For students Admitted from Onwards

Transcription

1 For students Admitted from Onwards

2 BATCH -I

3 SEMESTER: I CORE COURSE I Inst.Hour 5 Credit 4 Code 11K1M01 DIFFERENTIAL CALCULUS AND TRIGONOMETRY Methods of Successive Differentiation Leibnitz s Theorem and its applications- Increasing & Decreasing functions. (Chapter III: Sections , 2.1, 2.2& Chapter IV Sections 2.1, 2.2 of Text Book 1) Curvature Radius of curvature in Cartesian & in Polar Coordinates Centre of curvature Evolutes & Involutes (Chapter X Sections of Text Book 1) Expansions of sin(nx),cos(nx),tan(nx) Expansions of sin n x, cos n x 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) Hyperbolic functions Relation between hyperbolic & Circular functions- Inverse hyperbolic functions. (Chapter 2: Sections 2.1& 2.2 of Text Book 2) 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 [2]S. Arumugam, Issac & Somasundaram, Trigonometry and Fourier Series New Gamma Publications 1999Edition [1] S.Arumugam & others, Calculus Volume1. [2] S.Narayanan, Trigonometry.

4 SEMESTER: I CORE COURSE II Inst.Hour 3+3 Credit 6 Code 11K2M02 ANALYTICAL GEOMETRY OF 3- DIMENSIONS AND INTEGRAL CALCULUS Coplanar lines Shortest distance between two skew lines- Equation of the line of shortest distance (Chapter III Sections 7& 8 of Text Book 1 ) 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) Properties of Definite Integrals Integration by parts reduction formula (Chapter I Sections 11, 12 &13 of Text Book 2 ) Double integrals changing the order of Integration Triple Integrals. (Chapter V Sections 2.1, 2.2, 4 of Text Book 2) 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 Revised Edition. [2] S.Narayanan,T.K.Manickavasagam Pillai, Calculus Volume II S.V Publications 2003 Edition. [1] P.Duraipandian & Laxmi Duraipandian. Analytical Geometry Shanti Narayanan, Differential & Integral Calculus

5 SEMESTER : II CORE COURSE III Inst.Hour 4 Credit 4 Code 11K2M03 ALGEBRA AND THEORY OF NUMBERS Relation between roots & coefficients Symmetric functions Sum of the r th powers of the Roots Two methods. (Chapter 6 Sections of Text Book 1) 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) Theory of Numbers Prime & Composite numbers divisors of a given number N Euler s function (N) and its value The highest power of a prime P contained in N! (Chapter 5 Sections of Text book 2) The product of r consecutive integers is divisible by r! Congruence (Chapter 5 Sections of Text book 2) Fermat s Theorem, Wilson s and Lagrange s Theorems. (Chapter 5 Sections Text book 2) Text Book(s) [1] T.K. Manickavasagam Pillai,T.Natarajan, K.S.Ganapathy, Algebra Volume I, S.V Publications Revised Edition [2] T.K.Manickavasagam Pillai & others, Algebra Volume II S.V. Publications Revised Edition [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.

6 SEMESTER: III CORE COURSE IV Inst.Hour 5 Credit 4 Code 11K3M04 SEQUENCES AND SERIES 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 of Text Book) Infinite series Definition of Convergence, Divergence & Oscillation Necessary condition for convergence Convergence of p n 1 and 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) Cauchy s condensation Test, Cauchy s root test and their simple problems Alternative series with simple problems (Chapter 2 Section 15, (Omitting uniform Convergence) of Text Book ) 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) 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 Revised Edition [1] M.K.Singal & Asha Rani Singal, A first course in Real Analysis. [2].S.Arumugam, Sequences & series.

7 SEMESTER: III CORE COURSE V Inst.Hour 5 Credit 4 Code 11K3M05 DIFFERENTIAL EQUATIONS AND TRANSFORMS First order, higher degree Differential equations solvable for x, solvable for dy y, solvable for,clairaut s form Conditions of integrability of M dx + N dy =0 dx simple problems. (Chapter 4 section 1 to 4 & chapter 2 section 6) 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) Laplace Transforms standard formulae Basic Theorems & simple applications. (Chapter 9 Sections 1 to 5 of Text Book) Inverse Laplace Transform Use of Laplace Transform in solving ODE with constant coefficients. (Chapter 9 Sections 6 to 11 of Text Book) 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

