s.o.l even sem

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 2.

DEPARTMENT OF MATHEMATICS

MAJOR CORE 2 – MUTIVARIATE CALCULUS

SPECIFIC OUTCOMES OF LEARNING

Code: U15MA2MCT02No of Hours:5No of Credit:4

Classical Algebra:

Unit - I : Theory of equations1. Relates roots and coefficients2. Identifies the reciprocal equations.3. Transforms the given equation into another with the given condition.4. Determines the roots of the given equation.

Unit II: Theory of numbers1. Identifies the divisors of a number N.2. Recalls Fermat's theorem, Wilson's theorem and Lagrange's theorem.3. Determines the division of a given number, their sum, their product.

Trigonometry:

UNIT - III :Expansions and Approximations:-1. Recalls and derives the expansions for Sin , Cos2. Determines the expansion of Cos n , Sin n , tan n, Sin n, Cos n.3. Calculates the approximate value.

Unit – IV:Hyperbolic functions1. Recalls definitions of hyperbolic functions2. Relates and compares circular functions and hyperbolic functions3. Establishes the relationship between hyperbolic functions4. Recalls the relationship between inverse hyperbolic functions and logarithmic functions.5. Separates functions into real and imaginary parts.

Logarithm of complex numbers1. Recalls the definition of logarithm of a complex number.2. Determines the general value of logarithm .

Unit – V: Summation of Trigonometric Series

1. Identifies the type of trigonometric series2. Evaluates the sum.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2.


MAJOR CORE 3: ANALYTICAL GEOMETRY OF THREE DIMENSIONS AND VECTOR CALCULUS


No. of Hours : 5 No. of Credits: 5 Code:U08MA2MCT03 UNIT – I PLANES AND STRAIGHT LINES-Recalls the formulae for the distance between two points, area of a triangle, point of internal and external division in the given ratio and derermines them.-Recalls the definitions of direction cosines, direction ratios and standard forms of equations of plane.-Determines the equation of plane in various situations, in the form P + P1=0 and the birector planes.-Recalls the equations of a straight line and different forms of equation of straight lines and the angle between the plane and the straight line an determines them.-Identifies coplanar lines.-Determines the shortest distance between two skew lines &-Determines the equation of skew lines.

UNIT – II SPHERE-Recalls the equations of the sphere, equation of the sphere in the form S + S1 = 0 and S + P = 0 and the equation of the tangent plane.-Determines the radius, the centre and the equation of the sphere.

UNIT – III VECTOR DIFFERENTIATION-Recalls the definitions of vector point function, scalar point functions, derivatives of a vector, velocity and acceleration.-Determines velocity and acceleration.-Recalls the definitions of the vector differential operators, gradient, divergence and curl.-Determines the directional derivatives.-Recognises solenoidal and irrotational vectors.-Recalls the vector identities.

UNIT – IV VECTOR INTEGRATION-Recalls integration of vector functions.-Recalls and evaluates line integral, surface integral and volume integral.-Determines work done by a force and conservative field

UNIT – V INTEGRAL THEOREMS-Recalls Gauss' divergence theorem, Green's theorem and Stoke's theorems.-Evaluates integrals using Gauss divergence theorem, Greens theorem and Stoke's theorem.

HOLY CROSS COLLEGE (AUTONOMOUS)TIRUCHIRAPPALLI_2

DEPARTMENT OF MATHEMATICS.

ALLIED 3: MATHEMATICAL STATISTICS - III


Code:U10MA2ACT08No of Hours:4No of Credits3

UNIT : I

SAMPLING DISTRIBUTIONS- Recalls the definition of chi- square, t and F variables.- Determines the p.d.f. of chi- square, t and F distributions .- Identifies the various distributions and determines moments UNIT : IIESTIMATORS AND ESTIMATIONPoint Estimation :- Identifies the various Charactersitis of a good estomator.- Identifies Cramer Rao inequality.-Recalls Rao - Blackwell theorem.- Determines estimators by method of moments and M.L. estimators.

