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Course objective: To introduce the basic laws, principles and postulates governing static and dynamic systems.Unit  I (15 Hours) Definition – parallelogram of forces – resultant of two forces – triangle law of forces – perpendicular triangle of forces – lamis theorem – extended form of the parallelogram of forces – resolution of forces – components of a force along two given direction – theorem on resolved parts – resultant of any number of forces – condition of equilibrium of any number of forces acting at a point. Unit  II (15 Hours) Introduction – experimental results – statistical , dynamical and limiting friction – laws of friction – coefficient of friction – angle of friction – cone of friction – equilibrium of a particle on a inclined plane, under the force parallel to plane, under any force – problem on friction. Equation of common centenary – definitions – tension at any point – important formulae – geometrical properties. Unit  III (15 Hours) Definitiontwo fundamental principlespath of a projectile is a parabola – characteristic of the motion of a projectile – maximum horizontal range – the number of possible projections to reach the given range and a given point – velocity at the end of time ‘t’ – range on the inclined plane – motion on the surface of smooth inclined plane. Unit  IV (15 Hours) Definition – fundamental laws of impact – Newton’s experimental law – principle of conservation of momentum – impact of sphere on a fixed place – direct and oblique impact of two spheres – loss of kinetic energy. Unit  V (15 Hours) Simple harmonic motion in a straight line – general solution simple harmonic motion equation – geometrical representation –composition of two simple harmonic motion  loss or gain in the number of oscillation. Velocity and acceleration in polar coordinates – differential equation of central orbits – length of perpendicular from the pole with tangent  pedal equation of central orbit – two fold problems – apses and apsidal distance – given law of force to fund the orbit. Text Books: 1) Statics  Dr. M.K. Venkataraman , Agasthiar publications, Teppakulum Trichy, 1990 2) Dynamics Dr. M.K. Venkataraman , Agasthiar publications, Teppakulum Trichy, 1990
Reference books: 1) Dynamics  M.L. Khanna, Pragati Pragasam Ltd. Meerut, 1998 2) Statics  M.L. Khanna, Pragati Pragasam Ltd. Meerut, 1998 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM52 Semester : V No. of hours allotted : 5 Paper : Core 10 No. of credits : 4 Title of the Paper : Operations Research  I Course objective:
Unit – I (15 Hours) Operations Research – An Overview Introduction Origin and Development of O.R Applications of Operations Research Linear Programming Problem Mathematical Formulation of the Problem  Graphical Solution and Extension: Introduction – Graphical Solution Method – Some Exceptional CasesGeneral Linear Programming Problem – Canonical and Standard Forms of LPP Unit – II (15 Hours) Linear Programming Problem Simplex Method : Introduction – Fundamental Properties of Solutions The Computational Procedure Use of Artificial Variables Solution of Simultaneous Linear Equations Inverting a Matrix Using Simplex Method. Unit – III (15 Hours) Duality in Linear Programming : Introduction – General Primal – Dual Pair – Formulating a dual Problem – Primal – Dual Pair in Matrix Form – Duality and Simplex Method. Unit – IV (15 Hours) Transportation Problem : Introduction General Transportation Problem  The Transportation Table Loops in Transportation TableSolution of a Transportation Problem Finding an Initial Basic feasible Solution Test for Optimality – Degeneracy in Transportation Problem  Transportation Algorithm ( MODI Method ) Unit – V (15 Hours) Assignment Problem : IntroductionMathematical Formulation of the Problem – The Assignment method – Special Cases in Assignment ProblemThe Travelling Salesman Problem. Text Book: Operations Research – Kanti Swarup, P. K. Gupta, Man Mohan Sultan Chand & Sons, 2009