8 SEMESTER: IV CORE COURSE VI Inst.Hour 4 Credit 4 Code 11K4M06 VECTOR ANALYSIS AND FOURIER SERIES. 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 , of Text book 1) 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) Gauss Divergence Theorem Simple problems &Verification of the theorem (Chapter IV of Text book 1) Stoke s Theorem Green s Theorem (Theorems without Proof) Simple problems & Verification of the theorems (Chapter IV of Text book 1) 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. [1] M.L.Khanna, Vector Calculus [2] M.D.Raisinghania, Vector Calculus

9 SEMESTER: V CORE COURSE VIII ABSTRACT ALGEBRA Inst.Hour 5 Credit 4 Code 11K5M08 Subgroups Cyclic groups Order of an element Cosets and Lagrange s Theorem ( Chapter 3 section 3.5 to 3.8 ) Normal subgroups and Quotient groups Finite groups & Cayley tables Isomorphism & Homomorphism. (Chapter 3 Sections 3.9 to3.11) 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) 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) Characteristic Equation and Cayley Hamilton Theorem-Eigen Values and Eigen vectors-properties of Eigen Values. (Chapter 7 Sections ) Text Book [1] S.Arumugam & A. Thangapandi Issac, Modern Algebra, Scitech Publication - August Edition [1] M.L.Santiago, Modern Algebra. [2] I.N.Herstein. Topics in Algebra.

10 SEMESTER: V CORE COURSE XI REAL ANALYSIS Inst.Hour 5 Credit 5 Code 11K5M09 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) 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) 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) 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) 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. [1] Tom.M.Apostol, Mathematical Analysis,II Edition. [2] S.C.Malik, Elements of Real Analysis.

11 SEMESTER: V CORE COURSE X Inst.Hour 5 Credit 4 Code 11K5M10 STATICS UNIT1: Introduction and Basic ideas of forces Parallel forces. (Chapters 3) Moment of a Force about a point on a line Theorem on Moments &couples (Chapters 3 & 4 ) Equilibrium of three forces acting on a body Coplanar forces (Simple Problems only). (Chapter 5 upto section 7, Chapter 6 - upto section 13 ) Equilibrium of Strings under gravity Common catenary Parabolic catenary suspension bridge. (Chapter 11) Friction Laws of Friction Coefficient of Friction, Angle & cone of Friction Equilibrium of a particle on a rough inclined plane under a force parallel to the 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.

12 SEMESTER:IV CORE COURSE VII Inst.Hour 3 Credit 3 Code 11K4M07 OPERATIONS RESEARCH Introduction to Operations Research Elementary treatment of linear programming, Simplex Method for <,=,> constraints Application to Transportation problem Transportation Algorithm- Degeneracy in Transportation problem, Unbalanced Transportation problem Assignment problem The assignment algorithm unbalanced assignment problem. PERT and CPM network critical and sub critical jobs determining the critical path. Network calculation PERT networks probability aspect of PERT PERT time PERT cost (omitting crashing) Text Book [1] Kantiswarup, P.K.Gupta and Manmohan,.Operations Research. :- V.Sunderasan, K.S.Ganapathy Subramanian, K.Ganesan, Resource Management Techniques (Operations Research) [2] P.Mariappan, Operations Research Methods and Applications.

13 SEMESTER: V MAJOR BASED ELECTIVE 1 Inst.Hour 5 Credit 5 Code 11K5MELM1 PROGRAMMING IN C FOR NUMERICAL METHODS 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) Decision making & looping WHILE, DO, and FOR statements (Chapter 6 omitting section 6.5) 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 ) 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 [1] Programming in C - By Rajaraman [2] Let us C Yeshwant Kanetkar

14 SEMESTER: VI Inst.Hour 7 Credit 6 Code 11K6M11 CORE COURSE XI COMPLEX ANALYSIS 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) Elementary transformations Bilinear transformations Cross ratio fixed points of Bilinear Transformation Some special bilinear transformations. ( Chapter 3 Sections 3.1 to 3.5) Complex integration definite integral Cauchy s Theorem Cauchy s integral formula Higher derivatives. (Chapter 6 Sections 6.1 to 6.4) Series expansions Taylor s series Laurant s Series Zeroes of analytic functions Singularities. (Chapter 7 Sections 7.1 to 7.4) 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 2006 [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

15 SEMESTER: VI CORE COURSE XII Inst.Hour 7 Credit 6 Code 11K6M12 DYNAMICS UNIT1: Kinematics Velocity and acceleration Tangential & normal components Radial & transverse components. (Chapter to 3.32 & chapter 9 Section 9.2, Chapter 11-Section 11.2) 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) Simple Harmonic motion Simple Pendulum Load suspended by an elastic string. (Chapter 10 section , ) Projectile in Vacuum Maximum height reached, range, time of flight Projectile up / down an inclined plane. (Chapter 6 upto section 6.15) 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 ] S.Narayanan., Dynamics. 2] A.V.Dharmapadam, Dynamics.