INTERVAL ESTIMATION :

- Determines Confidence interval for the mean of the normal population, for the differences between means, for proportions of population, for the difference between two proportions.

UNIT : IIILARGE SAMPLES:Reca- lls the definitions of null hypothesis, region of acceptance and rejection.- Identifies the test to be applied and formulates the hypothesis.- Estabilishes the validity of the hypothesis based on normal distribution.

UNIT : IV SMALL SAMPLES:- Recalls the defenitions of 't' & 'F' distributions.- Identifies the test to be applied then formulate the hypothesis.- Determines the validity of the hypothesis based on 't' & 'F' distributions.

UNIT : VCHI –SQUARE TEST:- Recalls the definition of chi-square test, Recalls pearson's statistics.- Determines test for a specified population variance.- Determines the goodness of fit and indepence of attriburtes.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI -2


ALLIED 3- ALLIED MATHEMATICS III


No. of. Hours:4 Code U10MA2ACT09 No. of. Credits:3

UNIT : IPARTIAL DIFFERENTIAL EQUATIONS1. Recalls the definition of partial differential equation 2. Determines the partial differential equation from the solution 3. Recalls the definitions of general, particular, complete and singular integrals 4. Identifies the four standard forms of partials differential equation and determines the solution.5. Recognises Lagrange's equations and determines the solution.

UNIT : IILAPLACE TRANSFORM1. Recalls the definition of Laplace Transform.2. Determines Laplace transform of the functions.

UNIT : IIIINVERSE LAPLACE TRANSFORM1 Recalls the definition of Inverse Laplace transforms related to the above functions.2. Determines the solution of ordinary differential equations by using Laplace transforms.

UNIT : IV MESURES OF DISPERSION AND CORRELATION1. Recalls definitions of range, quartile, mean and standard deviation.2. Determines the above measures of dispersion.3. Recalls the definitions of Karl Pearson’s coefficient of correlation and Spearman’s rank correlation.4. Determines the correlation using the formulae.

UNIT :VREGRESSION AND TESTING OF HYPOTHESIS1. Recalls the definition for regression and their properties.2. Determines equations to lines of regression.3. Recalle the definitions of types of samples and parameters.4. Identifies the type of test.5. Concludes on testing of hypothesis.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 2


ALLIED 3: BUSINESS STATISTICS


No of Hours:4No of Credits:3

Code: U08MA2ACT10UNIT : I 1. Recalls the definitions of statistics in singular and plural form.2. Recalls the definitions of primary and secondary data.3. Indentifies different methods of collecting primary data.4. Recalls the sources of secondary data.5. Recalls the precautions to be taken while using secondary.6. Recalls the definitions of classification and tabulation.7. Recognises different types of classification and tabulation.8. Transforms the given data into diagrams and graphs.UNIT : II1. Identifies different types of series.2. Recalls the definitions of various measures of dispersion. 3. Recalls the formulae for various measures of dispersion.4. Determines various measures of dispersion.UNIT : III1. Recalls the definitions of positive and negative correlations.2. Determines coefficient of correlation using Kart-Pearson's formulae.3. Recalls the definitions of rank correlation-with and without ties.4. Determines coefficient of rank correlation using Spearman's formula.5. Recalls the definition and equations of regression lines.6. Estimates the value of X or Y, given the value of Y or X respectively, using regression equations.UNIT : IV1. Recalls the definitions of time series, components of time series, semi-average, moving

average, seasonal average, method of least squares and measures of seasonal variations.2. Determines the trend line using graphic method, method of semi-average, moving average.3. Determines seasonal indices using average method link relative method.UNIT : V1. Recalls the definitions of index numbers, unweighted aggregate price index, weighted

aggregate price index, Laspeyre’s, Paasche's, Fisher's index numbers.2. Determines the above mentioned index numbers.3. 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.4. Determines the above mentioned index numbers.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI -2


