for students admitted from 2011 -2012 onwards iii core course iv sequences and series unit 1:...

For students Admitted from

2011 -2012 Onwards

BATCH -I

SEMESTER: I CORE COURSE I

DIFFERENTIAL CALCULUS AND TRIGONOMETRY

UNIT 1: Methods of Successive Differentiation –Leibnitz’s Theorem and its applications- Increasing & Decreasing functions.(Chapter III: Sections 1.1-1.6, 2.1, 2.2& Chapter IV Sections 2.1, 2.2 of Text Book 1)

UNIT 2:Curvature – Radius of curvature in Cartesian & in Polar Coordinates – Centre of curvature –Evolutes & Involutes(Chapter X Sections 2.1 –2.6 of Text Book 1)

UNIT 3:Expansions of sin(nx) ,cos(nx) ,tan(nx) – Expansions of sin n x, cosnx –Expansions of sin(x) ,cos(x), tan(x) in powers of x and related problems.(Chapter 1: Sections 1.2 to 1.4 of Text Book 2)

UNIT 4:Hyperbolic functions – Relation between hyperbolic & Circular functions-Inverse hyperbolic functions.(Chapter 2: Sections 2.1& 2.2 of Text Book 2)

UNIT 5:Logarithm of a complex number -Summation of Trigonometric series-Difference method- Angles in arithmetic progression method –Gregory’s Series ( Chapter 3 & Chapter 4 : Sections 4.1,4.2 & 4.4 of Text Book 2 ) Text Book(s)[1] S.Narayanan,T.K.Manickavasagam Pillai, Calculus Volume I, S.V Publications -2004

[2]S. Arumugam , Issac & Somasundaram , Trigonometry and Fourier Series New Gamma Publications – 1999Edition

Additional Books for Reference

[1] S.Arumugam & others, Calculus Volume1.[2] S.Narayanan, Trigonometry .

Inst.Hour 5Credit 4Code 11K1M01

SEMESTER: I

CORE COURSE II

ANALYTICAL GEOMETRY OF 3- DIMENSIONS ANDINTEGRAL CALCULUS

UNIT 1:Coplanar lines – Shortest distance between two skew lines- Equation of the line of shortest distance(Chapter III Sections 7& 8 of Text Book 1 )

UNIT 2:Sphere – Standard equations –Length of tangent from any point–Sphere passing through a given circle – finding the centre and radius of the circle of intersection of a sphere and a plane – Tangent plane.(Chapter IV Sections 1-8 of Text Book 1)

UNIT 3: Properties of Definite Integrals– Integration by parts– reduction formula (Chapter I Sections 11, 12 &13 of Text Book 2 )

UNIT 4:Double integrals – changing the order of Integration – Triple Integrals.(Chapter V Sections 2.1, 2.2, 4 of Text Book 2)

UNIT 5:Beta & Gamma functions and the relation between them-Integration using Beta & Gamma functions. (Chapter VII Sections 2.1, 2.2, 2.3,3, 4 of Text Book 2)

Text Book(s)[1] T.K.Manickavasagam Pillai , Natarajan, A Text book of Analytical Geometry Part II (Three Dimensions) S.V Publications – 2000 -Revised Edition. [2] S.Narayanan ,T.K.Manickavasagam Pillai, Calculus Volume II S.V Publications 2003 Edition.


[1] P.Duraipandian & Laxmi Duraipandian. Analytical Geometry

[2] Shanti Narayanan, Differential & Integral Calculus

Inst.Hour 3+3Credit 6Code 11K2M02

SEMESTER : II

CORE COURSE III

ALGEBRA AND THEORY OF NUMBERSUNIT 1:Relation between roots & coefficients –Symmetric functions –Sum of the rth

powers of the Roots – Two methods. (Chapter 6 Sections 11-14 of Text Book 1)

UNIT 2:Transformations of Equations – Diminishing ,Increasing & multiplying the roots by a constant – Forming equations with the given roots-Reciprocal equations – all types– Descarte’s rule of Signs(statement only) –simple problems.(Chapter 6 Sections 15 to 20 & 24 of Text Book 1)

UNIT 3:Theory of Numbers – Prime & Composite numbers – divisors of a given number N – Euler’s function (N) and its value – The highest power of aprime P contained in N !(Chapter 5 Sections 5.1-5.10 of Text book 2)

UNIT 4: The product of r consecutive integers is divisible by r! – Congruence(Chapter 5 Sections 5.11-5.15 of Text book 2)

UNIT 5:Fermat’s Theorem, Wilson’s and Lagrange’s Theorems.(Chapter 5 Sections 5.16-5.18 Text book 2)

Text Book(s)[1] T.K. Manickavasagam Pillai ,T.Natarajan, K.S.Ganapathy, Algebra Volume I , S.V Publications - 2006 Revised Edition[2] T.K.Manickavasagam Pillai & others, Algebra Volume II S.V. Publications -2004 Revised EditionAdditional Books for Reference[1] M .Ray & Har Swarup Sharma, A text book of Higher Algebra , S.Chand & company (Pvt)Ltd[2] Frank Ayres ,Matrices - Schaum’s Outline Series.


SEMESTER: III

CORE COURSE IV

SEQUENCES AND SERIES

UNIT 1: Sequences (definition) ,Limit, Convergence – 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 . (Chapter 2 Section 4 –7.1 of Text Book)

UNIT 2:Infinite series– Definition of Convergence, Divergence & Oscillation – Necessary

condition for convergence –Convergence of ∑ pn

1and Geometric series.

Comparison test, D’Alembert’s ratio test, and Raabe’s test (Simple problems connected to these.)(Chapter 2 Sections 8 -14, 16, 18, 19 of Text Book)

UNIT 3:Cauchy’s condensation Test, Cauchy’s root test and their simple problems–Alternative series with simple problems(Chapter 2 Section 15, 17 21-24 (Omitting uniform Convergence) of Text Book )

UNIT 4:Binomial Theorem for a rational index–Exponential & Logarithmic series–Summation (Chapter 3 Sections 5, 6, 10, 11& Chapter 4 sections 1-3, 5-9 of Text Book)

UNIT 5:General summation of series including successive difference and recurring Series. (Chapter 5 of Text Book)

Text Book[1] T.K.ManickavasagamPillai, T.Natarajan, K.S.Ganapathy , Algebra Volume I , S.V Publications- 2006 Revised Edition

Additional Books for Reference[1] M.K.Singal & Asha Rani Singal, A first course in Real Analysis.[2] .S.Arumugam , Sequences & series.