16 SEMESTER: VI CORE COURSE XIII Inst.Hour 6 Credit 6 Code 11K6M13 GRAPH THEORY 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 & Chapter II Section ) 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)) Cut set Properties of a cut-set All cut-sets in a graph Fundamental circuits and cut sets Connectivity and separability. (Chapter IV Sections ) Planar graphs Kuratowski s two graphs Representation of a planar graph- Detection of Planarity-Geometrical dual Combinatorial dual. (Chapter V Sections ) 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 , 7.6,7.9 & Chapter VIII Sections ) Text Book [1] Narsingh Deo, Graph Theory with applications to Engineering & Computer Science, Prentice Hall of India, New Delhi.. [1] F.Harary, Graph Theory,Narosa Publishing House,New Delhi. [2] S.A.Choudum, Graph Theory, MacMillan India Ltd- New Delhi-Madras.

17 SEMESTER: VI MAJOR BASED ELECTIVE 2 Inst.Hour 5 Credit 5 Code 11K6MELM2 STOCHASTIC PROCESSES Specification of Stochastic processes Stationary Process Markov Chain Higher Transition Probabilities (Chapter , Chapter 3-3.1, 3.2) Classification of States and chains Determination of Higher Transition Probabilities-Graph theoretic Approach. (Chapter 3-3.4, 3.5, 3.7) Poisson Process and related distributions Generalization of Poisson Process (Chapter ) 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 ) 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.

18 SEMESTER: VI MAJOR BASED ELECTIVE 3 Inst.Hour 4 Credit 4 Code 11K6MELM3 NUMERICAL METHODS [In all units the values of a root may be calculated upto 3 decimal accuracy only] 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) 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, ) Numerical differentiation - Numerical Integration using Trapezoidal rule & Simpson s first & second rules - Theory & problems (Chapter 5 sections , &5.4.3) Solutions to Linear Systems Gaussian Elimination Method Jacobi & Gauss Siedal iterative methods Theory & problems. (Chapter 6 Section , 6.4) Numerical solution of ODE Solution (Derivation of the formula not needed) by Taylor Series Method, Picard s method, Euler s Method, Runge Kutta 2 nd &4 th order methods- Theory& problems using Adam s Predictor Corrector method (Chapter 7 Sections 7.2, 7.3, , 7.5&7.6 (omitting 7.6.2)) Text Book [1] S.S.Sastry, Introductory Methods of Numerical Analysis, Prentice Hall of India Pvt.Limited :- [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.

19 BATCH - II

20 SEMESTER: I Inst.Hour 5 Credit 4 Code 11K1M01 CORE COURSE I DIFFERENTIAL CALCULUS AND TRIGONOMETRY Methods of Successive Differentiation Leibnitz s Theorem and its applications- Increasing & Decreasing functions. (Chapter III: Sections , 2.1, 2.2& Chapter IV Sections 2.1, 2.2 of Text Book 1) Curvature Radius of curvature in Cartesian & in Polar Coordinates Centre of curvature Evolutes & Involutes (Chapter X Sections of Text Book 1) Expansions of sin(nx),cos(nx),tan(nx) Expansions of sin n x, cos n x 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) Hyperbolic functions Relation between hyperbolic & Circular functions- Inverse hyperbolic functions. (Chapter 2: Sections 2.1& 2.2 of Text Book 2) 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 [2]S. Arumugam, Issac & Somasundaram, Trigonometry and Fourier Series New Gamma Publications 1999Edition [1] S.Arumugam & others, Calculus Volume1. [2] S.Narayanan, Trigonometry.