ALLIED 3: APPLIED MATHEMATICS II


Code: U08MA2ACT11No of Hours:4No of Credits:3

UNIT : I Recalls the definition of Transportation problem.Recalls the algorithms for North West Corner Rule, Vogel's Approximation method, and Matrix Minima Method.Translates the algorithms into problem solving.UNIT : IIRecalls the definition of an Assignment problem.Recalls Hungarian Algorithm.Determines the optimum solution for Assignment problemUNIT : III -Recalls the Formulae of mean, median and mode -Determines the above measures for the given distribution after identifying the type of distributionRecalls the Formulae of range, quartile deviation, mean deviation, standard deviation, coefficient of variation.- Determines the above measures for the given distribution after identifying the type of distribution.- Determines coefficient of variation and compares two given distribution and establishes the relationships from the given data.- Recalls the concept of skewnessUNIT : IV Recalls the definition of attributes, classes and class frequencies Recalls the inadependence of attributes, association of attributes, Yule's coefficient of association and determines them.- Recalls the definition of simple correlation.- Determines correlation coefficient and establishes the relationship between the variables.- Recalls the definition of rank correlation.- Assigns ranks to data.- Determines rank correlation coefficient and establishes relationship between variables.UNIT :VLARGE SAMPLES:- Recalls the definitions of null hypothesis, region of acceptance and rejection.- Identifies the test to be applied and formulates the hypothesis.- Establishes the validity of the hypothesis based on normal distribution.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI-2


ALLIED 3 - BUSINESS MATHEMATICS AND STATISTICS FOR MANAGERS


No. of hours: 4 Code: U08MA2ACT12No. of credits: 3

UNIT-I:APPLICATION OF DIFFERENTIATION

Recalls the derivatives of xn, ex and logx and determines the derivatives of above functions.Recalls the definition of total cost,average cost and marginal cost and determines them.Recalls the definition of total,average and marginal revenue and determines them.Recalls the definition of maximum and minimum values of total cost, average cost, marginal cost and total revenue, average revenue, marginal revenues and determines them.

UNIT II:TRANSPORTATION AND ASSIGNMENT PROBLEM

Recalls the definition of Transportation Problem.Recalls the steps of of North West Corner Rule, Vogel’s Approximation Method, Row Minima Method, Column Minima Method. Computes the initial solution by the above methods.Recalls the definition of Assignment problem. Recalls Hungarian algorithm for solving assignment problem.Computes the optimal solution for a given assignment problem..UNIT III:COLLECTION AND PRESENTATION OF DATA

Recalls the definitions of primary and secondary data.Identifies different methods of collecting primary data.Recalls the sources of secondary data.Recalls the precautions to be taken while using secondary data.Recalls the definitions of classification and tabulation.Recognises different types of classification and tabulation.Transforms the given data into diagrams and graphs.

UNIT IV:MEASURES OF DISPERSION AND CORRELATION

Recalls the definitions of various measures of dispersion such as Range, Quartile deviation,Mean deviation,Standard deviation.Recalls the formulae for Range, Quartile deviation, Mean deviation, Standard deviation and determines them.Recalls the definition of positive and negative correlations.Determines the Coefficient of Correlation using Karl Pearson's formulae.Recalls the definition of Rank Correlation.Determines the coefficient of rank correlation using Spearman's formulae.

UNIT V:INDEX NUMBERS

Recalls the definition of weighted aggregate price index,Paasche's ,Fisher's,Boweley's Price indices.Determines the above mentioned index numbers.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.Determines the above mentioned index numbers.



MAIN CORE 6 – ALGEBRA


No. of Hours : 5 No. of Credits: 5 Code:U08MA4MCT06

UNIT - I GROUPS:

- Recalls the definition of cosets.- Recalls the proof of Lagrange's theorem.- Recalls the definitions of normal subgroups and quotient groups and related theorem.

- Recalls the definitions of isomorphism and homomorphism and proves the fundamental theorem of homomorphism.