SEMESTER: III

CORE COURSE V

DIFFERENTIAL EQUATIONS AND TRANSFORMS

UNIT 1:First order , higher degree Differential equations solvable for x, solvable for

y , solvable fordx

dy ,Clairaut’s form – Conditions of integrability of M dx + N dy =0 –

simple problems .(Chapter 4 section 1 to 4 & chapter 2 section 6)

UNIT 2: Particular integrals of second order Differential Equations with constant coefficients–Linear equations with variable coefficients –( Omitting third & higher order equations) (Chapter 5 Sections 3 to 5 of Text Book)

UNIT 3:Laplace Transforms –standard formulae –Basic Theorems & simple applications. (Chapter 9 Sections 1 to 5 of Text Book) UNIT 4:Inverse Laplace Transform – Use of Laplace Transform in solving ODE with constant coefficients.(Chapter 9 Sections 6 to 11 of Text Book)

UNIT 5:Formation of Partial Differential Equation – General , Particular & Complete integrals – Solution of PDE of the standard forms – Lagrange’s method of solving . (Chapter 12, Section 1-5 of Text Book)

Text Book[1] S.Narayanan &T.K.Manickavasagam Pillai, Differential Equations, S.V Publications, Revised1996, Reprint2001


[1] M.D.Raisinghania, Ordinary & Partial Differential Equations [2] M.L.Khanna Differential Equations


SEMESTER: IV

CORE COURSE VI

VECTOR ANALYSIS AND FOURIER SERIES.

UNIT 1: Vector differentiation –velocity & acceleration–Vector & scalar fields – Gradient of a vector– Directional derivative -Divergence & curl of vector solenoidal & irrotational vectors – Laplacian double operator – simple problems ((Chapter I, Chapter II -2.1- 2.2.5, 2.3-2.5 of Text book 1)

UNIT 2:Vector integration –Tangential line integral –Conservative force field –scalar potential– Work done by a force – Normal surface integral – Volume integral – simple problems.(Chapter III of Text book 1)

UNIT 3:Gauss Divergence Theorem –Simple problems &Verification of the theorem(Chapter IV- 4.1- 4.2.3 of Text book 1)

UNIT 4:Stoke’s Theorem– Green’s Theorem (Theorems without Proof) – Simple problems & Verification of the theorems (Chapter IV- 4.3- 4.5 of Text book 1)

UNIT 5:Fourier series – definition –Finding Fourier Series expansion of periodic functions with Period 2 and with period 2a – Use of odd & even functions in Fourier Series. Half range Fourier series – definition–Development in Cosine series & in Sine series (Chapter 6 Sections 1- 7 Text book 2)

Text Book(s) [1] K.Viswanatham & S.Selvaraj, Vector Analysis, Emerald Publishers Reprint 1986

[2] T.K.M Pillai & others, Calculus Volume III, S.V Publications 1985, Revised Edition. Additional Books for Reference

[1] M.L.Khanna, Vector Calculus [2] M.D.Raisinghania, Vector Calculus


SEMESTER: V

CORE COURSE VIII ABSTRACT ALGEBRA

UNIT 1: Subgroups – Cyclic groups – Order of an element – Cosets and Lagrange’s Theorem ( Chapter 3 section 3.5 to 3.8 )

UNIT 2:Normal subgroups and Quotient groups – Finite groups & Cayley tables–Isomorphism & Homomorphism.(Chapter 3 Sections 3.9 to3.11)

UNIT 3:Rings & Fields–definition & examples–Elementary properties of Rings–Isomorphism– Types of Rings–Characteristics of Rings –SubRings –Ideals-Quotient Rings – Homomorphism of Rings .(Chapter 4 Sec 4.1 to 4.8 & 4.10)

UNIT 4:Vector Spaces –definition & examples –Sub spaces –Linear Transformation-Span of a set– Linear independence - Basis & Dimension – Rank & Nullity . (Chapter 5 Sections 5.1 to 5.7)

UNIT 5:Characteristic Equation and Cayley Hamilton Theorem-Eigen Values and Eigen vectors-Properties of Eigen Values.(Chapter 7 Sections 7.7 - 7.8 )

Text Book[1] S .Arumugam & A. Thangapandi Issac, Modern Algebra, Scitech Publication - August 2003. Edition


[1] M.L.Santiago, Modern Algebra .[2] I.N.Herstein. Topics in Algebra .


SEMESTER: V

CORE COURSE XI REAL ANALYSIS

UNIT 1:Real Number system – Field axioms –Order relation in R. Absolute value of a real number & its properties –Supremum & Infimum of a set– order completeness property – countable & uncountable sets(Chapter 1 Sections 2-7&10 of Text Book 1)

UNIT 2:Continuous functions –Limit of a Function – Algebra of Limits – Continuity of a function – Types of discontinuities – Elementary properties of continuous functions –Uniform continuity of a function.(Chapter 5 of Text Book 1)

UNIT 3:Differentiability of a function– Derivability & continuity –Algebra of derivatives –Inverse Function Theorem – Daurboux’s Theorem on derivatives.(Chapter 6 Sections1-5 of Text Book 1)

UNIT 4:Rolle’s Theorem –Mean Value Theorems on derivatives– Taylor’s Theorem with remainder- Power series expansion . (Chapter 8 Sections 1-6 of Text Book 1)

UNIT 5:Riemann integration –definition – Daurboux’s theorem –conditions for integrability – Integrability of continuous & monotonic functions –Properties of Integrable functions – Integral functions –Continuity & derivability of integral functions –The First Mean Value Theorem and the Fundamental Theorem of Calculus(Chapter 6 of Text Book 2) Text Book(s)[1] M.K,Singhal & Asha Rani Singhal ,A First Course in Real Analysis , R. Chand & co June 1996 Edition.[2] Shanthi Narayan, A Course of Mathematical Analysis. Additional Books for Reference[1] Tom.M.Apostol, Mathematical Analysis ,II Edition.[2] S.C.Malik , Elements of Real Analysis.


SEMESTER: V

CORE COURSE X

STATICS UNIT1:Introduction and Basic ideas of forces – Parallel forces.(Chapters 3)

UNIT 2: Moment of a Force about a point on a line – Theorem on Moments &couples(Chapters 3 & 4 )

UNIT 3: Equilibrium of three forces acting on a body –Coplanar forces (Simple Problems only).(Chapter 5 –upto section 7, Chapter 6 - upto section 13 )

UNIT 4:Equilibrium of Strings under gravity – Common catenary –Parabolic catenary –suspension bridge .(Chapter 11)

UNIT 5:Friction – Laws of Friction –Coefficient of Friction, Angle & cone of Friction –Equilibrium of a particle on a rough inclined plane under a force parallel tothe plane and under any force – Problems on Friction. (Simple Problems only) (Chapter 7- upto Section13)

Text Book[1] M.K. Venkatraman, A Text Book of Statics , Agasthiar Publication.


[1] S.Narayanan., Statics .[2] A.V.Dharmapadham, Statics .


SEMESTER:IV

CORE COURSE VII

OPERATIONS RESEARCH

UNIT 1:

Introduction to Operations Research – Elementary treatment of linear programming, Simplex Method for < ,=,> constraints

UNIT 2:

Application to Transportation problem– Transportation Algorithm-Degeneracy in Transportation problem, Unbalanced Transportation problem

UNIT 3:

Assignment problem – The assignment algorithm – unbalanced assignment problem.

UNIT 4:

PERT and CPM network – critical and sub critical jobs – determining the critical path.