21 SEMESTER: I & II CORE COURSE II Inst.Hour 3+3 Credit 6 Code 11K2M02 ANALYTICAL GEOMETRY OF 3- DIMENSIONS AND INTEGRAL CALCULUS Coplanar lines Shortest distance between two skew lines- Equation of the line of shortest distance (Chapter III Sections 7& 8 of Text Book 1 ) 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) Properties of Definite Integrals Integration by parts reduction formula (Chapter I Sections 11, 12 &13 of Text Book 2 ) Double integrals changing the order of Integration Triple Integrals. (Chapter V Sections 2.1, 2.2, 4 of Text Book 2) 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 Revised Edition. [2] S.Narayanan,T.K.Manickavasagam Pillai, Calculus Volume II S.V Publications 2003 Edition. [1] P.Duraipandian & Laxmi Duraipandian. Analytical Geometry Shanti Narayanan, Differential & Integral Calculus

22 SEMESTER : II Inst.Hour 4 Credit 4 Code 11K2M03 CORE COURSE III ALGEBRA AND THEORY OF NUMBERS Relation between roots & coefficients Symmetric functions Sum of the r th powers of the Roots Two methods. (Chapter 6 Sections of Text Book 1) 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) Theory of Numbers Prime & Composite numbers divisors of a given number N Euler s function (N) and its value The highest power of a prime P contained in N! (Chapter 5 Sections of Text book 2) The product of r consecutive integers is divisible by r! Congruence (Chapter 5 Sections of Text book 2) Fermat s Theorem, Wilson s and Lagrange s Theorems. (Chapter 5 Sections Text book 2) Text Book(s) [1] T.K. Manickavasagam Pillai,T.Natarajan, K.S.Ganapathy, Algebra Volume I, S.V Publications Revised Edition [2] T.K.Manickavasagam Pillai & others, Algebra Volume II S.V. Publications Revised Edition [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.

23 SEMESTER: III CORE COURSE IV Inst.Hour 5 Credit 4 Code 11K3M04 SEQUENCES AND SERIES 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 of Text Book) Infinite series Definition of Convergence, Divergence & Oscillation Necessary condition for convergence Convergence of p n 1 and 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) Cauchy s condensation Test, Cauchy s root test and their simple problems Alternative series with simple problems (Chapter 2 Section 15, (Omitting uniform Convergence) of Text Book ) 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) 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 Revised Edition [1] M.K.Singal & Asha Rani Singal, A first course in Real Analysis. [2].S.Arumugam, Sequences & series.

24 SEMESTER: III CORE COURSE V Inst.Hour 5 Credit 4 Code 11K3M05 DIFFERENTIAL EQUATIONS AND TRANSFORMS First order, higher degree Differential equations solvable for x, solvable for dy y, solvable for,clairaut s form Conditions of integrability of M dx + N dy =0 dx simple problems. (Chapter 4 section 1 to 4 & chapter 2 section 6) 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) Laplace Transforms standard formulae Basic Theorems & simple applications. (Chapter 9 Sections 1 to 5 of Text Book) Inverse Laplace Transform Use of Laplace Transform in solving ODE with constant coefficients. (Chapter 9 Sections 6 to 11 of Text Book) 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

25 SEMESTER: IV CORE COURSE VI Inst.Hour 4 Credit 4 Code 11K4M06 VECTOR ANALYSIS AND FOURIER SERIES. 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 , of Text book 1) 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) Gauss Divergence Theorem Simple problems &Verification of the theorem (Chapter IV of Text book 1) Stoke s Theorem Green s Theorem (Theorems without Proof) Simple problems & Verification of the theorems (Chapter IV of Text book 1) 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. [1] M.L.Khanna, Vector Calculus [2] M.D.Raisinghania, Vector Calculus

26 SEMESTER: IV Inst.Hour 3 Credit 3 Code 11K4M07 CORE COURSE VII OPERATIONS RESEARCH Introduction to Operations Research Elementary treatment of linear programming, Simplex Method for <,=,> constraints Application to Transportation problem Transportation Algorithm- Degeneracy in Transportation problem, Unbalanced Transportation problem Assignment problem The assignment algorithm unbalanced assignment problem. PERT and CPM network critical and sub critical jobs determining the critical path. Network calculation PERT networks probability aspect of PERT PERT time PERT cost (omitting crashing) Text Book [1] Kantiswarup, P.K.Gupta and Manmohan,.Operations Research. :- V.Sunderasan, K.S.Ganapathy Subramanian, K.Ganesan, Resource Management Techniques (Operations Research) [2] P.Mariappan, Operations Research Methods and Applications.