UNIT - II RINGS :

- Recalls definitions of rings, types of rings, subrings, ideals, quotient rings, homomorphism and isomorphism of rings.- Identifies the type of rings.- Sets up homomorphism and isomorophism between rings.- Develops quotient rings.- Proves Fundamental Theorem of Homomorphism of Rings.

UNIT - III : VECTOR SPACES:

- Recalls the definitions and examples of vector spaces, linear transformation, span of a set and linear independence.- Determines the span of a set and linear independence of vectors.

UNIT - IV : VECTOR SPACES (continued)

- Recalls the definitions of basis dimension, rank and nullity of a linear transformation.- Determines basis, dimension of a vector space and also rank and nullity of a linear transformation.- Determines the matrix of a linear transformation given the transformation and viceversa.

UNIT V : INNER PRODUCT SPACES:

- Recalls the definitions of inner product spaces, norm of an element, orthogonality, orthogonal complement and orthonormal set.- Identifies inner product space.- Computes the norm of an element.- Checks for orthogonality.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2


MAJOR ELECTIVE 1- NUMERICAL METHODS


No. of hour: 5 Code: U08MA4MET01 No. of Credits: 5

UNIT – I: SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS.

- Solution of Algebraic and Transcendental Equations.- Recognises algebraic and transcendental equations.- Recalls the Bisection method, Iteration method, False position method and Newton Raphson method.- Determines the solution of the equation by bisection method, Iteration , False position method and Newton Raphson method.

UNIT – II: INTERPOLATION

- Recalls the definition of interpolation, forward and Backward differences. - Recalls Newtons formulae for forward, backward interpolation, central differences interpolation formulae. Gauss's, stirling's ,Bessel's, Everette's formulae.- Recognises the definition of interpolation with unevenly spaced points and Recalls the Lagrange's interpolation formula.- Determines the value of Y at X by using Lagrange's interpolation formula .

UNIT – III:NUMERICAL DIFFERENTIATION AND INTEGRATION

- Recognises differentiation and integration of a function.- Recalls Numerical differentiation, maximum and minimum values of a tabulated function, Numerical integration.- Recalls the Trapezoidal rule and simpson's 1/3 rule.- Determines the differential coefficient by Newton's forward and backward fromula.- Determines the maximum and minimum values of a tabulated function.- Determines the integral value by using Trapezoidal rule and Simpson's 1/3 rule.

UNIT – IV: SOLUTION OF LINEAR SYSTEMS OF EQUATIONS

- Recalls the definition of matrix and their types.- Calculates rank of a matrix, inverse of a matrix.- Examines consistency of a linear system of equations.- Calculates the solution of linear systems by using Gaussian elimination, Gauss Jordon Gauss Seidel and Gauss Jacobi methods.

UNIT –V: NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS - Identifies Initial value problem.- Recalls the formula of Taylor's series, Euler's, Modified Euler's, Runge kutta II order and IV order method, predictor - corrector, .- Determines the value of Y by using Taylor's series, Euler's Modified, Euler's Runge - Kutta, II and IV order,

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2.


ALLIED 5- ANALYTICAL GEOMETRY OF THREE DIMENSIONS ANDVECTOR CALCULUS AND LAPLACE TRANSFORMS


No.of Hours:4 Code:U11MA4AOT19No.of Credits:4

UNIT – I:PLANES-Recalls the formulae for the distance between two points, area of a triangle, point of internal and external division in the given ratio and determines them.-Recalls the definitions of direction cosines, direction ratios and standard forms of equations of plane.-Determines the equation of plane in various situations, in the form P + P1=0 and the bisector planes.

UNIT - II:STRAIGHT LINES -Recalls the equations of a straight line and different forms of equation of straight lines and the angle between the plane and the straight line an determines them.-Identifies coplanar lines.-Determines the shortest distance between two skew lines.-Determines the equation of skew lines.

UNIT – III:VECTOR DIFFERENTIATION-Recalls the definitions of vector point function, scalar point functions, derivatives of a vector, velocity and acceleration.-Determines velocity and acceleration.-Recalls the definitions of the vector differential operators, gradient, divergence and curl.-Determines the directional derivatives.-Recognises solenoidal and irrotational vectors.-Recalls the vector identities.

