S.O.L(III & V sem 2015-2016)

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 2DEPARTMENT OF MATHEMATICS

MAJOR CORE 4: SEQUENCES AND SERIESSPECIFIC OUTCOMES OF LEARNING

No.of.Hours:5No. of credits:5 Code : U12MA3MCT04

UNIT - I: TYPES OF SEQUENCES

a. Recalls the definition of sequences.b. Determines the limit of sequences.c. Recalls the definition of bounded sequences.d. Recalls Cauchy's principle of Convergence.e. Recalls the definition of monotonic sequence.f. Determines and concludes the nature of the sequence.

UNIT – II: CONVERGENCE OF SERIESa. Recalls the definition of infinite series, convergence, divergence and

oscillation of the series.

b. Recalls the condition for the convergence and divergence of the series ∑ 1

np

c. Determines the convergence, and divergence using comparison tests, Cauchy’s condensation test, D’Alemberts’ ratio test, Cauchy’s nth root test.

UNIT – III: ALTERNATING AND BINOMIAL SERIES

a. Recalls the definition of alternating series, absolute convergence and conditional convergence.

b. Recalls Leibnitz's test.c. Calculates and concludes the nature of the series.d. Recalls the statement and proof of Binomial theorem for rational index.e. Determines the sum of a series using Binomial Theorem.f. Determines the limit of a function using Binomial Theorem.

UNIT – IV: EXPONENTIAL AND LOGARITHMIC SERIES

a. Recalls the statements and proofs of Exponential and Logarithmic series.b. Identifies the type of the series.c. Determines the sum of the series.d. Determines the limit of a function using Exponential and Logarithmic Series.

UNIT – V: GENERAL SUMMATIONa. Identifies the type of the series.b. Recalls various methods of summation.c. Calculates the sum of various types of series.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI-2

DEPARTMENT OF MATHEMATICS

MAJOR CORE 5 - STATICS

SPECIFIC OUTCOMES OF LEARNING

No. of Hours: 5 Code: U08MA3MCT05No. of Credits: 5

UNIT -I: EQUILIBRIUM OF FORCES

1. Recalls the definition of force, equilibrium forces, resultant of the forces. 2. Recalls the different types of forces, principle of the transmissibility of a force.3. Determines the resultant of two forces acting at a point.4. Applies parallelogram of forces, triangle of forces, converse of the triangle of forces 5. Lami's theorem.6. Identifies the conditions of equilibrium of any number of forces acting upon a particle.7. Determines the magnitude and direction of the resultant of any number of coplanar

forces acting at a point.8. Determines the solution of the given problem using the above results.

UNIT – II: PARALLEL FORCES AND COUPLES

1. Determines the resultant of two like parallel forces & two unlike unequal parallel forces acting on a rigid body.

2. Recalls the resultant of a number of parallel forces acting on a rigid body. 3. Identifies the conditions of equilibrium of three coplanar parallel forces. 4. Recalls the statement of Varignon's theorem on moments and its applications. 5. Recalls the condition of equilibrium of two couples, resultant of coplanar couples & resultant of a couple and a force.6. Determines the solution of a given problem using the above principle.

UNIT –III: EQUILIBRIUM OF THREE FORCES

1. Recalls the conditions of equilibrium of three forces acting on a rigid body.2. Identifies the conditions of equilibrium on three coplanar forces.3. Recalls the two trigonometrically theorems 4. Determines the solution using the above conditions.

UNIT – IV: FRICTION

1. Recalls the definition of friction, force of friction, statical, dynamical and limiting friction.2. Recalls the laws of friction, co-efficient of friction, angle of friction.3. Applies the condition of the equilibrium of a particle on a rough inclined plane. 4. Determines the solution of the given problem using equilibrium of a particle on a rough inclined plane with different conditions.

UNIT – V: EQUILIBRIUM OF STRINGS

1. Recalls the equation of the catenary.2. Recalls the definitions of vertex, directrix, parameter, span & sag of a catenary. 3. Identifies the formulae relating to catenary and its properties.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 620 002.