UNIT 5:

Network calculation PERT networks probability aspect of PERT – PERTtime – PERT cost (omitting crashing)

Text Book

[1] Kantiswarup, P.K.Gupta and Manmohan,.Operations Research.

Additional Books for Reference:-

[1] V.Sunderasan , K.S.Ganapathy Subramanian, K.Ganesan, Resource Management Techniques (Operations Research) [2] P.Mariappan , Operations Research Methods and Applications .


SEMESTER: V MAJOR BASED ELECTIVE 1

PROGRAMMING IN C FOR NUMERICAL METHODSUNIT 1:Constants, Variables, data types symbolic constants –Operators & expressions –evaluation of Expressions –reading & writing a character –Formatted input & output –handling of character strings– Operations on strings – string handling functions. (Chapters 2, 3, 4 & 8)

UNIT 2 :Decision making and branching – Use of IF, IF-ELSE & nesting of IF-ELSE statements – ELSE-IF ladder – Switch statement –Conditional Operator –GOTO statement Decision making & looping –WHILE , DO and FOR statements. (Chapter 5)

UNIT 3: Decision making & looping – WHILE, DO, and FOR statements(Chapter 6 omitting section 6.5)

UNIT 4:Arrays – One dimensional ,two dimensional & multi dimensional groups –Structures – definition giving values to members – Initialization - comparison –Arrays of structures – Arrays within structures – structures within structures and functions. (Chapters 7 & 10 Section 10.1-10.8)

UNIT 5: User defined functions –The form of C functions, return values & their types – Calling a function – category of functions –no arguments & no return values –arguments but no return values argument with return values –Nesting of functions – Recursion. (Chapter 9 - upto Section 9.13)Text Book Programming in ANSI C - E. Balagurusamy II Edition

Additional Books for Reference[1] Programming in C - By Rajaraman[2] Let us C – Yeshwant Kanetkar

Inst.Hour 5Credit 5Code 11K5MELM1

SEMESTER: VI

CORE COURSE XI

COMPLEX ANALYSIS

UNIT 1: Functions of a Complex variable –Limits–Theorems on Limits –Continuous functions – Differentiability – Cauchy-Riemann equations – Analytic functions –Harmonic functions.(Chapter 2 Section 2.1 to 2.8)

UNIT 2:Elementary transformations – Bilinear transformations – Cross ratio – fixed points of Bilinear Transformation–Some special bilinear transformations.( Chapter 3 Sections 3.1 to 3.5)

UNIT 3:Complex integration – definite integral – Cauchy’s Theorem –Cauchy’s integral formula – Higher derivatives.(Chapter 6 Sections 6.1 to 6.4)

UNIT 4:Series expansions– Taylor’s series –Laurant’s Series – Zeroes of analytic functions – Singularities. (Chapter 7 Sections 7.1 to 7.4)

UNIT 5: Residues – Cauchy’s Residue Theorem –Evaluation of definite integrals (Chapter 8 Sections 8.1 to 8.3)

Text Book[1] S.Arumugam,A.Thangapandi Issac, A.Somasundaram, Complex Analysis, Scitech Publications, Copy Right 2006Additional Books for Reference

[1] P.P Gupta, Complex Variables, Kedarnath & Ramnath –Meerut -Delhi

[2] Sharma, Functions of a Complex variable, Krishna Prakasan Mandir

[3] T.K.M Pillai & others, Complex Analysis, Anantha Book Depot, Madras


SEMESTER: VI

CORE COURSE XII

DYNAMICS

UNIT1:Kinematics – Velocity and acceleration – Tangential & normal components– Radial & transverse components.(Chapter 3 –3.11 to 3.32 & chapter 9 –Section 9.2, Chapter 11-Section 11.2)

UNIT 2: Central Orbit – Central force – Differential equation to a central orbit in polar & pedal coordinates – Given the central orbit to find the law of force. (Chapter 11- Section 11.3 to 11.11)

UNIT 3:Simple Harmonic motion – Simple Pendulum –Load suspended by an elastic string. (Chapter 10 section 10.1-10.7, 10.12-10.16)

UNIT 4:Projectile in Vacuum – Maximum height reached, range, time of flight –Projectile up / down an inclined plane.(Chapter 6 upto section 6.15)

UNIT 5:Impulsive force – Impulse conversion of linear momentum – Direct & Oblique Impact – of two smooth spheres –Kinetic energy and Impulse (Chapter 7 & 8 of the Text Book )

Text Book[1] A Text Book of Dynamics by M.K. Venkatraman Published by Agasthiar Publication Eleventh Edition 2004


1] S.Narayanan. , Dynamics.2] A.V.Dharmapadam, Dynamics .


SEMESTER: VI

CORE COURSE XIII

GRAPH THEORY UNIT 1: Definition of a Graph – finite & infinite graphs – incidence & degree , isolated & pendent Vertices – isomorphisms –sub graphs – walks,paths & circuits –Connected & disconnected graphs – components – Euler graphs –Operations on Graphs –More on Euler graphs – Hamiltonian paths & circuits (Chapter I section 1.1 – 1.5 & Chapter II Section 2.1 – 2.9)

UNIT 2:Trees –properties of trees –pendent vertices in a tree – distances & centers in a tree –Rooted & binary trees –Spanning trees– fundamental circuits–Finding all spanning trees of a graph – Spanning trees in weighted graph.(Chapter III (Omitting Section 3.6))

UNIT 3:Cut –set –Properties of a cut-set –All cut-sets in a graph –Fundamental circuits and cut sets – Connectivity and separability.(Chapter IV Sections 4.1 – 4.5)

UNIT 4:Planar graphs– Kuratowski’s two graphs –Representation of a planar graph-Detection of Planarity-Geometrical dual –Combinatorial dual.(Chapter V Sections 5.1 – 5.7)

UNIT 5:Matrix representation of graphs – Incident Matrix-circuit matrix–fundamental circuit matrix – Cut-set matrix - Adjacency matrix. Chromatic number–Chromatic partitioning – Chromatic Polynomial.(Chapter VII Sections 7.1 – 7.4, 7.6,7.9 & Chapter VIII Sections 8.1 –8.3)

Text Book[1] Narsingh Deo, Graph Theory with applications to Engineering & Computer Science, Prentice Hall of India, New Delhi. . Additional Books for Reference[1] F.Harary, Graph Theory ,Narosa Publishing House ,New Delhi.[2] S.A.Choudum, Graph Theory, MacMillan India Ltd- New Delhi-Madras.


SEMESTER: VI

MAJOR BASED ELECTIVE 2

STOCHASTIC PROCESSES

UNIT 1: Specification of Stochastic processes– Stationary Process– Markov Chain –Higher Transition Probabilities(Chapter 2-2.1-2.3, Chapter 3-3.1, 3.2)

UNIT 2:Classification of States and chains—Determination of Higher Transition Probabilities-Graph theoretic Approach.

