALLI - 2.

B.SC. MATHEMATICS - SEMESTER V

MAJOR (OPTIONAL) OPTIMIZATION TECHNIQUES - I

No.of.Hours : 5 CODE:CU5MA:OM10A

No.of Credits: 5 Max Marks:100

UNIT I :

Mathematical formulation of the problem - Graphical solution methods - General Linear Programming Problem - Slack and Surplus variables. Canonical and standard forms of L.P.P.

UNIT II :

The Simplex Method - Simplex Algorithm - Artificial variables - Charnes Method of penalties ( Big - M method) - Problem of Degeneracy - Two-Phase Simplex method.

UNIT III :

Duality - Dual Simplex algorithm. Assignment Problem - Hungarian method - Unbalanced assignment problem - Travelling Salesman Problem.

UNIT IV :

Transportation Problem - Initial basic feasible solution - Northwest corner rule - Row minima method - Column minima method - Matrix minima Method - Vogel's approximation method - Optimal solution - u - v method - Degeneracy - Unbalanced Transportation Problem.

UNIT V :

Introduction - Problem of sequencing - Problems with n jobs and Two machines - Problems with n jobs and Three machines - problems with n jobs and m machines - Graphic solution.

Treatment as in "Operations research" by Kanti swarup,P.K.Gupta & Man mohan, Eighth thoroughly revised edition.

UNIT - I - Chapter 2 (2.1 to 2.6)

UNIT - II - Chapter 3 - Section 3.1 to 3.5

UNIT - III - Chapter 3 - Section 3.6, Chapter 4 (Omit section 4.3) & Chapter 7.

UNIT - IV - Chapter 6

UNIT V - Chapter 10


B.SC. MATHEMATICS

SEMESTER V

MAJOR (OPTIONAL) PROGRAMMING IN C FOR NUMERICAL METHODS

No. of Hours: 5 Max. Marks:100

No. of Credits:5

Code: CU5MA:OM11A

UNIT - I:

Constants, variables, data types, symbolic constants - operators and expressions - evaluation of expressions - reading and writing a character - formatted input and output - handling of character strings - operations on strings - string handling functions.

UNIT - II:

Decision making and branching - Using IF, IF-ELSE, Nesting of IF-ELSE statements - ELSE-IF ladder - Switch statement - the conditional operator - GOTO statement - Decision making and looping - the WHILE, DO, FOR statements.

UNIT - III:

Arrays - one dimensional, two dimensional, multi dimensional groups - structure - definition giving values to members - Initialization - Comparison - arrays of structures - Arrays within structures - structures within structures and functions - Unions - Size of structures.

UNIT - IV:User defined functions - the form of C functions - Return values and their types - calling a function - category of functions - no arguments and no return values - Arguments but no return values - Arguments with return values - Nesting of functions - Recursion -

Function and arrays - the scope and life time of variables in functions.

UNIT - V:

File management - Defining and opening a file - Closing a file - I/O operations on files

Scope and Treatment as in "Programming in ANSI C " Second Edition By

E. Balagurusamy.

UNIT - I: Chapters 2,3,4 and 8

UNIT - II: Chapters 5 and 6

UNIT - III: Chapters 7 and 10

UNIT - IV: Chapter 9

UNIT - V: Chapter 12

REFERENCE BOOKS:

Programming in C - V.Rajaraman Programming with C - Schaum's Series

ANNEXURE

C Programming for Theory and Practicals:

Roots of equations : Iterative Methods

1. Bisection Method

2. False Position Mehod

3. Newton - Raphson Method

INTERPOLATION:

Lagrange's Method

Newton - Forward Method

Newton - Backward Method

NUMERICAL DIFFERENTIATION:

Euler Method

Predictor - Corrector Method

Runge-kutta IV order method

NUMERICAL INTEGRATION:

Simpson's 1/3 rule

Trapezoidal rule

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HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2.

B.SC. MATHEMATICS - SEMESTER V

MAJOR ( OPTIONAL ) NUMERICAL METHODS

No.of Hours : 5 Max.Marks : 100

No.of Credits:5 Code: CU5MA:OM12A

UNIT I

Solution of algebraic and transcendental equations:

Introduction - Bisection Method - Iteration Method - The Method of False Position - Newton - Raphson Method - Generalized Newton's Method.

UNIT II:

Interpolation -Introduction -Finite Differences Forward andBackward differences - Newton's formula for interpolation - Central difference Interpolation formulae - Interpolation with unevenly spaced points - Lagrange's interpolation formula.

UNIT III:

Numerical differentiation and integration:

Introduction - Numerical differentiation - Maximum and minimum values of a tabulated function - Numerical integration Trape zoidal rule - Simpson's 1/3-rule.

UNIT IV:

Solution of linear Systems of equations:

Introduction - Consistency of a linear system of equations - Solution of linear systems -Direct methods - Matrix inversion method - Gaussian elimination method,Gauss - Jordan method - Gauss - Seidel method.

UNIT V:

Numerical Solution of Ordinary Differential Equations:

Introduction - Solution by Taylor's series - Picard's method of successive approximations - Euler's method - Modified Euler's method - Range-Kutta method - Predictor - Corrector method - Adams. Moulton method - Milne's method.

Treatment as in 'Introductory Methods of Numerical Analysis' by

S.S.Sastry 21Printing, Second edition, April 1995.

UNIT I: Chapter 2 - Sec. 2.1 to 2.5.1

UNIT II: Chapter 3 - Sec. 3.1, 3.3, 3.3.1, 3.3.2, 3.6, 3.7, 3.7.1 to 3.7.4, 3.9, 3.9.1

UNIT III: Chapter 5 - Sec. 5.1 to 5.4.2 (Omit 5.2.1)

UNIT IV: Chapter 6 - Sec.6.1,6.2.5,6.3 to 6.3.2, 6.4.

UNIT V: Chapter 7 - Sec 7.1 to 7.6 (Omit 7.4.1)

REFERENCE :

Engineering Maths - Singharavelu. Numerical Analysis- Narayanan & Manicavachagom Pillai.

Numerical Methods - S. Arumugam, A. Thangapandi Isaac & A. Somasundaram

Numerical Methods in Science and Engineering Dr. M.K. Venkataraman.


B.SC. MATHEMATICS

SEMESTER VI

MAJOR ( CORE ) THEORY OF FUNCTIONS OF A COMPLEX VARIABLE

No.of Hours : 5 Max Marks:100

No.of Credits:5 Code: CU5MA:EM13

UNIT I :

Analytic functions

Introduction - Definition - Continuous functions - Convergence of sequences and series absolute convergence - Uniform convergence - Cauchy - Riemann equations.

UNIT II :

Bilinear Transformations:

Elementary transformation - Bilinear transformation - Cross ratio - Fixed points of Bilinear transformation - some special bilinear transformation.

UNIT III :

Integration in the complex plane :

Complex integration - Cauchy's integral theorem (Reimanns proof only) and its extension - Cauchy's integral formula - Derivative of analytic functions - Morera's theorem - Cauchy's inequality for fn(z0), Liouville's Theorem.

UNIT IV :

Expansion of functions in Power Series

Taylor's theorem - Laurent's theorem - Singular points - Zeros - Pole - Essential singularity -Meromorphic function - Principle of the argument - Rouche's theorem - Fundamental Theorem of Algebra.