27 SEMESTER: V CORE COURSE VIII ABSTRACT ALGEBRA Inst.Hour 5 Credit 4 Code 11K5M08 Subgroups Cyclic groups Order of an element Cosets and Lagrange s Theorem ( Chapter 3 section 3.5 to 3.8 ) Normal subgroups and Quotient groups Finite groups & Cayley tables Isomorphism & Homomorphism. (Chapter 3 Sections 3.9 to3.11) 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) 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) Characteristic Equation and Cayley Hamilton Theorem-Eigen Values and Eigen vectors-properties of Eigen Values. (Chapter 7 Sections ) Text Book [1] S.Arumugam & A. Thangapandi Issac, Modern Algebra, Scitech Publication - August Edition [1] M.L.Santiago, Modern Algebra. [2] I.N.Herstein. Topics in Algebra.

28 SEMESTER: V CORE COURSE IX REAL ANALYSIS Inst.Hour 5 Credit 5 Code 11K5M09 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) 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) 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) 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) 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. [1] Tom.M.Apostol, Mathematical Analysis,II Edition. [2] S.C.Malik, Elements of Real Analysis.

29 SEMESTER: V CORE COURSE X Inst.Hour 5 Credit 4 Code 11K5M10 STATICS UNIT1: Introduction and Basic ideas of forces Parallel forces. (Chapters 3) Moment of a Force about a point on a line Theorem on Moments &couples (Chapters 3 & 4 ) Equilibrium of three forces acting on a body Coplanar forces (Simple Problems only). (Chapter 5 upto section 7, Chapter 6 - upto section 13 ) Equilibrium of Strings under gravity Common catenary Parabolic catenary suspension bridge. (Chapter 11) Friction Laws of Friction Coefficient of Friction, Angle & cone of Friction Equilibrium of a particle on a rough inclined plane under a force parallel to the 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.

30 SEMESTER: V MAJOR BASED ELECTIVE - 1 Inst.Hour 5 Credit 5 Code 11K5MELM1S PROBABILITY AND STATISTICS 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 ) Random variables Distribution functions Discrete & continuous random variables Probability mass & density functions Joint probability distribution functions. (Chapter-5 Sections ) 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 ) Correlation & Regression Properties of Correlation & regression coefficients Numerical Problems for finding the correlation & regression coefficients.. (Chapter 10 Sections 10.1 to ) 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, to and 7.3.8, Chapter 8 Section 8.2, to and 8.2.7) Text Book : Fundamentals of Mathematical Statistics by Gupta.S.C &Kapoor,V.K Published by Sultan Chand & sons,new Delhi Edition :- 1] Practical Statistics Thambidurai.P Rainbow publishers CBE (1991) 2] Probability and Statistics A.Singaravelu A.R.Publications 2002

31 SEMESTER: VI CORE COURSE XI Inst.Hour 7 Credit 6 Code 11K6M11 COMPLEX ANALYSIS 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) Elementary transformations Bilinear transformations Cross ratio fixed points of Bilinear Transformation Some special bilinear transformations. ( Chapter 3 Sections 3.1 to 3.5) Complex integration definite integral Cauchy s Theorem Cauchy s integral formula Higher derivatives. (Chapter 6 Sections 6.1 to 6.4) Series expansions Taylor s series Laurant s Series Zeroes of analytic functions Singularities. (Chapter 7 Sections 7.1 to 7.4) 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 2006 [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

32 SEMESTER: VI CORE COURSE XII Inst.Hour 7 Credit 6 Code 11K6M12 DYNAMICS UNIT1: Kinematics Velocity and acceleration Tangential & normal components Radial & transverse components. (Chapter to 3.32 & chapter 9 Section 9.2, Chapter 11-Section 11.2) 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) Simple Harmonic motion Simple Pendulum Load suspended by an elastic string. (Chapter 10 section , ) Projectile in Vacuum Maximum height reached, range, time of flight Projectile up / down an inclined plane. (Chapter 6 upto section 6.15) 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 ] S.Narayanan., Dynamics. 2] A.V.Dharmapadam, Dynamics.

33 SEMESTER: VI CORE COURSE XIII Inst.Hour 6 Credit 6 Code 11K6M13 GRAPH THEORY 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 & Chapter II Section ) 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)) Cut set Properties of a cut-set All cut-sets in a graph Fundamental circuits and cut sets Connectivity and separability. (Chapter IV Sections ) Planar graphs Kuratowski s two graphs Representation of a planar graph- Detection of Planarity-Geometrical dual Combinatorial dual. (Chapter V Sections ) 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 , 7.6,7.9 & Chapter VIII Sections ) Text Book [1] Narsingh Deo, Graph Theory with applications to Engineering & Computer Science, Prentice Hall of India, New Delhi.. [1] F.Harary, Graph Theory,Narosa Publishing House,New Delhi. [2] S.A.Choudum, Graph Theory, MacMillan India Ltd- New Delhi-Madras.