(Chapter 3-3.4, 3.5, 3.7)

UNIT 3: Poisson Process and related distributions– Generalization of Poisson Process(Chapter 4- 4.1-4.3)

UNIT 4: Birth and Death Process- Markov Process with discrete space.(Chapter 4- 4.4, 4.5)

UNIT 5 :Queuing Systems– General concepts –The Queuing model M/M/1 –Steady state behaviour -Transient behaviour of M/M/1 model(Chapter 10- 10.1-10.3)

Text Book:[1] J. Medhi, Stochastic Processes, Second Edition, New Age international Publication.


[1] S. K.Srinivasan, K.M. Mehata,Stochastic Processes, Tata McGraw Hill Pub.Company, New Delhi.


SEMESTER: VI


NUMERICAL METHODS [In all units the values of a root may be calculated upto 3 decimal accuracy only]UNIT 1: Algebraic & Transcendental equations– Finding a root of the given equation (Derivation of the formula not needed) using Bisection Method, Method of False Position , Newton Raphson Method ,Iteration method .(Chapter 2 section 2.1 to 2.5)

UNIT 2: Finite differences –Forward, Backward & Central differences–symbolic relations - Newton’s forward & backward difference interpolation formulae -Interpolation with unevenly spaced intervals –Application of Lagrange’s interpolating Polynomial (without Proof)–Divided differences and their Properties – Application of Newton’s General interpolating formula. (Proof not needed).(Chapter 3 Sections 3.1, 3.3, 3.6, 3.9, 3.9.1, 3.10, 3.10.1)

UNIT 3: Numerical differentiation - Numerical Integration using Trapezoidal rule & Simpson’s first & second rules - Theory & problems(Chapter 5 sections 5.4-5.4.1, 5.4.2 &5.4.3)

UNIT 4: Solutions to Linear Systems – Gaussian Elimination Method – Jacobi & Gauss Siedal iterative methods – Theory & problems . (Chapter 6 Section 6.3-6.3.2, 6.4)

UNIT 5: Numerical solution of ODE – Solution (Derivation of the formula not needed) by Taylor Series Method , Picard’s method, Euler’s Method, Runge Kutta 2nd &4th order methods- Theory& problems using Adam’s Predictor Corrector method (Chapter 7 Sections 7.2, 7.3, 7.4-7.4.2, 7.5&7.6 (omitting 7.6.2)) Text Book[1] S.S.Sastry, Introductory Methods of Numerical Analysis, Prentice Hall of India Pvt.LimitedAdditional Books for Reference:-[1] M.K.Jain, S.R.K.Iyengar & R.K.Jain Numerical Methods for Scientific & Engineering Computation [2] H.C.Saxena, Finite Differences & Numerical Analysis .


BATCH - II




UNIT 2:Curvature – Radius of curvature in Cartesian & in Polar Coordinates – Centre of curvature –Evolutes & Involutes(Chapter X Sections 2.1 –2.6 of Text Book 1)

UNIT 3:Expansions of sin(nx) ,cos(nx) ,tan(nx) – Expansions of sin n x, cosnx –Expansions of sin(x) ,cos(x), tan(x) in powers of x and related problems.(Chapter 1: Sections 1.2 to 1.4 of Text Book 2)

UNIT 4:Hyperbolic functions – Relation between hyperbolic & Circular functions-Inverse hyperbolic functions.(Chapter 2: Sections 2.1& 2.2 of Text Book 2)

UNIT 5:Logarithm of a complex number -Summation of Trigonometric series-Difference method- Angles in arithmetic progression method –Gregory’s Series ( Chapter 3 & Chapter 4 : Sections 4.1,4.2 & 4.4 of Text Book 2 )

Text Book(s)[1] S.Narayanan,T.K.Manickavasagam Pillai, Calculus Volume I, S.V Publications -2004





SEMESTER: I & II

CORE COURSE II







Text Book(s)[1] T.K.Manickavasagam Pillai , Natarajan, A Text book of Analytical Geometry Part II (Three Dimensions) S.V Publications – 2000 -Revised Edition. [2] S.Narayanan ,T.K.Manickavasagam Pillai, Calculus Volume II S.V Publications 2003 Edition.





SEMESTER : II

CORE COURSE III







Text Book(s)[1] T.K. Manickavasagam Pillai ,T.Natarajan, K.S.Ganapathy , Algebra Volume I , S.V Publications - 2006 Revised Edition[2] T.K.Manickavasagam Pillai & others, Algebra Volume II S.V. Publications -2004 Revised EditionAdditional Books for Reference[1] M .Ray & Har Swarup Sharma, A text book of Higher Algebra , S.Chand & company (Pvt)Ltd[2] Frank Ayres ,Matrices - Schaum’s Outline Series.


SEMESTER: III

CORE COURSE IV













SEMESTER: III

CORE COURSE V



y , solvable fordx






Text Book[1] S.Narayanan &T.K.Manickavasagam Pillai, Differential Equations, S.V Publications, Revised1996, Reprint2001




SEMESTER: IV

CORE COURSE VI











SEMESTER: IV

CORE COURSE VII

OPERATIONS RESEARCH

UNIT 1:


UNIT 2:


UNIT 3:


UNIT 4:


UNIT 5:

Network calculation PERT networks probability aspect of PERT – PERT time – PERT cost (omitting crashing)

Text Book





SEMESTER: V











SEMESTER: V

CORE COURSE IX REAL ANALYSIS







SEMESTER: V

CORE COURSE X










SEMESTER: V

MAJOR BASED ELECTIVE - 1

PROBABILITY AND STATISTICS

UNIT 1: Theory of Probability – Different definitions of probability - sample space –Probability of an event - Independence of events – Theorems on Probability – Conditional Probability – Baye’s Theorem.(Chapter-4, Sections 4.5-4.9)

UNIT 2:Random variables – Distribution functions – Discrete & continuous random variables – Probability mass & density functions –Joint probability distribution functions.(Chapter-5 Sections 5.1-5.5.5)

UNIT 3 :Expectation –Variance –Covariance-Moment generating functions –Theorems on Moment generating functions –moments –various measures.(Chapter-3, Section 3.9 & Chapter 6, Section 6.1 to 6.10.3)

UNIT 4: Correlation & Regression –Properties of Correlation & regression coefficients –Numerical Problems for finding the correlation & regression coefficients. .(Chapter 10 Sections 10.1 to 10.7.4)

UNIT 5 :Theoretical Discrete & Continuous distributions – Binomial, Poisson , Normal distributions - Moment generating functions of these distributions –additive properties of these distributions- Recurrence relations for the moments about origin , and mean for the Binomial, Poisson and Normal distributions –properties of normal distributions.(Chapter 7 Section 7.2 to 7.2.7, Section 7.3, 7.3.2 to 7.3.5 and 7.3.8 , Chapter 8 Section 8.2, 8.2.2 to 8.2.5 and 8.2.7)

Text Book : Fundamentals of Mathematical Statistics by Gupta.S.C &Kapoor,V.K Published by Sultan Chand & sons ,New Delhi -2000 Edition

Additional Books for Reference:-1] Practical Statistics – Thambidurai .P – Rainbow publishers – CBE (1991)