UNIT V :

Residue Theorem and Contour Integration

Residue at a pole - Residue theorem - Evaluation of Definite Integrals between limits

(-( to ( ) -Extension of the Result- Jordan's lemma ( Statement only)- Evaluation of

( Sinax f(x) dx, ( Cosax f(x)dx where a > 0 and (i) f(z) does not have a pole on the real axis

(ii) f(z) have poles on the real axis (Only Semi Circular contour is included).

UNIT I, III to V:

Treatment as in "Complex Analysis" by S.Narayanan & T.K. Manicava chagam Pillay, Revised 3rd Edition,1985 .

UNIT I: Chapter 1(Omit section 8)

UNIT III : Chapter 3 ( Omit section 13 & 14 )

UNIT IV : Chapter 4

UNIT V : Chapter 5 - sec 1 to 7

UNIT II:

Treatment as in " Complex Analysis" by S.Arumugam, A.Thankapandi Isaac and A.Somasundaram. CHAPTER 3 (Sec.3.1 To 3.5)


1. Functions of a Complex Variable - E.G. Phillips.

2. Complex Analysis - P.Duraipandian and Laxmi Duraipandian.

3. Complex Variable - Churchill.

4. Theory of functions of a Complex Variable - Shanthi Narayanan.

5. Complex Analysis by Sridharan.

*******************


B.SC. MATHEMATICS

SEMESTER VI

MAJOR (OPTIONAL) OPTIMIZATION TECHNIQUES -II

No. of Hours: 5 Max. Marks:100

No.of Credits:5 Code: CU5MA:EM14A

UNIT - I:

Game theory - Two person zero - sum games - the maximin and minimax principle - saddle points - graphical solution of 2 X n and m X 2 games Dominance property.

UNIT - II:

Queueing theory - Poisson process and exponential distribution - classification of queues - Poisson queues.

UNIT - III:

Inventory control - types of inventory - Economic order quantity - Deterministic inventory problem - EOQ problem with price breaks.

UNIT - IV:

Multi-item deterministic problem - Inventory problem with uncertain demand - systems of inventory control (Q system and P system) Probabilistic inventory problems.

UNIT - V:

Network scheduling by PERT - CPM time calculations in Networks -Critical path method ( CPM ) - PERT calculation. Scope and treatment as in "Operations Research" By antiswarup, P.K.Gupta and Manmohan, Eighth thoroughly revised edition.

UNIT - I: Chapter 9 ( Sec 9.1 to 9.7)

UNIT - II: Chapter 17 ( Sec 17.1 to 17.8)

UNIT - III: Chapter 18 ( Sec 18.1 to 18.7)

UNIT - IV: Chapter 18 ( Sec 18.8 to 18.11 )

UNIT - V : Chapter 21 ( Sec 21.1 to 21.7 )

*************

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI 2

B.SC., MATHEMATICS

VI SEMESTER.

MAJOR (OPTIONAL) INTRODUCTION TO FUZZY MATHEMATICS

.

NO. OF HOURS:5

MAX. MARKS:100

NO. OF CREDITS:5 CODE: CU5MA:EM15A

UNIT I :

Fuzzy Set Theory- Introduction-Concept of a fuzzy set-Relation between fuzzy sets-Numbers and Crisp set associated with a fuzzy set-Fuzzy sets associated with a given fuzzy set- Extension Principle.

UNIT II:

Operations on Fuzzy Sets-Introduction-Fuzzy Complement- Fuzzy Union-Fuzzy Intersection

UNIT III :

Fuzzy Relations-Introduction- Operations on Fuzzy Relations--cuts of Fuzzy Relations-Compositions of Fuzzy Relations-Projections of Relations-Cylindric Extensions.

UNIT IV :

Fuzzy Logic- Introduction-Three valued logics-N valued logics for N>4- Infinite valued logics- Fuzzy logic-Fuzzy Propositions and Rules- Reasoning.

UNIT V :

APPLICATIONS:

Fuzzy methods in Control Theory-Introduction-Fuzzy Expert Systems-Classical Control Theory Vs Fuzzy Control Theory-Examples-Components of FLC-Formulation of FLC.

BOOKS FOR STUDY:

For Units I,III,IV & V:

Introduction to Fuzzy Sets and Fuzzy Logic By M.Ganesh Edition2006-Prentice Hall of India Pvt. Limited, New Delhi.

UNIT I : CHAPTER 6 - Secs. 6.1 to 6.9.

UNIT III : CHAPTER 7 - Secs. 7.1 to 7.7

UNIT IV : CHAPTER 8 - Secs. 8.1 to 8.8

UNIT V : CHAPTER 9 - Secs. 9.1 to 9.8

For Unit II

Treatment as in Fuzzy Sets and Fuzzy Logic Theory and Applications by

George J .Kler /Bo yuan.

UNIT II : Chapter 3 secs (3.1 to 3.4)

BOOKS FOR REFERENCE :

1. Introduction to the theory of A.Kaufmann ,Academic press ,Newyork .

2. Fuzzy Set ,Uncertainity and information by Klir &Bouyal .

3. Uncertainity and Fuzzy Logic by George J.Klir & Bo yuan.

4. T.M.Ross ,Fuzzy Engg.Application TMH.


B.SC. MATHEMATICS - SEMESTER VI

MAJOR ( OPTIONAL) GRAPH THEORY

No.of Hours : 5 Max Marks:100

No.of Credits:5

Code:CU5MA:EM16A

UNIT I :

Introduction- graphs and subgraphs-isomorphism- Ramsey numbers Independent sets and coverings - intersection graphs and line graphs - Matrices - Operations on graphs.

UNIT II :

Degree sequence-graphic sequences-walks, trails and paths-connectedness & components-blocks-connectivity.

UNIT III :

Eulerian and Hamiltonian graphs and trees.

UNIT IV :

Directed Graphs :

Introduction Definitions and Basic Concepts Paths and Connections Digraphs and Matrices Tournaments .

UNIT V :

Applications of Graph Theory :

Introduction Connector Problem Shortest Path Problem Transformation and kinematic Graph Designing One Way Traffic System Applications - The travelling salesman problem Job sequencing problem.

Treatment as in "Invitation to Graph Theory" by Dr.S.Arumugam and Dr.S.Ramachandran 1994 edition.

UNIT I : Chapters 1 and 2

UNIT II : Chapters 3 and 4

UNIT III : Chapter 5 and 6

UNIT IV : Chapter 10

UNIT V : Chapter 11


1. Graph theory by Harary, Narosa Publishing House New Delhi, Bombay.

2. Graph theory with applications to Engineeering and Computer Science by

Narsingh Deo, Prentice Hall of India, New Delhi.


ALLIED: MATHEMATICAL STATISTICS - I

No. of Hours: 5

Max. Marks:100

No. of Credits: 5

CODE:CU5MA:OA1A

UNIT I:

Definition of Statistics Statistical data primary and secondary collection, classification and tabulation of data. Diagrammatic and graphical representation.

UNIT II:

Measures of dispersion calculation of Mean Deviation, Quartile deviation, standard deviation, coefficient of variation and moments for frequency distributions- concept of skewness and kurtosis and their measures.

UNIT III:

Simple Correlation rank correlation Linear regression. (Error analysis in chapter 12 omitted)

UNIT IV:

Curve Fitting Fitting straight lines and parabolic curves by the method of least squares and Index Numbers- Uses Types Laspeyres, Paaches, Fishers and Marshall

Edgeworth methods-Tests of Consistency Chain Base Index Fixed Base Index-Cost of Living Index Aggregate Expenditure Method Family Budget Method .

UNIT V: Analysis of time series- Secular Trend-Seasonal Variation-Cyclical Variation Irregular Variation.