34 SEMESTER: VI MAJOR BASED ELECTIVE 2 Inst.Hour 5 Credit 5 Code 11K6MELM2 STOCHASTIC PROCESSES Specification of Stochastic processes Stationary Process Markov Chain Higher Transition Probabilities (Chapter , Chapter 3-3.1, 3.2) Classification of States and chains Determination of Higher Transition Probabilities-Graph theoretic Approach. (Chapter 3-3.4, 3.5, 3.7) Poisson Process and related distributions Generalization of Poisson Process (Chapter ) 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 ) 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.

35 SEMESTER: VI MAJOR BASED ELECTIVE 3 Inst.Hour 4 Credit 4 Code 11K6MELM3 NUMERICAL METHODS [In all units the values of a root may be calculated upto 3 decimal accuracy only] 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) 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, ) Numerical differentiation - Numerical Integration using Trapezoidal rule & Simpson s first & second rules - Theory & problems (Chapter 5 sections , &5.4.3) Solutions to Linear Systems Gaussian Elimination Method Jacobi & Gauss Siedal iterative methods Theory & problems. (Chapter 6 Section , 6.4) Numerical solution of ODE Solution (Derivation of the formula not needed) by Taylor Series Method, Picard s method, Euler s Method, Runge Kutta 2 nd &4 th order methods- Theory& problems using Adam s Predictor Corrector method (Chapter 7 Sections 7.2, 7.3, , 7.5&7.6 (omitting 7.6.2)) Text Book [1] S.S.Sastry, Introductory Methods of Numerical Analysis, Prentice Hall of India Pvt.Limited :- [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.

36 BATCH III

37 SEMESTER: I Inst.Hour 5 Credit 4 Code 11K1M01 CORE COURSE I DIFFERENTIAL CALCULUS AND TRIGONOMETRY Methods of Successive Differentiation Leibnitz s Theorem and its applications- Increasing & Decreasing functions. (Chapter III: Sections , 2.1, 2.2& Chapter IV Sections 2.1, 2.2 of Text Book 1) Curvature Radius of curvature in Cartesian & in Polar Coordinates Centre of curvature Evolutes & Involutes (Chapter X Sections of Text Book 1) Expansions of sin(nx),cos(nx),tan(nx) Expansions of sin n x, cos n x 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) Hyperbolic functions Relation between hyperbolic & Circular functions- Inverse hyperbolic functions. (Chapter 2: Sections 2.1& 2.2 of Text Book 2) 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 [2]S. Arumugam, Issac & Somasundaram, Trigonometry and Fourier Series New Gamma Publications 1999Edition [1] S.Arumugam & others, Calculus Volume1. [2] S.Narayanan, Trigonometry.

38 SEMESTER: I & II Inst.Hour 3+3 Credit 6 Code 11K2M02 CORE COURSE II ANALYTICAL GEOMETRY OF 3- DIMENSIONS AND INTEGRAL CALCULUS Coplanar lines Shortest distance between two skew lines- Equation of the line of shortest distance (Chapter III Sections 7& 8 of Text Book 1 ) 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) Properties of Definite Integrals Integration by parts reduction formula (Chapter I Sections 11, 12 &13 of Text Book 2 ) Double integrals changing the order of Integration Triple Integrals. (Chapter V Sections 2.1, 2.2, 4 of Text Book 2) 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 Revised Edition. [2] S.Narayanan,T.K.Manickavasagam Pillai, Calculus Volume II S.V Publications 2003 Edition. [1] P.Duraipandian & Laxmi Duraipandian. Analytical Geometry Shanti Narayanan, Differential & Integral Calculus

39 SEMESTER : II Inst.Hour 4 Credit 4 Code 11K2M03 CORE COURSE III ALGEBRA AND THEORY OF NUMBERS Relation between roots & coefficients Symmetric functions Sum of the r th powers of the Roots Two methods. (Chapter 6 Sections of Text Book 1) 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) Theory of Numbers Prime & Composite numbers divisors of a given number N Euler s function (N) and its value The highest power of a prime P contained in N! (Chapter 5 Sections of Text book 2) The product of r consecutive integers is divisible by r! Congruence (Chapter 5 Sections of Text book 2) Fermat s Theorem, Wilson s and Lagrange s Theorems. (Chapter 5 Sections Text book 2) Text Book(s) [1] T.K. Manickavasagam Pillai,T.Natarajan, K.S.Ganapathy, Algebra Volume I, S.V Publications Revised Edition [2] T.K.Manickavasagam Pillai & others, Algebra Volume II S.V. Publications Revised Edition [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.