2] Probability and Statistics – A.Singaravelu – A.R.Publications – 2002

Inst.Hour 5Credit 5Code 11K5MELM1S

SEMESTER: VI

CORE COURSE XI

COMPLEX ANALYSIS











SEMESTER: VI

CORE COURSE XII

DYNAMICS










SEMESTER: VI

CORE COURSE XIII








SEMESTER: VI





(Chapter 3-3.4, 3.5, 3.7)








SEMESTER: VI


NUMERICAL METHODS [In all units the values of a root may be calculated upto 3 decimal accuracy only]UNIT 1: Algebraic & Transcendental equations– Finding a root of the given equation (Derivation of the formula not needed) using Bisection Method, Method of False Position , Newton Raphson Method ,Iteration method .(Chapter 2 section 2.1 to 2.5)

UNIT 2: Finite differences –Forward, Backward & Central differences–symbolic relations - Newton’s forward & backward difference interpolation formulae -Interpolation with unevenly spaced intervals –Application of Lagrange’s interpolating Polynomial (without Proof)–Divided differences and their Properties – Application of Newton’s General interpolating formula. (Proof not needed).(Chapter 3 Sections 3.1, 3.3, 3.6, 3.9, 3.9.1, 3.10, 3.10.1)

UNIT 3: Numerical differentiation - Numerical Integration using Trapezoidal rule & Simpson’s first & second rules - Theory & problems(Chapter 5 sections 5.4-5.4.1, 5.4.2 &5.4.3)

UNIT 4: Solutions to Linear Systems – Gaussian Elimination Method – Jacobi & Gauss Siedal iterative methods – Theory & problems . (Chapter 6 Section 6.3-6.3.2, 6.4)

UNIT 5: Numerical solution of ODE – Solution (Derivation of the formula not needed) by Taylor Series Method , Picard’s method, Euler’s Method, Runge Kutta 2nd &4th order methods- Theory& problems using Adam’s Predictor Corrector method (Chapter 7 Sections 7.2, 7.3, 7.4-7.4.2, 7.5&7.6 (omitting 7.6.2)) Text Book[1] S.S.Sastry, Introductory Methods of Numerical Analysis, Prentice Hall of India Pvt.LimitedAdditional Books for Reference:-[1] M.K.Jain, S.R.K.Iyengar & R.K.Jain Numerical Methods for Scientific & Engineering Computation [2] H.C.Saxena, Finite Differences & Numerical Analysis .


BATCH – III




UNIT 2:Curvature – Radius of curvature in Cartesian & in Polar Coordinates – Centre of curvature –Evolutes & Involutes(Chapter X Sections 2.1 –2.6 of Text Book 1) UNIT 3:Expansions of sin(nx) ,cos(nx) ,tan(nx) – Expansions of sin n x, cosnx –Expansions of sin(x) ,cos(x), tan(x) in powers of x and related problems.(Chapter 1: Sections 1.2 to 1.4 of Text Book 2) UNIT 4:Hyperbolic functions – Relation between hyperbolic & Circular functions-Inverse hyperbolic functions.(Chapter 2: Sections 2.1& 2.2 of Text Book 2)UNIT 5:Logarithm of a complex number -Summation of Trigonometric series-Difference method- Angles in arithmetic progression method –Gregory’s Series ( Chapter 3 & Chapter 4 : Sections 4.1,4.2 & 4.4 of Text Book 2 )

Text Book(s)[1] S.Narayanan,T.K.Manickavasagam Pillai, Calculus Volume I, S.V Publications -2004





SEMESTER: I & II

CORE COURSE II







Text Book(s)[1] T.K.Manickavasagam Pillai , Natarajan, A Text book of Analytical Geometry Part II (Three Dimensions) S.V Publications – 2000 -Revised Edition. [2] S.Narayanan ,T.K.Manickavasagam Pillai, Calculus Volume II S.V Publications 2003 Edition. Additional Books for Reference




SEMESTER : II

CORE COURSE III







Text Book(s)[1] T.K. Manickavasagam Pillai ,T.Natarajan, K.S.Ganapathy , Algebra Volume I , S.V Publications - 2006 Revised Edition[2] T.K.Manickavasagam Pillai & others, Algebra Volume II S.V. Publications -2004 Revised EditionAdditional Books for Reference[1] M .Ray & Har Swarup Sharma, A text book of Higher Algebra , S.Chand & company (Pvt)Ltd[2] Frank Ayres ,Matrices - Schaum’s Outline Series.


SEMESTER: III

CORE COURSE IV













SEMESTER: III

CORE COURSE V



y , solvable fordx






Text Book[1] S.Narayanan &T.K.Manickavasagam Pillai, Differential Equations, S.V Publications, Revised1996, Reprint2001 Additional Books for Reference



SEMESTER: IV

CORE COURSE VI











SEMESTER: IV

CORE COURSE VII

OPERATIONS RESEARCH

UNIT 1:


UNIT 2:


UNIT 3:


UNIT 4:


UNIT 5:

Network calculation PERT networks probability aspect of PERT – PERT time – PERT cost (omitting crashing)

Text Book





SEMESTER: V











SEMESTER: V

CORE COURSE IX REAL ANALYSIS







SEMESTER: V

CORE COURSE X










SEMESTER: V

MAJOR BASED ELECTIVE - 1

PROBABILITY AND STATISTICS

UNIT 1: Theory of Probability – Different definitions of probability - sample space –Probability of an event - Independence of events – Theorems on Probability – Conditional Probability – Baye’s Theorem.(Chapter-4, Sections 4.5-4.9)

UNIT 2:Random variables – Distribution functions – Discrete & continuous random variables – Probability mass & density functions –Joint probability distribution functions.(Chapter-5 Sections 5.1-5.5.5)

UNIT 3 :Expectation –Variance –Covariance-Moment generating functions –Theorems on Moment generating functions –moments –various measures.(Chapter-3, Section 3.9 & Chapter 6, Section 6.1 to 6.10.3)

UNIT 4: Correlation & Regression –Properties of Correlation & regression coefficients –Numerical Problems for finding the correlation & regression coefficients. .(Chapter 10 Sections 10.1 to 10.7.4)

UNIT 5 :Theoretical Discrete & Continuous distributions – Binomial, Poisson , Normal distributions - Moment generating functions of these distributions –additive properties of these distributions- Recurrence relations for the moments about origin , and mean for the Binomial, Poisson and Normal distributions –properties of normal distributions.(Chapter 7 Section 7.2 to 7.2.7, Section 7.3, 7.3.2 to 7.3.5 and 7.3.8 , Chapter 8 Section 8.2, 8.2.2 to 8.2.5 and 8.2.7)

Text Book : Fundamentals of Mathematical Statistics by Gupta.S.C &Kapoor,V.K Published by Sultan Chand & sons ,New Delhi -2000 Edition

Additional Books for Reference:-1] Practical Statistics – Thambidurai .P – Rainbow publishers – CBE (1991)