TREATMENT as in Statistics by R.S.N. Pillai and V. Bagavathi,

S.Chand & Co, New Delhi

UNIT I: Chapter 1,2,4,6, to 8

UNIT II: Chapters 10 and 11

UNIT III: Chapter 12 and 13 (Omit Error analysis in Chapter 12)

UNIT IV: Chapter 11 Section 11,9,4 & Chapter 14

UNIT V: Chapter 15.

REFERENCES :

1. Business Mathematics and Statistics by P.A. Navaneetham, Jai Publishers.

2. Statistics by M.C. Shukla and S.S. Gulshan, S.Chand & Co, New Delhi.

3. Advanced Practical Statistics by S.P. Gupta, S.Chand & Co, New Delhi.

**************


ALLIED : MATHEMATICAL STATISTICS - II

No. of Hours: 5

Max. Marks:100

No. of Credits: 5

CODE: CU5MA:EA2A

UNIT I: Random Variables

Discrete and continuous random variable, cumulative distributive function, properties of distribution function, function of a random variable, two dimensional random variable, joint probability function, marginal probability distribution, conditional probability distribution, independent random variables.

UNIT II: Expectation and Variance

Expectation of a random vaiable - expectation of a function of a random variable, theorems on expectation. Variance definition, theorems on variance, Tchebychevs inequality.

UNIT III:

Moments and Moment Generating Function, Characteristic Function

Moments definition, relation between central and raw moments, Moment generating function, properties of moment generating function. Characteristic function definition properties of characteristic function, moments from characteristic function, characteristic function of some special type of random variables, characteristic function of sum of independent random variables, inversion theorem on characteristic function.

(Probability generating function and cumulants are excluded)

UNIT IV: Discrete Distributions

Binomial distribution Definition, properties, binomial frequency distribution, moments, recurrence formula for moments, moment generating function, additive property, mode.

Poisson distribution Definition, properties, Poisson frequency distribution, Poisson distribution as limiting form of binomial distribution, moments, recurrence formula for moments, moment generating function, mode.

Unit V Continuous distributions

Normal Distribution Definition, moments, moment generating function, linearity property, mean deviation, mode, points of inflection, normal probability integral, properties of normal distribution.

Uniform distribution Definition, mean, variance, moment generating function.

Exponential distribution Definition , mean, variance, median, moment generating function.

TREATMENT as in Mathematical Statistics by Dr. P.R. Vittal, Margham Publications, T.Nagar,

Chennai 600 017. (2002 Publication)

Unit I

-Chapter 2

Unit II

-Chapters 3, 4

Unit III-Chapters 5, 6 (Probability generating function and cumulants are excluded)

Unit IV-Chapters 12, 13

Unit V

-Chapters 16, 17, 18

REFERENCES:1. Mathematical Statistics by Gupta & Kapoor

2. Mathematical Statistics by S. Venkataraman & P.R. Vittal.


ALLIED : MATHEMATICAL STATISTICS - III

No. of Hours: 5

Max. Marks:100

No. of Credits: 5

CODE: CU5MA:OA3A

UNIT I:

Sampling distribution Chisquare, student-t and F distributions.

UNIT II:

Point Estimation unbiased estimator, efficient estimator, Cramer- Rao inequality, Rao Blackwell theorem, consistent estimator, sufficient estimator, method of moments, method of maximum likelihood.

Interval Estimation Confidence interval for the mean of the normal population, for the difference between means, for the proportion of population, for the difference between two proportions.

UNIT III:

Large samples definitions, test of hypothesis test for a specified mean, for the equality of a means, for specified proportion, for the equality of 2 proportions, for standard deviation of the population, for equality of two standard deviations, for correlation coefficient.

UNIT IV:

SMALL SAMPLES : t Test for a specified population mean, for difference between two population means, for paired observations.

F test for Equality of two population variances, (Analysis of variance excluded).

UNIT V:

SMALL SAMPLES: Chi square Test definition, additive property, Pearsons Statistics, Uses of Chi-square test, test for a specified population variance, test of independence of attributes. Test of goodness of fit.

TREATMENT as in Mathematical Statistics by dr. P.R. Vittal, Margham Publications, T.Nagar, Chennai 17.

UNIT : I- Chapter 22

UNIT : II- Chapter 23

UNIT : III- Chapter 24

UNIT : IV- Chapter 25,26

UNIT : V- Chapter 27.


ALLIED MATHEMATICS PAPER I

No. of Hours: 5

Max. Marks:100

No. of Credits: 5

CODE:CU5MA:OA1B

UNIT I : ALGEBRA

Matrices Rank of a Matrix of order 2 and 3 Consistency of a system of linear non-homogeneous equations- Characteristic equation of a square matrix Evaluation of eigen values and eigen vectors Cayley Hamilton theorem (without proof) and simple problems.

UNIT II : TRIGONOMETRYExpansions of Cosn, Sinn and Tann (n being a positive integer) Expansions of Sinn and Cosn in a series of sines and cosines of multiples of (n being a positive integer and in radians) Expansions of Sin, Cos and Tan in a series of powers of approximations (Formation of equations excluded)

UNIT III :

Hyperbolic functions, inverse hyperbolic functions, separation into real and imaginary parts, Logarithms of complex numbers of the form x+iy and general value of logarithms.

UNIT IV : DIFFERENTIAL CALCULUS

Successive differentiation nth derivative of standard functions Leibnitz theorem (without proof) Application to simple problems Jacobians of two and three variables.

UNIT V : MULTIPLE INTEGRALS

Reduction formulae: 0 (/2 sinn x dx, 0 (/2 cosn x dx, 0 (/2sinn x cosn x dx (Problems only)

Introduction to evaluation of double (Change of order of integration excluded) and Triple integrals (in Cartesian only).

TREATMENT as in Ancillary Mathematics by S. Narayanan and T.K. Manicavachagom Pillay.

REFERENCES:

1. A Text Book on Algebra-I by Rs.S.Aggarwal Published by S.Chand &

Company(Pvt)Ltd.,New Delhi (1989).

2. A Text-Book on Trigonometry by P. Balasubrahmanyam, P.R. Venkatachary & G.R. Venkataraman, Published by ROC House & Sons(1972).

3. A Text Book on Differential Calculus by H.S. Dhami, Published by New Age International(P) Limited, New Delhi(1998).


ALLIED MATHEMATICS PAPER II

No. of Hours: 5

Max. Marks:100

No. of Credits: 5

CODE: CU5MA:EA2B

Analytical Geometry of Dimensions:

UNIT I:

Cartesian co-ordinates distance between points Direction Cosines Direction ratios angle between two lines - The Plane the general equation of the plane Standard forms of equations of planes.

UNIT II:

Skewlines Shortest distance between two skewlines equation of the line of shortest distance (Cartesian only) coplanarity of Straight lines Sphere. General equation tangent planes section of a sphere by a plane - sphere through a given circle.

Vector Calculus:

UNIT III: VECTOR DIFFERENTIATION

Velocity acceleration scalar and vector fields Gradient, Divergence and curl applications - Laplacian operator.

UNIT IV: VECTOR INTEGRATION

Line integral surface integral volume integral application of Gauss and Stokes theorems (Statement only) simple problems.

UNIT V: FOURIER SERIES

Fourier series full range and half range series Solution of wave equation and one dimensional heat equation by the method of separation of variables.

TREATMENT as in

UNIT I & II : Ancillary Mathematics by S. Narayanan and others.