SKILL BASED ELECTIVE 3: APTITUDE MATHEMATICS


No. of Hours: 2 Code: U08MA3SBT03 No. of Credits: 2

UNIT- I:

1. Recalls the definitions of number system and various tests for divisibility.2. Provides knowledge on simplification using formula and rules.3. Recalls the definitions of H.C.F and L.C.M.

UNIT- II:

1. Recalls the definition of percentage.2. Recalls the definition of average and solves problems involving averages.

UNIT- III:

1. Recalls the definitions of ratio and proportions2. Solves problems using formulae for profit and loss.

UNIT- IV:

1. Recalls the relationship between time and work and solves problems using formulae.

2. Solves problems involving cisterns and pipes.3. Interprets bar chart and pie diagram.

UNIT- V:

1. Determines the solution in case of time and distance problems.2. Solves problems involving boats and streams, trains.

HOLY CROSS COLLEGE(AUTONOMOUS),TIRUCHIRAPPALLI-2


ALLIED OPTIONAL 4: COMPUTER FUNDAMENTALS AND PC SOFTWARES


NO. OF HOURS:4 CODE:U11MA3AOT22

NO. OF CREDITS:3

UNIT I:COMPUTER APPRECIATION

1. -Recalls the history of computers2. -Architecture of a computer3. -Study on Personal computer,Operating system and Networking

concepts.

UNIT II:WINDOWS

1. -Recalls the history of Windows2. -To start and exit Windows3. -Arranging Icons on the desktop4. -Working with windows and windows accessories:5. -Concepts about Moving and Copying Files6. -Ideas about Notepad, Calculator, Wordpad and Paint

UNIT III:MS WORD

1. -Introduction to MS WORD2. -Uses of Menus and Toolbars3. -Study on Text concepts4. -Spelling and Grammar concepts5. -Working with graphics6. -Labelling and mail merge

UNIT IV:MS EXCEL

1. -Basic ideas about Electronic Spreadsheet2. -Introduction to MS Excel3. -Study on Worksheet concepts

UNIT V:POWERPOINT

1. -Introduction to presentation Software2. -Identify the various slides3. -Adding headers and footers4. -Wizard presentation

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 2


ALLIED- 4 - APPLIED MATHEMATICS-III

SPECIFIC OUTCOMES OF LEARNINGNo. of hour : 4 Code :U11MA3AOT13 No. of credits :3 UNIT – I:INTERPOLATION AND SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS

1. Solution of Algebraic and Transcendental Equations.2. Recognises algebraic and transcendental equations.3. Recalls the Bisection method, False position method and Newton Raphson 4. method. 5. Determines the solution of the equation by Bisection method, False position method

and Newton Raphson method. 6. Recalls the definition of interpolation, forward and backward differences, symbolic 7. relations.8. Recalls Newtons formulae for forward and backward interpolation.9. Recognises the definition of interpolation with unevenly spaced points 10. Recalls the Lagrange's interpolation formula.11. Determines the value of Y at X by using Lagrange's interpolation formula.

UNIT II:SOLUTION OF SIMULTANEOUS EQUATIONS1. Calculates the solution of linear systems by using Gaussian elimination method,

Gauss Jordon method and Gauss Seidel method Gauss Jacobi method.2. Determines inverse of a matrix using Gauss elimination method

UNIT – III:NUMERICAL INTEGRATION1. Recalls the Trapezoidal rule and simpson's 1/3 rule.2. Determines the integral value by using Trapezoidal rule and simpson's 1/3 rule.3. Recalls the formula of Euler's, Range kutta II order and IV order method(first

order differential equations only)4. Determines the value of Y by using Euler's Runge - Kutta, II and IV order.

UNIT- IV:ANALYSIS OF TIME SERIES

1. Recalls the definition of Time series, components of Time series.2. Determines trend values for a given data by graphic method, semi-

averages method, moving average method.3. Compares original and trend values.

4. - Determines seasonal indices by the method of simple average, Ratio to trend, moving average and method of link relatives.