2] Probability and Statistics – A.Singaravelu – A.R.Publications – 2002


SEMESTER: VI

CORE COURSE XI

COMPLEX ANALYSIS











SEMESTER: VI

CORE COURSE XII

DYNAMICS










SEMESTER: VI

CORE COURSE XIII








SEMESTER: VI





(Chapter 3-3.4, 3.5, 3.7)








SEMESTER: VI MAJOR BASED ELECTIVE 3

DISCRETE MATHEMATICSUNIT 1:

Recurrence relation - Permutation functions - Growth of functions(Chapter 3 - 3.5, Chapter 5 - 5.3, 5.4)

UNIT 2:Partially ordered sets - External elements of partially ordered sets –Lattices(Chapter 7 - 7.1 to 7.3)

UNIT 3:Finite Boolean algebra – Functions of Boolean algebra- Expressing Boolean functions as Boolean polynomials(Chapter 7 - 7.4 to 7.6)

UNIT 4:Coding of Binary information and Error Detection(Chapter 11 – 11.1)

UNIT 5:Decoding and Error Correction(Chapter 11- 11.2)

Text Book:[1] Kolman Busby Ross, Discrete Mathematical Structure (3rd Edition – Twelth printing) Prentice-Hall of India, New Delhi, 2001.Additional Books for Reference[1] J.P.Tremblay and R.Manohar., Discrete Mathematical structures with Applications to Computer Science [2] John E.Hopcroft, Jeffery D.Ullman, Introduction to Automata Theory, Languages and Computation


ALLIED COURSES

OFFERED BY

MATHEMATICS DEPARTMENT

1. Allied Mathematics for B.Sc., Physics and Chemistry Major.

2. Allied Mathematics for B.Sc., Computer Science Major.

3. Allied Mathematics for B.Sc., Mathematics Major.

SEMESTER I

Allied Course I: Mathematics

CALCULUS AND VECTOR CALCULUSFor B.Sc. Physics & Chemistry Major

UNIT 1: Higher derivatives – nth derivative of standard functions – Leibnitz’s Theorem (proof not needed) for the nth derivative of a product of functions – applicable to suitable problems(Chapter 1-Sec-1.1-1.6, 2.1, 2.2 of Text Book 1)

UNIT 2: Curvature and radius of curvature in Cartesian only.(Chapter 10 Sec2.1-2.3 of Text Book 1)

UNIT 3: General properties of definite integrals -Reduction formula for (when n is a positive integer)

1] dxxe nax 2] xdxnsin 3] xdxncos

4] x

nax dxxe0

5] 2

0

sin

xdxn 6] 2

0

cos

xdxn

7] Without proof 2

0

cossin

xdxx mn - and illustrations (problems only)

Evaluation of double & triple integrals (omitting -changing the order of integration(Chapter 1 Sec11, Sec13-13.1, 13.3, 13.4, 13.5 of Text Book 2) and (Chapter 5 Sec 2.2 & 4)

Inst.Hour 5Credit 4

Code 11K1CH/PAM1

UNIT 4: Vector differentiation–Gradient of a vector- Directional derivative – divergence & curl of a vector, solenoidal & irrotational vectors.(Chapter2 Sections2.1, 2.2, 2.2.1-2.2.4, 2.3, 2.3.1, 2.3.2, 2.4, 2.4.1-2.4.3, 2.5, 2.5.1 of text Book 3)

UNIT 5: Vector integration –Line Integral- surface integral - Volume integral – simple problems. Gauss Divergence Theorem – Stoke’s Theorem – problems only (Verification of the theorems).(Chapter3 Sec: 3.2-3.7 Chapter 4 Sec: 4.2, 4.2.3, 4.4, 4.4.3 of Text book 3)Text Books : [1] S.Narayanan, T.K.Manickavasagam Pillai, Calculus Volume I, S.V Publishers 2004 [2] S.Narayanan, T.K.Manickavasagam Pillai, Calculus Volume II, S.VPublishers 2003 [3] K.Viswanatham ,S.Selvaraj ,Vector Analysis , Emerald Publishers 1984

Reference Books:

[1] A.Singaravelu,Calculus .

[2] M.L.Khanna, Vector Calculus.

SEMESTER I and II

Allied Course II - Mathematics ALGEBRA, ANALYTICAL GEOMETRY (3D) & TRIGONOMETRY

For B.Sc. Physics & Chemistry Major UNIT 1: Binomial, Exponential and Logarithmic series (Formulae Only) – summation &approximation related problems only.(Chapter2 Sec: 1, 2, 3, Chapter3 Sec1-5of Text Book 1)

UNIT 2: Various types of matrices – Characteristic equation, eigen values, eigen vectors (Chapter2 Sec: 16, 16.3, 16.4 of Text Book 2)

UNIT 3: Finding the Shortest distance between two skew lines and the equation of the plane containing them– Tangent plane – Plane section of a sphere - Finding the center & radius of the plane section of the sphere (Chapter3 Sec: 7, Chapter4 Sec 4-6Text Book 4)

UNIT 4 : Expansion of sin n ,cos n ( n being a positive integer ) - Expansion of nsin , cos n in a series of sines & cosines of multiples of ( - given in radians ) &

simple problems.(Chapter 3 Sec: 1, 4, 4.1,5 of Text Book 3)

UNIT 5 : Euler’s formula for e i - Definition of Hyperbolic functions –Formulae involving Hyperbolic functions -Relation between Hyperbolic & circular functions –Expansion of sinh x , cosh x , tanh x in powers of x- Expansion of Inverse hyperbolic functions sinh x1 ,cosh x1 and tanh x1 . (Chapter 4 Sec: 1, 2, 2.1-2.3 of Text Book 3)

Text Books : [1] S .Narayanan, T.K.Manicavachagom Pillai and others, Ancillary Mathematics BookI[2] T.K.Manicavachagom Pillai & others,Algebra Volume II [3] S.Narayanan &T.K. Manicavachagom Pillai, Trigonometry[4] Narayanan and Hanumantharao, Ancillary Mathematics Book4

Reference Books: [1] A.Singaravelu,Allied Mathematics Paper II, 1998[2] P.Duraipandian, Laxmi Duraipandian & Muhilan, Analytical Geometry of 3D – Emerald Publications

Inst.Hour 3+2Credit 3Code 11K2CH/PAM2

SEMESTER II Allied Course III- Mathematics

DIFFERENTIAL EQUATIONS AND TRANSFORMSFor B. Sc. Physics & Chemistry Major

UNIT 1 : Ordinary Differential Equation of first order but of higher degree –Equations

solvable for x , solvable for dx

dy, Clairaut’s form (simple cases only) – Linear equations

with constant coefficients.(Chapter4 Sec: 1, 2, 2.1, 2.2, 3.1, of Text Book1Chapter 3 Sec 1-4, 4.1, 4.2of Text Book2)