UNIT III & IV : Vector analysis by K. Viswanathan and S. Selvaraj.

UNIT V: Engineering Mathematics (Third year Part B) by Dr. M.K. Venkatraman.

********************


ALLIED MATHEMATICS PAPER III

No. of Hours: 5

Max. Marks:100

No. of Credits: 5

CODE: CU5MA:OA3B

UNIT I : Partial Differential Equations

Formation of equations by eliminating arbitrary constants and arbitrary functions; definition of general, Particular, complete and singular integrals solutions of first order equations in their standard forms 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), Z = px+qy+f(p,q), Lagranges equations Pp+Qq = R

UNIT II : Laplace Transform

Laplace transforms of the functions eat, e-at, cosat, sinat, tn, e-at cosbt, e-at sinbt, e-at tn,

f(t), f(t), fn(t) (where n is a positive integer)

Inverse Transforms

Inverse transforms relating to the above standard functions application to solution of ordinary differential equations with constant coefficients.

Unit III: Numerical Methods

(Derivation of formulae not expected)

Interpolation shift operator Newtons forward difference formula backward difference formula Lagranges formula.

Unit IV: Statistics

Measures of dispersion Range Quartile deviation Mean deviation Standard deviation and their coefficients.

Correlation Coefficient

Karl Pearsons coefficient Definition and evaluation (frequency distribution not included) and Spearmans rank correlation.Unit V

Simple linear regression definition, stating properties on regression lines and problems.

Tests of significance based on normal distribution difference between proportions difference between means difference between standard deviations (Problems only)

TREATMENT as in

Ancillary Mathematics (Volume I Part II Section B) by Narayanan and T.K. Manicavachagom Pillay (Printed in 1990) for units I and II.

Unit I : chapter 5 under differential equations section

Unit II: chapter 4 under differential equations section

Introductory Methods of Numerical Analysis (second Edition) by S.S. Sastry for units III.

Chapter 3 sections 3.1, 3.3, 3.5, 3.9, 3.9.1

Statistics by R.S.N. Pillai and Bagavathy for Unit IV& V.

*******************


APPLIED MATHEMATICS I

NO. OF HOURS/WEEK: 5

MAX. MARKS : 100

NO. OF CREDITS: 5

CODE: CU5MA:OA1C

UNIT : I

Matrices and Determinants: Product of determinants Solution of system of linear equations-Cramers rule-matrixes linear independents and dependence Eigen values and Eigen vectors of a matrix Cayley Hamiltons Theorem(without proof).

UNIT : II

Differential Equation: First Order: Variable separable Homogeneous and non homogeneous equations linear type equations Bemoullis equations.

UNIT : III

Second Order: Particular integrals methods for finding particular integrals all types of equations including variable coefficients (Second Order only).

UNIT : IV

Laplace Transforms: Definition properties sufficient conditions Laplace Transform of periodic functions solving differential equations using Laplace Transforms the inverse transforms.

UNIT : V

Fourier Series: Fourier Series: Even and odd functions properties of odd and even functions Half range Fourier series Development in sine and cosine series (omitting general interval).

BOOK FOR STUDY:

Unit : I

1. Ancillary Mathematics Volume 1 - Part I Algebra,

S. Narayanan, R. Hanumantharao, T.K. Manicavachagom Pillay &

Kandaswamy.

Unit II, III & IV:

2. Narayanan and Manickavasagam Pillai, Ancillary Mathematics Volume 1 :

Part II (Section B)-Integral Calculus and Differential equations.

Unit V:

3. Dr. M.K. Venkataraman, Engineering Mathematics (Vol II), Third Edition,

1988.


APPLIED MATHEMATICS II

NO. HOURS/WEEK: 5

MAX. MARKS : 100

NO. OF CREDITS:5

CODE: CU5MA:EA2C

Unit I:

Definition-Axiomatic approach to probability-Finite sample space-Conditional probability-Multiplicative law of probability-probability of an event in terms of conditional probability-Bayes theorem-Independence events.

Chapter 18 in book 1(page no:582-613)

Chapter 1 in book 2:(page no:1-33)

Unit II:

Binomial distribution-Poisson distribution-Properties of distributions(only mean,variance and standard deviation)-Practial problems under distributions.

Unit III:

Continuous distributions-Normal distribution-Beta distribution-Gamma distribution(practical problems only).

Unit IV:

Test of significance based on normal distribution-Difference between proportions-Difference between means-Difference between standard deviation(problems only).

Unit V:

Analysis of time series:

Definition-Uses-Time series models-Secular trend-Seasonal variation-Preparation of data for analysis-Measurement of secular trend-Graphic method of least squares-Parabolic curve-Shifting the origin-Logarithmic trend-Measurement of seasonal variations-Method of simple average-Practical problems.

Chapter 15 in book 1(page no:470-501)

Books for study:

1.Statistics(theory and practice)third edition 1993 by Mr.R.S.N.Pillai & V.Bagavathi

2.Mathematical Statistics first edition 1973(reprint 1974)by S.Venkataraman & P.R.Vital.

3.Statistics by Mr.R.S.N.Pillai & V.Bagavathi


APPLIED MATHEMATICS III

NO. HOURS/WEEK: 5

MAX. MARKS : 100

NO. OF CREDITS:3

CODE: CU5MA:OA3C

UNIT : I

INTERPOLATION:

Newton Gregory forward and backward interpolation formulae-Lagranges Interpolation formula.

Solving algebraic and transcendental equations Bisection, False position and Newton Raphson methods.

UNIT : II

SOLVING SIMULTANEOUS EQUATIONS:

Gauss elimination Finding inverse of a matrix using Gauss elimination method Iterative methods. Gauss Jacobi and Gauss Seidal methods.

UNIT : III

NUMERICAL INTEGRATION:

Trapezoidal rule and simpsons 1/3 rule. Solving differential equations (1st order differential equations only) solutions by Eulers method runge Kutta 2nd and 4th order method.

UNIT : IV

MEASURES OF LOCATION:

Mean Median Mode Measures of variation: Range standard deviation Coefficient of Skewness.

UNIT : V

ASSOCIATION OF ATTRIBUTES:

Yules coefficient of association. Correlation coefficient rank correlation.

Note: Stress May be on the application problems.

BOOK FOR STUDY:

Unit I, II & III:

1.Dr. M.K. Venkataraman, Numerical Methods in Science and Engineering, 2nd Edition, 1987.

Unit IV & V:

2.R.S.N. Pillai and V. Bagavathi, Statistics, S. Chand and Co. Ltd., 1995.


ALLIED: BUSINESS MATHEMATICS

No. of Hours: 5

Max. Marks:100

No. of Credits: 5

CODE:CU5MA:OA1D

UNIT I:

Mathematics of finance Simple interest Recurring deposit Compound interest Depreciation discounting.

UNIT II:

Matrices - inverse of a matrix rank of a matrix solution of a system of three linear equations- Arithmetic and geometric progressions finding nth term and sum to n terms only.

UNIT III:

Differentiation Applications of the derivative - Integration with applications.

UNIT IV:Transportation problem Initial basic feasible solution North West Corner rule Vogels Approximation method Matrix minima method (optimal solution excluded)

UNIT V:

Assignment problem (Travelling salesman problem excluded) Sequencing problems (Problems with n jobs and 2 machines only)

TREATMENT as in

Business Mathematics and Statistics by Prof. P.A. Navaneetham, Jai Publishers.

