# Thiagarajar college (autonomous), madurai – 9

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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)

Definition-two fundamental principles-path 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 co-ordinates – 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

 Unit Book Chapter/section I 1 2(full-articles 2.1 to 2.16) II 1 7(articles 7.1 to7.13 up to pages 256 only) 11(articles 11.1 to 11.6 up to pages 391 only) III 2 6(6.1 to 6.16) IV 2 8(8.1 to 8.9) V 2 10(10.1 to 10.7, 10.12 to 10.16) 11(11.1 to 11.3 only)

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:

• To know the origin and development of Operations Research.

• To develop the skills of formulation of LPP and different techniques to solve it.

• To know the application of Transportation and Assignment problems.

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 Cases-General 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 Table-Solution 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 : Introduction-Mathematical Formulation of the Problem – The Assignment method – Special Cases in Assignment Problem-The Travelling Salesman Problem.

Text Book: Operations Research – Kanti Swarup, P. K. Gupta, Man Mohan

Sultan Chand & Sons, 2009

 Unit Chapter/section I 1 :: 1.1, 1.2, 1.7 2:: 2.1,2.2 3:: 3.1 – 3.5 II 4 :: 4.1 – 4.6 III 5 :: 5. 1 – 5.4, 5.7 IV 10 :: 10.1 – 10.3, 10.5, 10.8 – 10.10, 10.11,10. 12 V 11 :: 11.1 – 11.4, 11.6

Reference Books: 1) Operations Research – S.D. Sharma,

Kedar Nath Ramnath & Co. 13th edition, 2002

2) Operations Research – V.K. Kapoor

Sultan Chand and Sons, 3rd 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 Set-Keywords and identifiers –Constants-Variables-Data types-Declaration of variables-Assigning values to variables-Defining symbolic constants-Arithmetic Operators-Relational Operators-Logical Operators-Assignment Operators-Increment and Decrement Operators-Conditional Operator-Bit wise Operators-Special Operators-Arithmetic Expressions-Type Conversion-Operator Precedence-Mathematical Functions

Unit - II (15 Hours)

Input ,Output Operators, Arrays and Strings : Reading and Writing Characters-Formatted input and output-One Dimensional Arrays-Two Dimensional Arrays-Initialization-Multidimensional Arrays - Arithmetic operations on characters – String handling functions – Table of strings.

Unit - III (15 Hours)

Decision Making-Branching and Looping : Simple If Statement –The IF ELSE Statement-Nesting of IF-ELSE Statements-The ELSE-IF Ladder-The switch Statement-The ?: operator-The GOTO Statement-The WHILE Statement-The DO Statement –The FOR Statement-Jumps in loops

Unit - IV (15 Hours)

User-Defined Functions: The form of C functions - Categories of functions –Nesting of Functions-Recursion- Functions with arrays-The scope and lifetime of variables in functions

Unit - V (15 Hours)

Structures, Unions, Pointers and File management : Structure definition-Giving values to members-Structure initialization-Comparison of Structure variables-Arrays of Structures-Arrays within Structures-Structures within Structures-Unions – 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 McGraw-Hill Publishing Company Limited, Third Edition, 2004

 Unit Chapter/section I 2.1-2.11, 3.1-3.16 II 4.1-4.5, 7.1-7.7, 8.5, 8.8, 8.9 III 5.1-5.9, 6.1-6.5, IV 9.1-9.19 V 10.1-10.10, 10.12, 11.1 – 11.6, 11.10-11.12, 12.1-12.4

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 –C-R 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=Z2,W = eZ, W = sin Z, W=1/z, W = (z + 1/z) only.

Unit - III (15 Hours)

Contour integration : Contour integration-the Cauchy – Goursat theorem (statement only)-Cauchy integral formula-Higher derivatives-Morera’s theorem-Liouville’s theorem-fundamental theorem of algebra-Maximum modulus theorem.

Unit – IV (15 Hours)

Series expansions : Taylor series, Laurent’s series, Zeros of an analytic functions-singularities

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

 Unit Chapter/section I 2(2.1 to 2.9) II 3(3.1 to3 .5) 5(5.1, 5.3, 5.4, 5.6) III 6(6.1 to 6.4) IV 6(6.1 to 6.4) V 8(8.1 to 8.3)

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 ZeroSum Games – Some Basic Terms - The Maximin - Minimax Principle - Games without Saddle Points-Mixed Strategies - Graphic Solution of 2xn and mx2 Games - Dominance Property

Unit –III (15 Hours)

Inventory Control : IntroductionTypes 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 : IntroductionNetwork: 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

 Unit Chapter/section I 12.1 to 12.6 II 17.1 to 17.7 III 19.1 to 19.8 IV 20.1 to 20.8 V 25.1, 25.2, 25.4, 25.6, 25.7, 25.8

Reference Book:

Operations Research – S.D. Sharma,

Kedar Nath Ramnath & Co. 13th 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)

Cut-Sets and Cut-Vertices : Cut-Sets – Some properties of a cut set – All cut sets

in a graph – Fundamental circuits and Cut-Sets - 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, Prentice-Hall of India, 2005

 Unit Chapter/Section I 1 : 1.1 to 1.5,2: 2.1 to 2.5 II 2: 2.6 to 2.10 III 3: 3.1 to 3.5,3.7,3.9 IV 4: 4.1 to 4.6 V 5:5.2,5.3, 7: 7.1, 8:8.1 to 8.3

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 Method-Regula falsi method – Horner’s method.

Unit – II (12 Hours)

Simultaneous linear algebraic equations: Gauss elimination method –Gauss Jordan method-Method 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 interpolation-Inverse interpolation

Unit – IV (12 Hours)

Numerical differentiation and integration: Newton’s forward, backward formula for derivatives-Trapezoidal rule- Simpson’s 1/3 rule

Unit-V (12 Hours)

Numerical solution of ordinary differential equation: Taylor series method-Euler’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.

 Unit Chapter/section I 3(2, 3, 4, 5 and 6) II 4(2, 3, 4, 6) III 6(1, 2, 3 and 4) 8(3 and 4 only) IV 9(2, 3, 8, 10) V 11(6, 10, 13, 16, 17, 18, 20 only)

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

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