40 SEMESTER: III Inst.Hour 5 Credit 4 Code 11K3M04 CORE COURSE IV SEQUENCES AND SERIES 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 of Text Book) Infinite series Definition of Convergence, Divergence & Oscillation Necessary condition for convergence Convergence of p n 1 and 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) Cauchy s condensation Test, Cauchy s root test and their simple problems Alternative series with simple problems (Chapter 2 Section 15, (Omitting uniform Convergence) of Text Book ) 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) 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 Revised Edition [1] M.K.Singal & Asha Rani Singal, A first course in Real Analysis. [2].S.Arumugam, Sequences & series.

41 SEMESTER: III Inst.Hour 5 Credit 4 Code 11K3M05 CORE COURSE V DIFFERENTIAL EQUATIONS AND TRANSFORMS First order, higher degree Differential equations solvable for x, solvable for dy y, solvable for,clairaut s form Conditions of integrability of M dx + N dy =0 dx simple problems. (Chapter 4 section 1 to 4 & chapter 2 section 6) 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) Laplace Transforms standard formulae Basic Theorems & simple applications. (Chapter 9 Sections 1 to 5 of Text Book) Inverse Laplace Transform Use of Laplace Transform in solving ODE with constant coefficients. (Chapter 9 Sections 6 to 11 of Text Book) 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

42 SEMESTER: IV CORE COURSE VI Inst.Hour 4 Credit 4 Code 11K4M06 VECTOR ANALYSIS AND FOURIER SERIES. 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 , of Text book 1) 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) Gauss Divergence Theorem Simple problems &Verification of the theorem (Chapter IV of Text book 1) Stoke s Theorem Green s Theorem (Theorems without Proof) Simple problems & Verification of the theorems (Chapter IV of Text book 1) 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. [1] M.L.Khanna, Vector Calculus [2] M.D.Raisinghania, Vector Calculus

43 SEMESTER: IV CORE COURSE VII Inst.Hour 3 Credit 3 Code 11K4M07 OPERATIONS RESEARCH Introduction to Operations Research Elementary treatment of linear programming, Simplex Method for <,=,> constraints Application to Transportation problem Transportation Algorithm- Degeneracy in Transportation problem, Unbalanced Transportation problem Assignment problem The assignment algorithm unbalanced assignment problem. PERT and CPM network critical and sub critical jobs determining the critical path. Network calculation PERT networks probability aspect of PERT PERT time PERT cost (omitting crashing) Text Book [1] Kantiswarup, P.K.Gupta and Manmohan,.Operations Research. :- V.Sunderasan, K.S.Ganapathy Subramanian, K.Ganesan, Resource Management Techniques (Operations Research) [2] P.Mariappan, Operations Research Methods and Applications.

44 SEMESTER: V CORE COURSE VIII ABSTRACT ALGEBRA Inst.Hour 5 Credit 4 Code 11K5M08 Subgroups Cyclic groups Order of an element Cosets and Lagrange s Theorem ( Chapter 3 section 3.5 to 3.8 ) Normal subgroups and Quotient groups Finite groups & Cayley tables Isomorphism & Homomorphism. (Chapter 3 Sections 3.9 to3.11) 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) 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) Characteristic Equation and Cayley Hamilton Theorem-Eigen Values and Eigen vectors-properties of Eigen Values. (Chapter 7 Sections ) Text Book [1] S.Arumugam & A. Thangapandi Issac, Modern Algebra, Scitech Publication - August Edition [1] M.L.Santiago, Modern Algebra. [2] I.N.Herstein. Topics in Algebra.

45 SEMESTER: V CORE COURSE IX REAL ANALYSIS Inst.Hour 5 Credit 5 Code 11K5M09 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) 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) 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) 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) 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. [1] Tom.M.Apostol, Mathematical Analysis,II Edition. [2] S.C.Malik, Elements of Real Analysis.