(Chapters 1,2,4 (excluding section 13), 6,7 (Sections 1 and 2 and 4 only) and

8 (upto section 7 only) for Units I, II and III

UNITS IV & V

Operations Research by Kanti Swarup, P.K. Gupta, Man Mohan,

Sultan Chand & Sons, New Delhi.

Chapter 6, Section 6.1 & 6.5

Chapter 10 Sections 10.1, 10.2 and 10.3

REFERENCES:

1. Algebra by T.K. Manicavachagom Pillay, T. Natarajan, K.S. Ganapathy,

S. Viswanathan Printers & Publishers Private Limited, Chennai.

2. Business Mathematics by B.M. Aggarwal, Sultan Chand & Sons, New Delhi.

3. Problems in Opperations Research by P.K. Gupta, D.S. Hira,

S.Chand & Co, New Delhi.

4. Linear Programming by M.K. Venkataraman, The National Publishing Company, Chennai.

**************


ALLIED: BUSINESS STATISTICS

No.of Hours:5

Max. Marks:100.

No. of Credits:5

Code:CU5MA:EA2D

UNIT:I

Introduction - Collection of Data - Classification and Tabulation - Diagrammatic representation.

UNIT:II

Measures of Dispersion - Range - Quartile Deviation - Mean Deviation - Standard Deviation - Relative measures - Measures of Skewness and Kurtosis.

UNIT:III

Correlation - Scatter Diagram - Karl Pearson's Coefficient of Correlation - Rank Correlation - (Correlation of a bivariate fequency distribution and Coefficient of concurrent Deviation to be excluded)

Regression - Properties, Regression lines and problems.

UNIT:IV

Time Series - components of Time Series - measurement of trend - measures of seasonal variation problems (Deseasonalization is excluded)

UNIT:V

Index Numbers - methods of construction of Index Numbers - tests for Index Numbers - cost of living Index Number - uses of Index Numbers general problems in the construction of Index Numbers. (Shifting of Base and Splicing of Index Numbers are excluded)

Treatment as in Business Statistics by Dr. P.R. Vittal

UNIT I - Chapters 1 to 4

UNIT II - Chapters 6, 7

UNIT III - Chapters 8, 9

UNIT IV - Chapter 13

UNIT V - Chapter 14

HOLY CROSS COLLEGE (AUTONOMOUS) TRICHIRAPPALLI 620002

SEMESTER-I

ALLIED- BUSINESS MATHEMATICS & STATISTICS

No of hours :5

Max marks : 100

No of Credits :5

Code : CU5MA:OA1E

UNIT I :

Application of derivatives marginal functions elasticity increasing and decreasing functions maxima and minima Linear Programming Problemformulation & graphic solution .

UNIT II :

Transportation Problem North-West Corner Rule Matrix minima method-Vogels approximation method (only initial basic feasible solution ) Assignment Problem Hungarian method.

UNIT III :

Statistics meaning and scope collection of data classification and tabulation diagrams and graphs histogram-polygon cumulative frequency curves .

UNIT IV :

Measures of dispersion range, quartile deviation ,mean deviation standard deviation merits demerits Karl Pearsons coefficient of correlation ,Rank correlation Regression(Raw data only).

UNIT V :

Index numbers

Treatment as in Statistics By R.S.N Pillai and V.Bagavathi for

Units I , II & III

And Business Mathematics by P.A. Navaneetham & Operations Research by Kanti Swarup , Man Mohan & P.K Gupta for Units IV & V

REFERENCES:

1. A Text-Book on Business Statistics by G.V.Shenoy, U.K. Srivastava & S.C.Sharma Published by V.S. Johsi for wiley Eastern Limited, New Delhi(1998).

2. A Text Book on Business Statistics by M.Wilson, Published by Himalaya, Mumbai(2003).


ALLIED : BUSINESS MATHEMATICS & STATISTICS FOR MANAGERS

No.of Hours:5

Max. Marks:100

No.of Credits:5

Code:CU5MA:EA2F

Unit I :

Mathematics of finance-Simple Interest-Recurring Depoist-Compound Interest-Depreciation-Discounting.

Unit II :

Differentiation-Applications of the derivative-Integration with applications. .

Unit III :

Statistics-Meaning & scope- Collection of data- Classification & Tabulation-Diagram&Graphs(Histogram,polygon, Cumulative) Measures of central tendency,(Mean,Median,Mode).

Unit IV:

Measures of Dispersion(Range,Quartile Deviation, Mean deviation, Standard deviation ,Correlation- Co-efficient- Regression equation.

Unit V:

Index Numbers - methods of construction of Index Numbers - tests for Index Numbers - cost of living Index Number - uses of Index Numbers general problems in the construction of Index Numbers. (Shifting of Base and Splicing of Index Numbers are excluded)

BOOKS FOR STUDY:

TREATMENT as in

UNIT I & II,III : Business Mathematics and Statistics by P.R.Navaneethan.

UNIT IV,V: - Business Statistics by P.R.Vittal.



SEMESTER IV

ALLIED (OPTIONAL) :FORTRAN 90 AND ITS APPLICATIONS

No. Of. Hrs:5

Max. Marks:100

No. of Credits:5

Code:CU5MA :EA4A

UNIT: I :

FORTRAN Numeric constants scalar variables declaration named constants .

Arithmetic operators - integer expressions - real expressions - precedence of operators in expressions - assignment statements - intrinsic functions .

UNIT : II

Conditional Statements - relational operators The BLOCK IF construct .

Elementary Format Specifications - Format description for numerical DATA ( READ Statement )- Format description for PRINT Statement - Multi record formats Printing character strings -Reading and writing logical quantities.

UNIT : III

Implementing Loops in Programs - The BLOCK DO Loop - Count controlled DO Loop - Rules regarding Do Loops.

UNIT : IV :

Logical expressions and more control statements - Logical constants, variables and expressions-precedence rules for logical operators - The CASE statement.

Defining and manipulating Arrays Arrays variables use of multiple subscripts DO type notations for INPUT / OUTPUT statements initialising Arrays terminology used for multidimentional Arrays.

UNIT : V :

Functions and Subroutines - Function Subprograms- Syntax rules for Function Subprograms - Generic functions.

Subroutines - Internal procedures Comparison of Function Subprograms and Subroutines.

TREATMENT AS IN Computer Programming in FORTRAN 90 and 95 by V. Rajaraman

UNIT I : CHAPTERS 3 AND 4 (Omit 4.8 )

UNIT II : CHAPTERS 6 AND 11 ( Omit 11.6 and 11.7 )

UNIT III : CHAPTER 7

UNIT IV : CHAPTERS 8 AND 10 (Omit 10.7 and 10.8 )

UNIT V : CHAPTER 9

ANNEXURE : PROGRAMS (only the following programs are expected )

UNIT II

1. To find the area of a triangle when the sides of a triangle are known .

*2. To pick the largest of three given numbers.

*3 . To solve a quadratic equation.

*4. To do income tax calculation.

UNIT III

*5. To find the average height of boys and girls in a class.

6. To add the digits of a given integer and to reverse it.

*7. To print the result of students in an examination.

8. To compute discount.

9. To find the number of days in the months of a year.

UNIT IV

10.To find the average of n given numbers.

*11.To find the biggest of n given numbers.

*12.To arrange the n given numbers in ascending / descending order.

UNIT V

13.To determine the value of a given function.

14.To calculate the interest for various amounts.

*15.To determine n! and use it to find ncr and npr.

16.To evaluate a second order determinant and use it to determine the value of a third order

determinant.

*17.To add or subtract two given matrices.