UNIT – IV:LAPLACE TRANSFORMS

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) and determines the laplace transforms of the above functions.

UNIT – V:INVERSE TRANSFORMSRecalls the definition of inverse transforms relating to the above standard functions - Determines the solution of ordinary differential equations with constant coefficients by using Laplace transforms

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002.DEPARTMENT OF MATHEMATICS

ALLIED 5:DECISION MAKING TECHNIQUES.SPECIFIC OUTCOMES OF LEARNING

No. of Hours:4 Code:U11MA4AOT23 No. of Credits:4

UNIT I:LINEAR PROGRAMMING PROBLEM - Recalls the method of formulating a problem as linear programming problem. -Recogonizes the method of solving a L.P.P graphically. -Recalls the definitions of objective functions, constraints, non negative restrictions, solution, feasible solution and optimal solution.

UNIT - II:GAME THEORY

- Recalls the definition of two person zero sum games.- Recalls the maximin and minimax principle.- Recalls the definition of saddle point.- Determines the saddle point for the given pay-off matrix.- Recalls the concept of mixed strategy.- Recalls the method of solving problems with mixed strategy.- Recalls the graphical method of solving 2xn and mx2 games and determines the value of the game.

UNIT : III:TRANSPORTATION PROBLEM

- Recalls the definition of Transportation problem- Initial basic feasible solution of Transportation problem- Recalls North west corner rule, row minima, matrix minima method and Vogel's pproximation method of finding initial basic feasible solution- Recalls the definition of unbalanced TP- Determines the initial basic feasible solution of unbalanced TP.- Determines the initial basic feasible solution which maximizes the profit

UNIT – IV:INVENTORY CONTROL- Recalls the definition of inventory control.- Recalls the definitions of various costs in inventory control.- Recalls the definition of E.O.Q. and determines E.O.Q. for Economic Lot Size problems.

-Recalls Deterministic inventory Problem- Determines E.O.Q. problems with price breaks.

UNIT – V:NETWORK MODELS- Recalls the definition of NETWORK, PERT, CPM.- Determines the graphic representation.- Determines critical path for a given network.- Determines the different times required to find critical path.- Determines Expected value and variance using PERT calculations

HOLY CROSS COLLEGE(AUTONOMOUS),TIRUCHIRAPALLI-620002DEPARTMENT OF MATHEMATICS

ALLIED 5: FORMAL LANGUAGES AND AUTOMATA THEORY


No of Hours :4No of credits:4 CODE:U11MA4AOT24

UNIT-I:Defines basic structure of grammarFormation of different grammarsExplains phase structure languages and hierarchyProves preliminary theorems.Introduces the concept of ambiguity.

UNIT-II:Introduces the concept of context free grammarProves related theoremsExplains finite state automaton.Defines regular grammar.

UNIT-III:Introduces the concept of Automata with examples.Defines DFA and NFA.Proves equivalence of DFA and NFA.Explains regular grammar and expressions.Explains automata with ε moves.

UNIT IV:Defines push-down automata.Defines informal description of push down automata.Proves related theorems.Introduces context free languages.

UNIT V:Proves related context free languagesIntroduces pumping lemma for CFL’SRecalls properties of CFL particularly closure properties.

Explains theorems of closure property of CFL’S.

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

ALLIED 6 : NUMERICAL AND STATISTICAL METHODSSPECIFIC OUTCOMES OF LEARNING

No. of Hours: 4No. of Credits: 3 Code: U11MA4AOT25

UNIT – ISOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS- Solution of Algebraic and Transcendental Equations.

- Recognises algebraic and transcendental equations.

- Recalls the Bisection method, False position method, Newton Raphson method.

- Determines the solution of the equation by bisection method, False position method, Newton Raphson

method

UNIT - II - INTERPOLATION

- Recalls Newtons formulae for forward, backward interpolation.