Reference Books: 1) Operations Research – S.D. Sharma, Kedar Nath Ramnath & Co. 13^{th} edition, 2002 2) Operations Research – V.K. Kapoor Sultan Chand and Sons, 3^{rd} thoroughly revised edition, New Delhi – 110 002, 1998 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM53 Semester : V No. of hours allotted : 5 Paper : Core 11 No. of credits : 4 Title of the Paper : C  Programming Course objective: To develop logical and programming skills using C. Unit – I (15 Hours) Constants, Variables, Operators and Expressions : Character SetKeywords and identifiers –ConstantsVariablesData typesDeclaration of variablesAssigning values to variablesDefining symbolic constantsArithmetic OperatorsRelational OperatorsLogical OperatorsAssignment OperatorsIncrement and Decrement OperatorsConditional OperatorBit wise OperatorsSpecial OperatorsArithmetic ExpressionsType ConversionOperator PrecedenceMathematical Functions Unit  II (15 Hours) Input ,Output Operators, Arrays and Strings : Reading and Writing CharactersFormatted input and outputOne Dimensional ArraysTwo Dimensional ArraysInitializationMultidimensional Arrays  Arithmetic operations on characters – String handling functions – Table of strings. Unit  III (15 Hours) Decision MakingBranching and Looping : Simple If Statement –The IF ELSE StatementNesting of IFELSE StatementsThe ELSEIF LadderThe switch StatementThe ?: operatorThe GOTO StatementThe WHILE StatementThe DO Statement –The FOR StatementJumps in loops Unit  IV (15 Hours) UserDefined Functions: The form of C functions  Categories of functions –Nesting of FunctionsRecursion Functions with arraysThe scope and lifetime of variables in functions Unit  V (15 Hours) Structures, Unions, Pointers and File management : Structure definitionGiving values to membersStructure initializationComparison of Structure variablesArrays of StructuresArrays within StructuresStructures within StructuresUnions – Understanding pointers – Accessing the address of the variable – Declaring pointer variable – Initialization of pointer variables – Accessing a variable through its pointer – Pointers and arrays – Pointers and character strings – Defining and opening a file – closing a file – Input/Output operations on files. Text Book : Programming in ANSI C  E. Balagursamy Tata McGrawHill Publishing Company Limited, Third Edition, 2004
Reference Book: Let us C  Yashwant Kanetkar, PB Publications, Sixth Edition, 2005 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM61 Semester : VI No. of hours allotted : 6 Paper : Core 12 No. of credits : 4 Title of the Paper : Complex Analysis Course objective: To introduce the concepts of an analytic function, bilinear transformations, contour integration and Taylor and Laurent’s series expansions Unit  I (15 Hours) Analytic functions : Limit and continuity – analyticity –CR Equations –Analytic functions – Harmonic functions – Conformal mapping. Unit  II (15 Hours) Bilinear transformations : Elementary transformations – Bilinear transformations cross ratio fixed point of Bilinear transformations mapping by elementary functions W=Z^{2},W = e^{Z}, W = sin Z, W=1/z, W = (z + 1/z) only. Unit  III (15 Hours) Contour integration : Contour integrationthe Cauchy – Goursat theorem (statement only)Cauchy integral formulaHigher derivativesMorera’s theoremLiouville’s theoremfundamental theorem of algebraMaximum modulus theorem. Unit – IV (15 Hours) Series expansions : Taylor series, Laurent’s series, Zeros of an analytic functionssingularities Unit  V (15 Hours) Calculus of residues : Residues, Cauchy’s residue theorem  Evaluation of definite integrals Text Book : Complex Analysis  S. Arumugam and others SciTech publications Chennai, 2002
Reference book: Complex analysis  T.K. Manickavasagam Pillay and others, S. V. Publishers, Chennai, 2008 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM62 Semester : VI No. of hours allotted : 5 Paper : Core 13 No. of credits : 4 Title of the Paper : Operations Research  II Course objective: To understand Sequencing Problem, Queuing theory, Inventory control, Network and its Applications Unit I (15 Hours) Sequencing Problem: Introduction  Problem of Sequencing  Basic Terms Used in Sequencing  Processing n Jobs through Two Machines  Processing n Jobs through k  Machines  Processing 2 Jobs through k Machines Unit – II (15 Hours) Games and Strategies : Introduction –Two  Person Zero – Sum Games – Some Basic Terms  The Maximin  Minimax Principle  Games without Saddle PointsMixed Strategies  Graphic Solution of 2xn and mx2 Games  Dominance Property Unit –III (15 Hours) Inventory Control : Introduction – Types of Inventories  