*18.To multiply two given matrices.

*PROGRAMS FOR PRACTICALS.

************

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPALLI-2.

DEPARMTENT OF MATHEMATICS

SEMESTER - IV

ALLIED ( OPTIONAL ) CALCULUS AND TRIGONOMETRY

No.of.Hours: 5 Max.Marks: 100

No.of.Credits: 5 Code:CU5MA:EA4B/CU5MA:EA6C

UNIT I:

TRIGONOMETRY:

Expansions of Cosn, Sinn and Tann (n being a positive integer) Expansions of Sinn and Cosn in a series of sines and cosines of multiples of (n being a positive integer and in radians) Expansions of Sin, Cos and Tan in a series of powers of approximations (Formation of equations excluded)

UNIT II:

Hyperbolic functions, inverse hyperbolic functions, separation into real and imaginary parts, Logarithms of complex numbers of the form x+iy and general value of logarithms.

UNIT III :

DIFFERENTIAL CALCULUS:

Successive differentiation nth derivative of standard functions Leibnitz theorem (without proof) Application to simple problems Jacobians of two and three variables.

UNIT IV :

PARTIAL DIFFERENTIAL EQUATIONS:

Solutions of first order equations in their standard forms 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), Z = px+qy+f(p,q), Lagranges equations Pp+Qq = R

UNIT V:

FOURIER SERIES:

Fourier series-full range and half range series.

BOOKS FOR STUDY:

UNIT I,II,III,IV : ANCILIARY MATHEMATICS BY S.NARAYANAN AND T.K.MANICAVACHAGOM PILLAY.

UNIT V: ENGINEERING MATHEMATICS(THIRD YEAR-PART- B) BY Dr.M.K.VENKATRAMAN



SEMESTER - V

ALLIED( OPTIONAL) ANALYTICAL GEOMETRY OF 3D, VECTOR CALCULUS & LAPLACE TRANSFORMS

No. of Hours: 5

Max. Marks:100

No. of Credits: 5 Code:CU5MA:OA5B

UNIT I:

Analytical Geometry of Three Dimensions:

Cartesian co-ordinates distance between points Direction Cosines Direction ratios angle between two lines - The Plane the general equation of the plane Standard forms of equations of planes.

UNIT II:

Skewlines Shortest distance between two skewlines equation of the line of shortest distance (Cartesian only) coplanarity of Straight lines Sphere. General equation tangent planes section of a sphere by a plane - sphere through a given circle.

Vector Calculus:

UNIT III:

Vector differentiation: Velocity acceleration scalar and vector fields Gradient, Divergence and curl applications - Laplacian operator.

UNIT IV:

Laplace Transform:

Laplace transforms of the functions eat, e-at, cosat, sinat, tn, e-at cosbt, e-at sinbt, e-at tn,

f(t), f(t), fn(t) (where n is a positive integer)

UNIT V:

Inverse Transforms:

Inverse transforms relating to the above standard functions application to solution of ordinary differential equations with constant coefficients.

TREATMENT as in

UNIT I & II : Ancillary Mathematics by S. Narayanan

UNIT III : Vector analysis by K. Viswanathan and S. Selvaraj.

UNITS IV & V: Ancillary Mathematics (Volume I Part II Section B) by Narayanan and T.K. Manicavachagom Pillay.



SEMESTER - VI

ALLIED (OPTIONAL) NUMERICAL AND STATISTICAL METHODS

No. of Hours: 5

Max. Marks:100

No. of Credits: 5 Code:CU5MA:EA6B

UNIT I:

Solving algebraic and transcendental equations Bisection, False position and Newton -Raphson methods.

UNIT II:

Interpolation:

Newtons Forward and backward interpolation formulae-Lagranges Interpolation formula.

UNIT : III

Numerical differentiation and integration:

Introduction - Numerical differentiation - Maximum and minimum values of a tabulated function - Numerical integration Trapezoidal rule - Simpson's 1/3-rule.

Unit IV: Statistics

Measures of dispersion Range Quartile deviation Mean deviation Standard deviation and their coefficients.skewness-measures of skewness-Karl pearsons coefficient of skewness-Bowleys coefficient of skewness

Unit V:

Moments-kurtosis-Association of attributes-Yules coefficient of association

Note : Derivations not included Numerical problems only.

BOOK FOR STUDY:

Treatment as in "Introductory methods of Numerical Analysis" ( Third Edition, Twenty third printing, June, 1998) By S.S.Sastry

UNIT - I: Chapter 2. Sections 2.1, 2.2, 2.4 & 2.5(2.5.1 omitted)

UNIT - II: Chapter 3. Sections 3.6 ,3.9 & 3.9.1

UNIT - III:Chapter 5. Sections 5.1, 5.2(5.2.1 omitted) 5.3, 5.4.1,5.4.2

BOOK FOR STUDY:

UNIT IV,V: - Statistics by R.S.N. Pillai and Bagavathy

***********

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI -2


SEMESTER III/V

I.D.COURSE : MATHEMATICS FOR COMPETITIVE EXAMINATIONS

No. of Hours : 4 Max.Marks:100

No. of Credits: 4 Code:CU5MA:OI1

UNIT: I

Number system - Sum and difference, Multiplication and division, squares and square roots, L.C.M. & H.C.F. of 2 or more numbers, Fractions and Decimal fractions - A.P. & G.P.

UNIT: II

Problems involving ratio and proportion - Profit and Loss -Percentage Averages.

UNIT: III

Time and work - Time and Distance - Problems involving boats and streams - trains- cisterns and pipes.

UNIT: IV

Simple interest, compound interest and partnership.

UNIT: V

Formulae - results relating to perimeters and areas of square, rectangle, Circle, Triangle, Cube, Sphere, Cone & Cylinder Data Interpretation -Bar chart - Pie Diagram.

REFERENCES :

Text books of Matriculation School.

Arithmetic for Competitive Examinations by R.S.Aggarwal.

Arithmetic for Competitive Examinations by V.K. Subburaj.

Competition Success Review for Bank Probationary Officer's Exam.

Competition Success Review for MBA entrance Examinations.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPALLI-2.

DEPARMTENT OF MATHEMATICS

SEMESTER IV

I.D. COURSE - ELEMENTARY NUMERICAL METHODS

No.of Hours : 4 Max.Marks: 100

No. of Credits : 2 Code: CU5MA:EI2

UNIT - I:

Solution of Algebraic and Transcendental Equations:

Introduction - The Bisection method - The method of false position - Newton _ Rapshon method.

UNIT - II:

Interpolation:

Introduction - Finite differences - Forward differences Backward differences - Newton's formulae for interpolation - shift operator - Lagranges interpolation formula ( with out proof)

UNIT - III:

Numerical Differentiation:

Numerical differentiation of first order only.

UNIT - IV:

Solution of Linear System of Equations:

Matrix inversion method - Gaussian elimination method - Gauss - Jordan method.

UNIT - V:

Numerical solution of ordinary differential equations:

Solution by Taylor's series method - Euler's method - R.K. method of second order and fourth order ( Problems only).

Treatment as in "Introductory methods of Numerical Analysis" ( Third Edition, Twenty third printing, June, 1998) By S.S.Sastry

UNIT - I: Chapter 2. Sections 2.1, 2.2, 2.4 & 2.5

UNIT - II: Chapter 3. Sections 3.1, 3.3.1, 3.3.2, 3.6 & 3.9.1

UNIT - III:Chapter 5. Sections 5.2

UNIT - IV: Chapter 6. Sections 6.3.1, 6.3.2

UNIT - V: Chapter 7. Sections 7.2, 7.4, 7.5



SEMESTER IV/VI

I.D. COURSE:DECISION MAKING TECHNIQUES.