UNIT 2 : Formation of Partial differential equations by eliminating constants and by elimination of arbitrary functions – definition of general , particular & complete solutions – Singular integral ( geometrical meaning not required ) – Solutions of first order equations in the standard forms f(p,q) =0 , f (x,p,q)=0 , f (y,p,q)=0 , f(z,p,q)=0, f1(x,p) = f2 (y,q) , z = xp+yq+f(p,q).(Chapter 6 Sec: 1, 2, 2.1.2, 3, 4, 5, 5.1-5.4 of Text Book 2) UNIT 3 : Laplace Transform –Definition –L(e at ) ,L( cos(at) ) , L (sin (at) ) L( tn ) , where n is a positive integer .Basic theorems in Laplace Transforms (formula only)-L [e st cosbt] ,L [e st sinbt ], L [e st f(t) ] – L [ f(t)],L[f(t)], L [f (t) ] and related Problems(Chapter 4 Sec1, 2, 3 Text Book2)

UNIT 4: Inverse Laplace Transforms relating to the above standard forms – Solving ODE with constant coefficients using Laplace Transforms. (Chapter 4 Sec4, 5, 6 Text Book2)UNIT 5: Fourier series- definition-Finding Fourier series expansion of periodic functions with Period 2 – Use of odd & even functions in Fourier series – Half Range Fourier series.Chapter 4 Sec1, 2, 3, 3.1, 3.2, 4, 5.1, 5.2 Text Book2)Text Books : [1] S.Narayanan, T.K.Manickavasagom Pillai,Differential Equations, Viswanatham Publishers 2001[2] S.Narayanan, T.K.Manickavasagom Pillai, Ancillary Mathematics Book2, Calculus volume II Reference Books: [1] S.Arumugam , Issac ,Trigonometry & Fourier Series

[2] B.R.Subramanian, Laplace Transform

Inst.Hour 5Credit 3Code 11K2CH/PAM3

SEMESTER I

Allied Course I: Mathematics

NUMERICAL METHODS AND GRAPH THEORYFor B. Sc Computer Science Major

UNIT1: Algebraic Equations - Method of false position – Bisection method – Iteration method – Solving by Newton Raphson method -Numerical integration by Trapezoidal and Simpson’s rule.(In all problems Approximation upto 2 decimals only)(Chapter2:Sec2.1-2.4, Chapter5:5.4.1-5.4.3of Text Book 1)

UNIT 2: Euler’s method of solving an ordinary differential equation numerically; Runge-Kutta’s second order method of solving ordinary differential equations.(In all problems Approximation upto 2 decimals only)(Chapter7: Sec 7.4, 7.4.1, 7.4.2, 7.5 of Text Book 1)

UNIT 3: Graphs: Definition and examples – Graph models – Precedence Graphs and concurrent processing - Graph terminology – The hand shaking theorem – Underlying undirected graph - bipartite graphs – Union of two graphs (Chapter6:Sec6.1- 6.62 of Text Book2)

UNIT 4: Representation of graphs – (By using adjacency list) - undirected simple graphs (By using Adjacency matrices) – Any undirected graph (By using adjacency matrix) -directed graphs (By adjacency matrix) – undirected graph (by using incidence matrix) –graph isomorphisms.(Chapter6: Sec 6.63-6.85 of Text Book2)

UNIT 5: Connectivity – Path circuits and isomorphisms – Euler & Hamiltonian path –Algorithm for constructing Euler circuits – Hamiltonian paths and circuits.(Chapter6: Sec 6.86 -6.90, 6.115-6.137 of Text Book2)

Text Books:[1] S.S. Sastry, An introductory Methods of Numerical Analysis, Prentice Hall of India II edition[2] G. Ramesh ,C.Ganesamoorthy, Discrete Mathematics ,2003

Reference Books: [1] S.Arumugam, Graph Theory.

[2] Narsingh Deo,Graph Theory with Applications to Engineering and Computer Science

Inst.Hour 5Credit 4Code 11K1CSAM1

SEMESTER I & II Allied Course II - Mathematics

INTEGRAL CALCULUS, DIFFERENTIAL EQUATIONS ANDTRANSFORMS

For B. Sc. Computer Science Major

UNIT 1: Integration by parts -Properties of Definite Integrals – Multiple integrals.(Simple problems only)(Chapter 1 section 12,Chapter 4:Sec 6,Chap5: 2.1,2.2,3,3.1,3.2,4 of Text Book1)

UNIT 2: Fourier series for functions of period 2π– odd and even functions – Half range sine and cosine series and problems to the relevant concepts only.(Chapter6:sec 1,2,3,3.1,3.2,4,5.1,5.2,6,6.1,6.2,7 of Text Book2)

UNIT 3: First order first degree ordinary differential equations – Linear equations –Bernoulli’s equations.(Chapter 1: Sec 1.1-2.5 of Text Book2)

UNIT 4: Equations of first order but of higher degree – simultaneous linear differential equations – second order differential equations with constant coefficients. (Chapter 1: Sec 5, 5.1-7.3, Chapter 2: Sec 1-4 of Text Book2)

UNIT 5: Laplace Transforms – Conditions for the existence of the Laplace Transforms –General theorems – Inverse transforms – Solving the second order ordinary differential equations with constant coefficients using the Laplace transforms (simple problems only).(Chapter5: Sec 1, 1.1, 1.2, 2-12 of Text Book2)

Text Books:[1] S.Narayanan , T.K.M.Pillai, Calculus Volume II , S.Viswanathan Publication 2003[2] S.Narayanan , T.K.M.Pillai, Calculus Volume III, S.Viswanathan Publication 2002

Reference Books:[1] A.Singaravelu, Calculus [2] M.D.Raisinghania, Ordinary & Partial Differential Equations [3] M.L.Khanna, Differential Equations

Inst.Hour 3+2Credit 3Code 11K2CSAM2

SEMESTER II

Allied Course III- Mathematics

PROBABILITY AND STATISTICSFor B.Sc. Computer Science Major

UNIT 1: Theory of Probability –Different definitions of probability sample space –Probability of an event - Independence of events (Chapter 4: sec4.3, 4.3.1, 4.3.2, 4.5.1, 4.5.2, 4.7.3)

UNIT 2: Random variables – Distribution functions – Discrete & continuous random variables – Probability mass & density functions (Chapter 5: Sec 5.1-5.4)

UNIT 3: Expectation –Variance –Covariance (Chapter 6: Sec 6.1-6.7)

UNIT 4: Correlation & Regression –Properties of Correlation & regression coefficients –Numerical Problems for finding the correlation & regression coefficients.(Chapter 10:Sec10.1-10.4, 10.7.2-10.7.5)

UNIT 5 : Theoretical Discrete & Continuous distributions – Binomial, Poisson , Normal distributions- Moment generating functions of these distributions –additive properties of these distributions - and mean for the Binomial, Poisson and Normal distributions (simple problems) ( Chapter 7: Sec7.1,7.2,7.2.1,7.2.4,7.2.6,7.2.7,7.3.0,7.3.2,7.3.4,7.3.5,7.3.8 & Chaptert 8-Topics Relevant to normal Distribution)

Text Book :[1] Gupta.S.C &Kapoor,V.K, Fundamentals of Mathematical Statistics, Sultan Chand & Sons, NewDelhi -1994 Edition

Reference Book[1] Thambidurai .P., Practical Statistics , Rainbow publishers – CBE (1991)

Inst.Hour 5Credit 3Code 11K2CSAM3

SEMESTER: I Allied Course I

NUMERICAL METHODS –IFor B.Sc. Mathematics Major

UNIT 1: Finite Differences –Operators and their relations- Forward Differences –Backward Differences– Interpolation- Newton’s Backward and Forward Formula for Interpolation.