- Recognises the definition of interpolation with unevenly spaced points and Recalls the

Lagrange's inverse interpolation formula.

- Determines the value of Y at X by using Lagrange's interpolation formula, and X at Y by

using Lagrange's inverse interpolation formula.

UNIT - III

NUMERICAL DIFFERENTIATION AND INTEGRATION

- Recognises differentiation and integration of a function.

- Recalls Numerical differentiation, maximum and minimum values of a tabulated function,

Numerical integration.

- Recalls the Trapezoidal rule and simpson's 1/3 rule.

- Determines the maximum and minimum values of a tabulated function.- Determines the integral value by

using Trapezoidal rule and simpson's 1/3 rule.

Unit IV

MEASURES OF DISPERSION

- Recalls the definitions of range, quartile deveiation, mean deviation, standard

deviation, coefficient of variation.

- Determines the above measures for the given distribution after identifying the type of

distribution.

- Determines coefficient of variation and compares two given distribution and

establishes the relationships from the given data.

Unit V

CORRELATION

- Recalls the concept of skewness.

- Determines Karl Pearson’s coefficient of skewness and Bowley’s coefficient of

skewness

- Recalls the definitions of moments.

- Determines moments ant measures of skewness

- Recalls the definition of correlation and scatter diagram.

- Recalls and determines Karl Pearson’s and Spearman’s correlation coefficients.



ALLIED 6- INTERNET AND WEB DESIGNING


No of Hours:4No of Credits:3

CODE:U11MA4AOT26 UNIT I:

Determines the various protocols used in the Internet.Compare the features of FTP, Gopher and WWW.Determines the circuit connection for Internet connectivity.Illustrates the facilities of shell, TCP/ IP accounts and ISDN services.Analyze the bandwidth of telephone cables.Sees relationship between dial up & leased line connection.Determines the concept of Internet Explorer and Netscape Navigator.

UNIT II: Recalls the history and generations of HTML. Develop a homepage using various tags. Creates HTML documents using hyperlinks. Illustrates the concept of hot text using anchor tags. Determines the various attributes of head and body section.UNIT III:

Creates a web page using Heading printing Images and pictures Aligning the headings Horizontal rule Paragraph indent and break Tab settings

Determines the concept of an image map.Determine the different methods to list the items in an HTML document.

UNIT IV:Develop HTML codes for showing table in a Web Page.Deals with tables in which a cell may span several rows or columns.Discuss the cell width and height specifications.Defines DHTML, style sheets and its elements.Determines the various methods of linking style sheets to an HTML document.

UNIT V:Develop a HTML document using frameset tag.Develops a tool to improve user interface in the web.Designing a web page using form tag.

Illustrates the various attributes of the form tag.

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

ALLIED 6 : NUMERICAL METHODS AND TESTING OF HYPOTHESISSPECIFIC OUTCOMES OF LEARNING

No. of Hours: 4No. of Credits: 3 Code: U11MA4A0T27

UNIT – ISOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS- Solution of Algebraic and Transcendental Equations.

- Recognises algebraic and transcendental equations.

- Recalls the Bisection method, False position method, Newton Raphson method.

- Determines the solution of the equation by bisection method, False position method, Newton Raphson

method

UNIT - II - INTERPOLATION

- Recalls Newtons formulae for forward, backward interpolation.

- Recognises the definition of interpolation with unevenly spaced points and Recalls the

Lagrange's inverse interpolation formula.

- Determines the value of Y at X by using Lagrange's interpolation formula, and X at Y by

using Lagrange's inverse interpolation formula.

UNIT - III

NUMERICAL DIFFERENTIATION AND INTEGRATION

- Recognises differentiation and integration of a function.

- Recalls Numerical differentiation, maximum and minimum values of a tabulated function,

Numerical integration.

- Recalls the Trapezoidal rule and simpson's 1/3 rule.