Reasons for carrying Inventories  The inventory Decisions  Objectives of Scientific Inventory Control  Costs Associated with Inventories  Factors Affecting Inventory Control  An Inventory Control Problem  The Concept of EOQ  Deterministic Inventory Problems with No Shortages Deterministic Inventory Problems with Shortages – Problem of EOQ with Price Breaks. Unit – IV (15 Hours) Queueing Theory : Introduction – Queueing System – Elements of a Queueing System Operating Characteristics of a Queueing System – Probability Distributions in Queueing System – Classification of Queueing Models – Definition of Transient and Steady States – Poisson Queueing Systems ( Model I to V ) Unit –V (15 Hours) Network Scheduling by PERT/CPM : Introduction – Network: Basic Components – Rules of Network Construction – Critical Path Analysis – Probability Consideration in PERT – Distinction between PERT and CPM. Text Book: Operations Research – Kannti Swarup, P. K. Gupta and Man Mohan Sultan Chand & Sons, 2009
Reference Book: Operations Research – S.D. Sharma, Kedar Nath Ramnath & Co. 13^{th} edition 2002 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM63 Semester : VI No. of hours allotted : 4 Paper : Core 14 No. of credits : 4 Title of the Paper : Graph Theory Course objective: To understand the basic concepts of Graph Theory and applications of Trees, Euler Line, Hamiltonian Cycle, Coloring, Chromatic numbers and Networks. Unit  I (12 Hours) Introduction: What is a graph? Application of graphs – Finite and Infinite graphs – Incidence and degree – Isolated Vertex, Pendant Vertex and Null graph. Paths and Circuits: Isomorphism – Subgraphs – Walks, Paths and Circuits – Connected graphs, disconnected graphs and components. Unit  II (12 Hours) Euler graphs – Operations on graphs – More on Euler graphs. Hamiltonian Paths and Circuits – The Travelling Salesman Problem. Unit  III (12 Hours) Trees and Fundamental Circuits: Trees – Some properties of trees – Pendant Vertices in a tree – distance and centers in a tree – Rooted and Binary tree – Spanning trees – Spanning trees in a Weighted graph. Unit  IV (12 Hours) CutSets and CutVertices : CutSets – Some properties of a cut set – All cut sets in a graph – Fundamental circuits and CutSets  Connectivity and Seperability – Network flows Unit  V (12 Hours) Planar and Dual graphs: Planar gaphs – Kuratowski’s two graphs. Matrix Representation of graphs: Incidence Matrix. Coloring, Covering and partitioning: Chromatic Number, Chromatic Partitioning and Chromatic Polynomial. Text Book: Graph Theory with Applications to Engineering and Computer Science – Narsingh Deo, PrenticeHall of India, 2005
Reference book: Graph Theory Harary F, Addison – Wesley Publishing Company, 1969 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM64 Semester : VI No. of hours allotted : 5 Paper : Core 15 No. of credits : 4 Title of the Paper : Numerical Methods Course objective: To develop the skills in solving algebraic, transcendental, differential and integral equations numerically. Unit I (12 Hours) The solution of Numerical algebraic and transcendental equations : The bisection method – iteration method –Newton – Raphson MethodRegula falsi method – Horner’s method. Unit – II (12 Hours) Simultaneous linear algebraic equations: Gauss elimination method –Gauss Jordan methodMethod of triangularisation Gauss Seidal method of iteration Unit – III (12 Hours) Interpolation : Gregory Newton forward interpolation, backward interpolation –Newton’s divided difference interpolation –Lagrange’s interpolationInverse interpolation Unit – IV (12 Hours) Numerical differentiation and integration: Newton’s forward, backward formula for derivativesTrapezoidal rule Simpson’s 1/3 rule UnitV (12 Hours) Numerical solution of ordinary differential equation: Taylor series methodEuler’s method Runge kutta method of fourth order only, Milne’s predictor and corrector method Text Book: Numerical methods in Science and Engineering  Dr. M.K. Venkataraman, The National publishing company, 2000.
Reference Book: Numerical methods  Dr. S. Arumugam, Sci Tech publication (pvt)Ltd, 2003. THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : ENM31 Semester : III No. of hours allotted : 2 Paper : NME No. of credits : 2 Title of the Paper : Mathematical Aptitude for Competitive Examinations 