UNIT- IV:INDEX NUMBERS

1. Recalls the definition of principle of least squares.2. Recalls the definition of normal equations.3. - Recalls the definition of weighted aggregate price index, Paasche's,

Fisher's,4. Boweley's Price indices.5. -Determines the above mentioned index numbers.6. -Recalls the definitions of Quantity index number, Laspeyre's, Paasche's,

Fisher's quantity index numbers, cost of livings index numbers, chain base index, fixed base index.

7. -Determines the above mentioned index numbers.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 2


ALLIED 4 - CALCULUS AND TRIGONOMETRY


No. of Hours:4 Code:U11MA3AOT14

No. of Credits:3

UNIT I: TRIGONOMETRY EXPANSIONS AND APPROXIMATIONS:

1. Recalls the formula learnt earlier. 2. Determines the expansion of Cos nq, Sin nq, tan nq, Cos nq, Sin nq. 3.Determines the expansion of cosq, sinq, tanq

UNIT II:HYPERBOLIC FUNCTIONS:

1.Recalls the definition of hyperbolic functions.2.Establishes the relation between hyperbolic functions.3.Determines inverse hyperbolic functions.

UNIT III:SUCCESSIVE DIFFERENTIATION:

1.Recalls the n th derivative of standard functions.2.Recognises the type.3.Calculates the n th derivative of various functions.4.Formulates equations involving higher derivatives and establishes relationships.5.Recalls the Leibnitz theorem.6.Translates the formula into problem solving.

UNIT IV:PARTIAL DIFFERENTIAL EQUATIONS

1.Identifies the four standard forms of partial differential equations and determines the solution.2.Recognises Lagrange's equations and determines the solution.

UNIT V:FOURIER SERIES:

1.Recalls the form of fourier series.2.Determines the Fourier constants and hence the Fourier series.3.Recalls the properties of odd and even function.4.Recognises half-range Fourier Series.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALI-2


MAJOR CORE :7- REAL ANALYSIS


No. of hours: 5 Code: U08MA5MCT07No. of credits: 4

UNIT -I:REAL NUMBERS

1. Recalls the definition of real number system as a complete ordered field. 2. Discriminates Countable and uncountable sets.

UNIT –II:NEIGHBOURHOOD AND LIMIT POINTS

1. Recalls definition of neighbourhoods, open sets and closed sets.2. Classifies the various sets as open and closed sets.3. Determines the limit point of set.4. Determines closure of a set and interior of a set.5. Determines compactness and connectedness of a set.

UNIT –III:LIMITS AND CONTINUITY

1. Recalls the definition of limits and continuous function.2. Identifies the types of discontinuities for a given function.3. Proves algebra of continuous functions, intermediate value theorem and

inverse function theorem.4. Determines whether a function is uniformly continuous.

UNIT -IV:DERIVATIVES

1. Determines the derivability and continuity of a given function.2. Proves inverse function theorem and Darboux theorem.3. Proves Rolle’s theorem, Mean value theorem and Taylor's theorem.

4. Applies Taylor's series expansion to specified functions.

UNIT –V:RIEMANN INTEGRATION

1. Recalls the definition of Riemann integration.2. Identifies particular classes of integrable functions.3. Proves Fundamental theorem

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALI - 2


MAJOR CORE 8- DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS


No. of hours : 5 Code : U08MA5MCT08No. of credits :4

UNIT I: ORDINARY DIFFERENTIAL EQUATIONS

1. Transforms linear homogeneous equation with variable coefficients to equations with constant coefficients by the transformation z=log x and determines the solution.

2. Determines the solution to the equations reducible to the linear homogeneous equation.

3. Recalls the method of variation of parameters and hence determines the solution.

UNIT II: PARTIAL DIFFERENTIAL EQUATIONS

1. Recognizes the constants or functions present in a solution.2. Recalls the method of eliminating constants or functions from Partial differential

equations. 3. Recalls the definitions of complete, particular and general integrals.4. Recalls the four standard forms of equation and hence determines the solution.5. Identifies Lagrange’s form of partial differential linear equation.6. Recalls the method of solving the Lagrange’s form of partial differential linear

equation.