UNIT :IVLARGE SAMPLES:- Recalls the definitions of null hypothesis, region of acceptance and rejection.- Identifies the test to be applied and formulates the hypothesis.- Establishes the validity of the hypothesis based on normal distribution.- Recalls chi-square test for 2 X 2 contigency table

UNIT : V SMALL SAMPLES:- Recalls the defenitions of 't' & 'F' distributions.- Identifies the test to be applied then formulate the hypothesis.- Determines the validity of the hypothesis based on 't' & 'F' distributions.


DEPARTMENT OF MATHEMTICS

MAJOR CORE 11-THEORY OF FUNCTIONS OF A COMPLEX VARIABLE

SPECIFIC OUTCOMES OF LEARNINGNo of Hours:6No of Credits:5 Code: U08MA6MCT14

UNIT – I- Recalls the definitions of the complex number. - Recalls the definitions of continuous functions.- Recalls the definitions of differentiability.- Defines an analytic function and Harmonic functions.- Recalls the necessary & sufficient condition for a function to be analytic. - Derives Cauchy-Riemann equations. - Determines analyticity – C-R equations and Harmonic functions.

UNIT – II- Defines elementary transformation bilinear transformation, cross ratio and fixed points of bilinear transformation.- Identifies some special type of bilinear transformations.

UNIT – III - Definition of Complex integration. - Derives Cauchy’s Theorem, Cauchy’s Integral Formula. - Proofs of Higher derivatives of an analytic functions. - Recalls the Cauchy’s inequality theorem for fn(Zo), Liouville’s theorem,Morera’s theorem. - Evaluates integrals using above theorems.

UNIT – IV- Recalls the statements and proof of Taylor’s Theorem and Laurent’s Theorem – determines the

expansions of various functions using sthe above theorems –- Recalls the definitions of singular points- Recognises types of singular points.- Recalls proofs of theorems on poles and zeros.- Recalls the definition of Meromorphic function.- Determines the nature of singular points.

UNIT - V - Recalls the definition of the residue at a pole.- Evaluates the residue at a pole.- Recalls the statement and proof of Cauchy’s Residue Theorem.- Determines the principle of argument.- Recalls the statement & proof of Rouche’s Theorem.

- Evaluates integrals of types ∫0

2π

f (cos , sin)d and ∫−∞

∞g(x )h (x)

dx

- Recalls the definition and proof of Jordan’s Lemma.

- Evaluates integrals of types and ∫−∞

∞g(x )h (x)

Cos ax dx and ∫−∞

∞g(x )h (x)

Sin ax dx



MAJOR CORE 12-OPTIMIZATION TECHNIQUES - II

SPECIFIC OUTCOMES OF LEARNINGNo. of hours:6 Code:U08MA6MCT15No. of credits:5

UNIT - I- Recalls the definition of two person zero sum games.- Recalls the maximin and minimax principle.- Recalls the definition of saddle point.- Determines the saddle point for the given pay-off matrix.- Recalls the concept of mixed strategy.- Recalls the method of solving problems with mixed strategy.

- Recalls the graphical method of solving 2xn and mx2 games and determines the value of the game.- Recalls the dominance property and determines the solution.

UNIT – II- Recalls the definition of Queueing Theory and the characteristics of a Queue.- Recalls the poission and exponential distribution.- Recalls the classification of Queues.- Recalls Poisson queues and their characteristics.- Identifies the given problem and determines the different characteristics.

UNIT – III- Recalls the definition of inventory control.- Recalls the definitions of various costs in inventory control.- Recalls the definition of E.O.Q. and determines E.O.Q. for Economic Lot Size problems.- Recalls the definition of shortages and determines E.O.Q. for problems with shortages.- Determines E.O.Q. for multi-item deterministic problem. -Determines E.O.Q. for purchase inventory problems with price breaks.

UNIT – IV- Recalls the techniques of inventory control.- Determines E.O.Q. for multi-item deterministic problem.-Determines E.O.Q. for probabilistic inventory problems

UNIT - V- Recalls the definition of NETWORK, PERT, CPM.- Identifies a problem and determines the graphic representation.- Determines critical path for a given network.- Determines the different times required to find critical path.