(Chapter 5- 5.1, 5.2 chapter6 -6.1,6.2,6.3 of Text Book)

UNIT 2: Interpolation with unequal intervals–Divided differences and their properties –Newton’s divided difference formula.

(Chapter 8 -8.1-8.3, 8.5 of Text Book)

UNIT 3: Factorial Polynomial- Inverse Operator- Summation of Series (Chapter 5 -5.4, 5.6, 5.7, 5.8of Text Book)

UNIT 4: Numerical Differentiation – Maximum and Minimum of the function, given the Tabular values.

(Chapter 9- 9.1-9.4, 9.6 of Text Book)

UNIT 5: Numerical Integration – Trapezoidal Rule –Simpson’s 1/3 Rule – Simpson’s 3/8 Rule.

(Chapter 9- 9.7-9.11,9.13-9.15 of Text Book)

***(In all the Units SIMPLE PROBLEMS ONLY)Text Books:1.Kandasamy.P, Thilagavathy. K., Gunavathi.K., Numerical Methods ,S.Chand& Company Ltd 2005.

Reference Books:

[1] S.S.Sastry, Introductory Methods of Numerical Analysis, Prentice Hall of India, Private Limited, New Delhi – 11, Fourth Edition.

[2] H.C.Saxena, Finite Differences and Numerical Analysis, S.Chand & Company Limited, New Delhi-110055, Ninth Edition.

Inst.Hour 5Credit 4Code 11K1MAM1

SEMESTER: I & II ALLIED COURSE - II

NUMERICAL METHODS II- PRACTICALS **For B.Sc. Mathematics Major

1. Bisection Method.2. False position method.3. Fixed point iteration.4. Newton – Raphson method.5. Lagrange Interpolation.6. Newton’s Forward Method.7. Newton’s Backward Method.8. Gauss Elimination Method.9. Gauss Jordan method.10. Gauss Seidal method for solving Simultaneous Linear equation.11. Jacobi’s method for solving Simultaneous Linear equation.12.Trapezoidal rule.13. Simpson’s 1/3 rule.14. Euler’s Method.15. Modified Euler’s Method.16. Runge-Kutta Method of order second and four.17. Adams-Moulton Method for Predictor – Corrector Method.18. Standard deviation.19. Correlation coefficient.20. Method of least squares (straight line).21. Jacobi’s method for Laplace’s equation.22. Gauss-Seidel Method for Laplace’s equation. **The Algorithm may be given to the problems. The Problems are framed in such a manner that “C” Programming may be developed for solving the problems. For Practicing “C” Language the problems may be helpful.

Inst.Hour 3+2Credit 3Code 11K2MAM2P

SEMESTER: II Allied Course III

NUMERICAL METHODS - III(For B.Sc. Mathematics Major)

UNIT I: Solutions of Algebraic and Transcendental Equations – Bisection Method –The Method of False Position - The Iteration Method– Newton-Raphson Method .

(Chapter 3-3.1-3.4 of Text Book)

UNIT II: Solution of Linear Systems – Gauss Elimination Method – Gauss-Seidal Method and Jacobi Method.

(Chapter 4- 4.1, 4.2, 4.7-4.9 of Text Book)

UNIT III: Difference Equations: Definition, Method of solutions, first order linear difference equation with constant and variables coefficients, second order linear difference equation with constant coefficients – particular Integrals of the type (i)ax (ii) xm (iii) xmax (Simple Problems)

(Chapter 10-10.1-10.4 of Text Book)

UNIT IV: Numerical Solution of Ordinary Differential Equations – Solution by Taylor’s Series – Picard’s Method of Successive Approximations – Euler’s Method and Modified Euler’s Method – Runge-Kutta Method of Second and Four.

(Chapter 11-11.5, 11.8, 11.9, 11.11, 11.13 of Text Book)

UNIT V: Numerical Solution of Partial Differential Equations –Laplace’s Equations –Jacobi’s Method – Gauss-Seidal Method – Parabolic Equations.

(Chapter 12 -12.5, 12.6, 12.8, 12.9 of Text Book)

(In all the Units SIMPLE PROBLEMS ONLY)Text Books:1. Kandasamy.P, Thilagavathy,K, Gunavathi.K., Numerical Methods ,S.Chand& Company Ltd 2005Reference Books [1] S.S.Sastry, Introductory Methods of Numerical Analysis,Prentice Hall of India Private Limited, Fourth Edition.[2] M.K.Venkataraman, Numerical Analysis, The National Publishing Company, Madras, Fifth Edition.

Inst.Hour 5Credit 3Code 11K2MAM3

NON –MAJOR ELECTIVE COURSES

OFFERED BY

DEPARTMENT OF MATHEMATICS

1. OPERATIONS RESEARCH-I

2. OPERATIONS RESEARCH-II

SEMESTER: II

NON MAJOR ELECTIVE 1

OPERATIONS RESEARCH-IUNIT 1: Introduction to OR Section: 1.1-1.8

UNIT 2: Formulation of LPP

Section: 2.1-2.3

UNIT 3: Graphical solution

Section: 2.5

UNIT 4: Transportations model North-West Corner Rule-Least cost method.

Section: 7.1

UNIT 5:Assignment problem. Section: 8.1-8.5

(In all the units applications of concept only. No Book work)

Text Book:[1] V.Sundaresan, Resource Management Techniques, A.R.Publications, Fourth Edition,2007..

Reference Books:

[1] Operations Research by Kanti Swarup,Gupta.P.K.& Manmohan. (8th edition, 1997)[2] Problems in Operational Research by Gupta.P.K. & Manmohan[3] Operational Research by Hamdy A.Taha(Third Edition)

Inst.Hour 2Credit 2Code 11K2MEL01

SEMESTER: V

NON MAJOR ELECTIVE 2

OPERATIONS RESEARCH-IIUNIT 1:

Construction of Network Section 15.1, 15.2, 15.3

UNIT 2:

Network Computations and Critical Path – Floats. Section 15.4&15.5

UNIT 3:

Pert Method Section 15.6

UNIT 4:

Inventory Models Sections 12.1 – 12.6

UNIT 5:Deterministic Inventory models.Section 12.7 (Model I only)

Text Book:

[1] V.Sundaresan, Resource Management Techniques, A.R.Publications, Fourth Edition,2007..

Reference Books:

[1] Operations Research by Kanti Swarup,Gupta.P.K.& Manmohan. (8th edition, 1997)[2] Problems in Operational Research by Gupta.P.K. & Manmohan[3] Operational Research by Hamdy A.Taha(Third Edition)

Inst.Hour 2Credit 2Code 11K5MEL02

for students admitted from 2011 -2012 onwards iii core course iv sequences and series unit 1:...

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