UNIT III: LAPLACE TRANSFORMS

1. Recalls the definition of Laplace Transforms for functions eat,e -at, cosat, sinat, tn (where n is a positive integer) e-at cosbt, e-at sinbt, e-at tn, f'(t), f''(t)& f(n)(t)

2. Determines the Laplace transforms of the above functions.

UNIT IV: INVERSE LAPLACE TRANSFORMS

1. Recalls the definition of inverse transforms relating to the standard functions.

2. Determines the solution of ordinary differential equations with constant coefficients by using Laplace transforms.

UNIT V: SOLUTION OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS

1. Determine's the complete solution of second order partial differential equation with constant coefficients.

2. Recalls the method of finding complementary function and particular integral for functions of the type eax+by, sin(ax+by), cos(ax+by), xr, ys .

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2.


MAJOR CORE 9 - GRAPH THEORY


No. of Hours : 5 No. of Credits: 4 Code:U08MA5MCT10

UNIT : I1. Recalls the konigsberg Bridge problem and Four colour problem that led to the

discovery of graphs.2. Defines Graphs and subgraphs.3. Recalls some more basic concepts of graph theory with a variety of examples. 4. Recalls the definition of isomorphism between two Graphs 5. Recalls the definitions of Independent sets and covering, 6. Derives the relation between the independence number and covering number.7. Recalls the definition of matrices along with some operation on Graphs.

UNIT - II1. Recalls the definitions of Degree sequence and Partition.2. Defines Graphic sequences and derives the necessary and sufficient condition

for a partition to be graphical3. Defines walks, Trails and paths of a Graph together with some examples.4. Recalls the definitions and the basic properties of connected and disconnected

graphs with related theorems.5. Recalls the definitions of cut point, Bridge and Block of a given graph proving

some related theorems6. Defines two parameters of a graph, its connectivity and edge connectivity.

UNIT: III EULERIAN GRAPH AND HAMILTONIAN GRAPH

1. Defines Eulerian graph and Hamiltonian graph.2. Determines that the Petersen graph is non-hamiltonian.

3. Recalls the definitions of trees, the eccentricity, radius and centre of a tree.

UNIT: IV DIRECTED GRAPHS1. Defines the concept of directed graph, indegree, outdegree and degree pair.2. Recalls the concept of isomorphism, Paths and connectedness of a digraph.3. Defines the various matrices related with digraphs.4. Defines the concept of Tournament.

UNIT: V APPLICATIONS OF GRAPH THEORY1. Applies Kruskal’s algorithm, Dijkstra’s algorithm.2. Defines the concept of Kinematic graph.3. Application of the one way traffic system, Travelling sales man problem and Job

sequencing problem.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2


MAJOR CORE 10 : OPTIMIZATION TECHNIQUES – I


No. of hour : 5 Code :U08MA5MCT12No. of credits :5

UNIT – I: LINEAR PROGRAMMING PROBLEM

1. Recalls the various steps of the mathematical formulation of linear programming problem.

2. Recalls the definition of slack and surplus variables of L.P.P.3. Recognises the canonical and standard from of L.P.P.4. Determines the mathematical formulation of given L.P.P.5. Determines the solution of L.P.P. by graphical method.

UNIT – II: SIMPLEX METHOD

1. Recalls the definition of feasible, basic feasible , degenerate and non-degenerate solutions.

2. Recalls the algorithms of Simplex method, Charne’s method of penalties and Two-Phase method.

3. Determines the solution of L.P.P. by Simplex method, Charne’s method of penalties and Two-Phase method.

UNIT - III: ASSIGNMENT PROBLEM.

1. Recalls the definition of assignment problem, unbalanced assignment problem and Travelling salesman problem.

2. Recalls the algorithm of assignment problem. 3. Determines the assignment schedule using Hungarian method.4. Determines the sequence of minimum cost by Travelling salesman problem.

UNIT - IV: TRANSPORTATION PROBLEM

1. Recalls the definition of transportation problem, initial basic faesible solution, degenerate solution and optimum solution.

2. Recalls the steps of Northwest corner rule, Row minima method, column minima method, Matrix minima method and Vogel’s approximation method.