No. of Hours:4 Max.Marks:100

No.of.credits:4 Code: CU5MA:EI3

Unit I :(Chapter 2: 2.1 2.5)

Introduction to Linear Programming Problem Mathematical formulation Graphical Solution Method.Definitions of objective functions,constraints,non negative restrictions,solution,feasible solution and optimal solution

Unit II : ( Chapter 9: 9.1 to 9.6)

Introduction to Game Theory Two person zero sum game The maximin minimax principle Games without saddle Solution of 2 x 2 rectangular games Graphical method.

Unit III: (Chapter 6: 6.5,6.9)

Transportation Problem Definition Mathematical formulation-Initial basic feasible solution North West Corner rule-Row Minima Method-Column Minima Method-Matrix Minima Method- Vogels Approximation Method Unbalanced Transportation Problem-Maximization type.

Unit IV: (Chapter 18: 18.1, 18.2, 18.4 18.6,18.7(Cases(1and 2)0nly)

Inventory Control Types of inventory Economic order quantity Deterministic inventory problem (with and without shortages(instantaneous replenishment only)) EOQ problem with price breaks.

Unit V: (Chapter 21: 21.1 21.7)

Network scheduling PERT CPM time calculation in Networks Critical Path Method (CPM) PERT calculation. (Expected value and variance of i only)

Treatment as in Operations Research by KantiSwarup, Gupta and ManMohan.

REFERENCE BOOKS:

1. Problems in Operations Research by P.K.Gupta and D.S.Hira

2.Operations Research by Hamdy, Taha ,Prema Publishers,1995,Bangalore

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI -2


CERTIFICATE COURSE

APTITUDE MATHEMATICS

No. of Hours :30/Semester Max.Marks:100

UNIT: I

Number system Simplification using formulae and rules.- L.C.M. & H.C.F. of 2 or more numbers Odd man out and Series (A.P. and G.P. nth term and sum only )

UNIT: II

Problems involving Ratio and Proportion - Profit and Loss .

UNIT: III

Percentage - Average - Mixture or allegation.

UNIT: IV

Time and work - Cisterns and Pipes Data Analysis.

UNIT: V

Time and Distance - Problems involving Boats and Streams Trains.

TREATMENT as in Arithmetic (Subjective and Objective ) for Competitive Examinations by R. S.Agarwal, S. Chand and Company Ltd., Ram Nagar, New Delhi.

UNIT I : CHAPTERS 1,2,4 AND 30

UNIT II : CHAPTERS 8,9 AND 16

UNIT III: CHAPTERS 6,7 AND 17

UNIT IV : CHAPTERS 11, 12, AND 29

UNIT VI : CHAPTERS 13,14 AND 15.

REFERENCES :

Text books of Matriculation School.

Arithmetic for Competitive Examinations by V.K. Subburaj.

Competition Success Review for Bank Probationary Officer's Exam.

Competition Success Review for MBA entrance Examinations.

(SHIFT II)

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHY 620 002.


CURRICULUM STRUCTURE (CAFETERIA)

B.SC. MATHEMATICS WITH SPECILIZATION IN

COMPUTER APPLICATIONS

( 2005 2008) (2006-2009)

1. Foundation Courses F

2. Major Compulsory and Optional courses M

3. Allied Compulsory and Optional courses A

4. Interdisciplinary Courses ID

5. Extra Projects and Placements.

SemCom

PonentCode NoCourseSubject TitleHrs/

WeekCredits

1F1CU5T:01Language 1

Paper 155

F2CU5E:01Language II

Paper 166

F3RESCAPESCapacity Building11

F4Life Oriented

Education1

M1CU5MA:OM1Major CoreCalculus and Fourier Series77

M2CU5MA:OM2Major CoreClassical Algebra &Trigonometry66

A1CU5MA:OA1AAllied Compulsory-Paper 1Mathematical Statistics-I 55

TOTAL3031

IIF1CU5T:E2Language 1

Paper II55


Paper II66

F3RESCAPESEnvironmental Studies4


M3CU5MA:EM3Major CoreAnalytical Geometry of Three Dimensions and Vector Calculus77

M4CU5MA:EM4Major CoreSequences and Series66

A2CU5MA:EA2AAllied Compulsory Paper IIMathematical Statistics -II55

TOTAL3034

IIIF1CU5T:O3Language I -

Paper III55

F2CU5E:O3Language II

Paper III66

F3RESCAPESEnvironmental Sustenance Project --1


M5CU5MA:OM5Major CoreStatics44

M6CU5MA:OM6BMajor CoreProgramming in

Fortran 90 55

A3CU5MA:OA3AAllied Compulsory Paper IIIMathematical

Statistics -III55


TOTAL3031

IVF1CU5T:E4Language I

Paper IV55


Paper IV66

F3RESCAPES Environmental Sustenance Project1


M7CU5MA:EM7Major CoreDynamics44

M8CU5MA:EM8BMajor CoreProgramming in C for Numeric Methods 55

A4 Allied Optional

Paper I 55


TOTAL3031

VF3RESCAPESImpact Study1


M9CU5MA:OM9Major CoreReal Analysis55

M10CU5MA:OM10BMajor OptionalProgramming in C++

55

M11CU5MA:OM11BMajor OptionalDifferential Equations & Laplace Transforms55

M12CU5MA:OM12BMajor OptionalVisual Programming 55

A5 Allied Optional

Paper II55


SemCom

PonentCodeTOTAL

CourseSubject Title30

Hrs/

Week31

Credits

VIF3RESCAPES Project (optional)

F4Life Oriented Education 11

M13CU5MA:EM13Major CoreTheory of Functions of a Complex Variable55

M14CU5MA:EM14BMajor OptionalStatistical Packages

55

M15CU5MA:EM15BMajor OptionalAlgebra

55

M16CU5MA:EM16BMajor OptionalDiscrete Mathematics

55

A6Allied Optional

Paper III55


TOTAL3030

SEMESTER WISE CREDIT DISTRIBUTION

ISEMESTER

31

IISEMESTER

34

IIISEMESTER

31

IVSEMESTER

31

VSEMESTER

31

VISEMESTER

30

--------

Total 188

--------



B.Sc., MATHEMATICS

SEMESTER I

MAJOR (CORE) CALCULUS AND FOURIER SERIES

No. of Hours: 7

Max. Marks:100

No. of Credits: 7

CODE:CU5MA:OM1

UNIT I:

Successive differentiation Leibnitz theorem (with proof) Curvature radius of curvature centre of curvature circle of curvature (both in Cartesian and polar coordinates) and evolute.

UNIT II:

Partial differentiation Total differential coefficient Homogeneous functions-Partial derivatives of a function of two functions Jacobian of two and three variables-Maxima and minima of functions of two variables.

UNIT III:

Reduction formulae: 0 (/2 sinn x dx, 0 (/2 cosn x dx, 0 (/2 sinn x cosn x dx

Multiple integrals Evaluation of double integrals in cartesian and polar co-ordinates. Triple integrals (evaluation in Cartesian Co-ordinates only) - Change of order of Integration.

UNIT IV:

Beta and gamma functions Definition, recurrence formula of gamma functions Properties of Beta functions-Relations between Beta and Gamma functions Evaluation of simple integrals.

UNIT V:

Fourier cosine and sine series Half range Cosine and Sine series.