3. Recalls the steps of u-v method and unbalanced Transportation problem.4. Determines the initial basic feasible solution by using, Northwest corner

rule, Row minima 5. method, Column minima method, Matrix minima method and Vogel’s

approximation method.6. Determines the optimal solution by u-v method .

UNIT – V:SEQUENCING PROBLEM

1. Recalls the definition of sequencing problem.2. Recalls the algorithms of solving sequencing problem.3. Determines the sequences using optimal sequencing algorithms.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2DEPARTMENT OF MATHEMATICS

MAJOR ELECTIVE 2-C PROGRAMMING AND ITS APPLICATION TO NUMERICAL METHODS


No. of hours : 5 Code :U08MA5MET02 No. of credits :5

UNIT –I: INTRODUCTION1. Recalls the definition of constants, variables, data type, operators and

expressions.2. Identifies the types of constants, variables, data types.3. Compares different data types.4. Determine the values of expressions.5. Recalls the definitions of I/O functions.6. Identifies the type of I/O functions to be used in programs.7. Recalls the definitions of character strings.

UNIT – II: DECISION MAKING AND CONTROL STATAMENTS1. Recalls the definitions of different control structures.2. Determines the type of control structure to be used for a given program.3. Classifies the types of control structures.4. Sees relationships between control structures.

UNIT - III: ARRAYS AND STRUCTURES1. Recalls the definitions of arrays, structures and unions.2. Compares different types of arrays.3. Determines the type of array to be used for a given program.4. Determines the type of structure to be used for a given program.

UNIT - IV: USER DEFINED FUNCTIONS1. Recalls the definition of user defined functions.2. Compares procedure and functions.3. Compares different types of parameters used.4. Determines the type of parameter to be used.5. Illustrates the use of parameters.6. Translates the parameters into programs.

UNIT - V: FILE MANAGEMENT1. Recalls the definition of file, types of files.2. Sees relationships between file functions.3. Identifies the type of function to be used in program.

NOTE:1. Regarding the list of programs given in annexure.2. Recalls the algorithm for the Numerical Methods.3. Identifies the algorithm for a given problem.4. Translates the algorithm into programs.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2


SKILL BASED ELECTIVE 4 –PROGRAMMING SKILLS


No. of hours :2 Code : U08MA5SBT04No. of credits :2

UNIT : I

1. Recalls the definition of flow chart and various symbols of flow chart.2. Develop flow charts of specified work.

UNIT : II

1. Recalls the definition of algorithms.2. Write specified algorithms.

UNIT : III

1. Recalls the definition of constants, variable, arithmetic operators, integer and real expressions.

2. Identifies FORTRAN constants & variable, real and integer expressions.3. Recalls precedence of arithmetic operators in expressions.4. Translates mathematical expressions into arithmetic expressions.

UNIT : IV

1. Recalls I/O statements and Assignment statement.2. Recalls BLOCK IF construct.3. Identifies loops in programs.4. Recalls rules regarding BLOCK DO LOOP.

UNIT : V

1. Define & manipulates arrays.2. Identifies READ and PRINT statements in arrays.3. Develops mentioned programs.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 620 002.


NON MAJOR ELECTIVE 1 - QUICK MATHEMATICS


No. of Hours: 2 Code: U08MA5NMT01 No. of Credits:2

UNIT- I:

1. Recalls the definitions of number system,prime numbers and tests of divisibility..2. Determines the solutions in case of addition, subtraction, multiplication and division

of them3. Recalls the definitions of H.C.F and L.C.M.

UNIT- II:

1. Recalls the definition of percentage.2. Recalls the definition of average and solves problems involving averages.

UNIT- III:

1. Recalls the definitions of ratio and proportions2. Solves problems using formulae for profit and loss.

UNIT- IV:

1. Recalls the relationship between time and work and solves problems using formulae.

2. Solves problems involving cisterns and pipes.3. Interprets bar chart and pie diagram.

UNIT- V:

1. Determines the solution in case of time and distance problems.2. Solves problems involving boats and streams, trains.

S.O.L(III & V sem 2015-2016)

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Transcript of S.O.L(III & V sem 2015-2016)