TREATMENT as in

CALCULUS (Vol I) by S. Narayanan and T.K. Manicavachagom Pillay for units

I and II.

Unit I Chapter III, Chapter X Sec2 (from 2.1 to 2.6)

Unit II- Chapter VIII (Sec 1 and Sec.4)

CALCULUS (Vol II) by S. Narayanan and T.K. Manicavachagom Pillay for units III and IV

Unit III- Chapter V Sections 1 to 4

Unit IV Chapter VII Sections 2,3,4,5

Engineering Mathematics Third year (Part B), 11th Edition by Dr. M.K. Venkatraman for unit V.

Unit V Chapter I (Section 1 to 6, Section 8, Section 10)

REFERENCES:

Schaums Outline series Theory and problems of Advanced Calculus.

Differential and Integral Calculus by N. PISKUNOV Mir Publishers.

Advanced Calculus David V. Widder Prentice Hall of India

(II Edition)

Calculus and Analytic Geometry Thomas/Finney Narosa Publishing House.

Calculus with Computer Applications:- Ransom V. Lynch,

Donald R. Ostberg & Robert G. Kuller.

Xerox College Publishing.

Schaums Outline series Theory and Problems of Laplace Transforms.

********************************


B.Sc., MATHEMATICS

SEMESTER I

MAJOR ( CORE ) CLASSICAL ALGEBRA AND TRIGONOMETRY

No. of Hours: 6

Max. Marks:100

No. of Credits: 6

CODE:CU5MA:OM2

CLASSICAL ALGEBRA

UNIT I:

Theory of Equations:

Relation between roots and coefficients symmetric functions of roots in terms of the coefficients Sum of the powers of the roots of an equation-Newtons Theorem on the sum of the powers of the roots - Transformation of equations Reciprocal equations To increase or Decrease the roots by a given quantity Removal of terms To form an equation whose roots are any power of the roots of a given equation - Descartes rule of signs.

UNIT II:

Theory of Numbers:

Introduction Divisors of a given number N Eulers function (N) highest power of a prime p contained in n! congruences numbers in arithmetical progression Fermats theorem-Wilsons theorem Lagranges theorem.

TRIGONOMETRY

UNIT III:

Expansions of Cosn, Sinn, tann where n is a positive integer (excluding formation of equations); Expansions of Cosn, Sinn in a series of sines and cosines of multiples of , ( in radians) and expansion of Cos, Sin, tan in a series of powers of approximations.

UNIT IV:

Hyperbolic functions in verse hyperbolic functions, separation into real and imaginary parts. Logarithm of complex numbers x+iy general value of logarithm.

UNIT V:

Summation of trigonometric series-method of differences sum of sines of n angles in A.P. sum of cosines of n angles in A.P. summation of series using complex quantities.

TREATMENT as in:

UNIT I: Algebra Vol I by T.K. Manicavachagom Pillay, T. Natarajan and K.S. Ganapathy

Chapter 6 Sec: 11 to 21,24.

UNIT II: Algebra Vol II by T.K. Manicavachagom Pillay, T. Natarajan and K.S. Ganapathy

Chapter 5 fully.

TREATMENT as in Trigonometry by Narayanan and Manicavachagom Pillay for UNIT III,

IV & V.

UNIT III: Chapter III (Formation of Equations Excluded)

UNIT IV: Chaper IV and in Chapter V (Sec 5 only)

UNIT V: Chapter VI (Sec. 1 to Sec.3)

REFERENCES:

3. Set Theory, Number System and Theory of Equations by Arumugam and

Thangapandi Issac, New Gamma Publishing House.

4. Trigonometry by P.R. Vittal, Margham Publisher.

3. Trigonometry by P.P. Gupta, Oxford University Press.

4. Trigonometry by P. Duraipandian, Emerald Publications.

****************************


B.Sc., MATHEMATICS

SEMESTER II

MAJOR( CORE) ANALYTICAL GEOMETRY OF THREE DIMENSIONS AND VECTOR CALCULUS

No. of Hours: 6

Max. Marks:100

No. of Credits: 6

CODE:CU5MA:EM3

UNIT I:

Cartesian coordinates- Distance between points Direction Cosines Direction ratios angle between two lines. The plane the general equation of the plane standard forms of equations of planes Equation of the plane in the form P+ P = Bisector planes.

UNIT II:

Different forms of equations of a straight line the plane and the straight line coplanar lines the shortest distance between two skew lines equations of two skew lines.

UNIT III:

Equation of a sphere Length of the tangent from a point Tangent planes. The plane section of a sphere - Intersection of two spheres.

VECTOR CALCULUS

UNIT IV:

Differentiation:

Derivatives of vector functions velocity and acceleration differential operators directional derivatives, gradient, divergence and curl solenoidal and irrotational vectors vector identities.

UNIT V:

Integration:

Integration of vector functions velocity and acceleration Line integrals work done by a force conservative field surface integral and its applications volume integral and its applications Integral theorems (without proof ) - Gauss divergence theorem, Greens theorem, Stokes theorem and their applications.

Treatment as in A Text Book of Analytical Geometry (Part II Three Dimensions) By

T.K. Manicavachagom Pillay and T. Natarajan. Revised Edition 1996, Reprint July 2000.

UNIT I: Chapters I and II

UNIT II: Chapter III (excluding sections 9,10 & 11)

UNIT III: Chapter IV for the Sphere

Reference:

Analytical Geometry (3 Dimensional) by P.Duraipandian,Laxmi Duraipandian & D.Mahilan Emerald Publishers(1990)

For Vector calculus, Treatment as in Vector Calculus By K. Viswanathan and S. Selvaraj Emerald Publishers)

UNIT IV: Chapters 1 and 2

UNIT V: Chapters 3 and 4.

Reference:

Vector Analysis by P.Duraipandian ,Laxmi Duraipandian Emerald

Publishers (1998)

************************************


B.Sc., MATHEMATICS

SEMESTER II

MAJOR (CORE) SEQUENCES AND SERIES

No. of Hours: 6

Max. Marks:100

No. of Credits: 6

Code: CU5MA:EM4

UNIT I:

Sequences sets Sequences Limit of a sequence bounded sequences Cauchys general principle of convergence monotonic sequence.

UNIT II:

Infinite Series- definition of convergence, divergence and oscillation some general theorems convergence of 1/ n p and Geometric Series.

Tests of convergence.

5. Comparison tests

6. Cauchys condensation test

7. DAlemberts Ratio Test

8. Cauchys Root test

9. Raabes test (simple problems only)

UNIT III:

Alternating Series : Absolute convergence conditional convergence Leibnitzs test and simple problems.

Binomial theorem for rational index summation of series and approximations:

UNIT IV:

Exponential and Logarithmic Series summation and approximations.

UNIT V:

General summation of series Application of partial fractions summation by difference series recurring series.

TREATMENT as in Algebra volume I by Manicavachagom Pillay, Natrarajan & Ganapathy.

UNIT I: Chapter 2 Section 4, Section 6, Section 7.

UNIT II: Chapter 2 Section 8 to Section 20.

UNIT III: Chapter 2 Section 21 to Section 24.

Chapter 3 Section 5,10 & 14.

UNIT IV: Chapter 4

UNIT V: Chapter 5

REFERENCES:

4. A first course in Real Analysis by M.K. Singal and Asha Rani Singal,

R. Chand & Co, New Delhi.

5. Sequences and Series by

Documents

2006-2009 Batch(CU5MA).doc