MAJOR CORE 12 –PROGRAMMING IN C++


No of Hours: 6 No of Credits: 5 Code:U08MA6MCT16

UNIT – I:BEGINNING WITH C++

- Recalls the definition of tokens , keywords , identifiers and constants.- Identifies the basic, user-defined and derived data types.- Compares different data types.- Determine the types of expressions.

- Recalls the definitions of operators.- Identifies the type of operators to be used in programs.- Recalls the definitions of different control structures.- Classifies the types of control structures.- Sees relationships between control structures.

UNIT - II:FUNCTIONS,CLASSES AND OBJECTS

- Recalls the types of functions.- Compares the functions in C and C++.- Identifies the type of function to be used in a program.- Determines the reference variables.- Determines friend and virtual functions.- Determines how to specify classes and objects.- Defines data members and member functions.- Translates a C++ program with class.- Determines the type of arrays within a class. UNIT - III: CONSTRUCTORS,DESTRUCTORS AND OPERATOR OVERLOADING - Defines Constructors and destructors.- Sees relationships between types of constructor.-Defines Operator overloading.-Recalls the type of conversions.-Identifies the overloading of unary and binary operators.- Identifies the type of function to be used in program.

UNIT- IV:INHERITANCE AND CLASSES

-Defines derived classes and nesting of classes.-Determines the various types of inheritance..

UNIT- V:I/O OPERATIONS AND FILE FUNCTIONS

-Determines managing console I/O operations.- Recalls the definition of file, types of files.- Sees relationships between file functions.

HOLY CROSS COLLEGE(AUTONOMOUS),TRICHIRAPALLI-2


MAIN CORE 13- INTRODUCTION TO FUZZY MATHEMATICS.


CODE:U08MA6MCT17No of Hours:6No of Credits:5UNIT I:1.Recalls the definitions of fuzzy sets,fuzzy numbers.2.Recalls the definitions of crisp set( α- cuts) associated with fuzzy set.3.Recalls the relationship between fuzzy sets and fuzzy numbers.4.Recognizes the Extension principle.

UNIT II:1.Recalls the definition of union of fuzzy sets.2.Recalls the definitions of intersection and compliment of fuzzy sets.3.Determines the union ,intersection , compliment of fuzzy sets.

UNIT III:1.Recalls the definition of fuzzy relation.2.Recalls the definition of basic operations on fuzzy relation.3.Recalls the definition of α- cuts of fuzzy relations.4.Recognizes the projections,cylindrical extensions.

5.Determines the α- cuts,projections,cylindrical extensions.

UNIT IV:1.Recalls the definition of fuzzy logic.2.Recalls the definitions of linguistic variable.3.Recognizes the three valued logic, N valued logic, and infinite valued logic.4.Determines the propositions using three valued logic.5.Recalls the definition of rule reasoning and proposition.

UNIT V:1.Recalls the definition of fuzzy methods. 2.Recalls the definition of classical control theory.3.Recalls the fuzzy control theory.4.Recognizes the FLC.5.Determines the formulation of FLC.

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPALLI – 620 002


MAJOR CORE 13- INTRODUCTION TO VISUAL BASIC

SPECIFIC OUT COMES OF LEARNING

No. of hours:6 Code : U08MA6MCT18No. of credits:5UNIT I:Introducing visual basic:

Recalls how to Start and Exit Visual Basic Identifies the use of Project Explorer, Properties Window and Tool Box Recalls how to work with Forms and Projects

Using intrinsic visual basic controls: Identifies the use of Label, Textbox, Command Button, Frame, Check Box, Option Button, Listbox,

Combobox, Drive Listbox, Directory Listbox, File Listbox, Formatting Controls, Control Arrays, Tab Order

UNIT II:Variables in Visual Basic:

Identifies the variables, data types, scope of variable and arrays. Understanding the code window, procedure, subroutines and function

Using control statements: Identifies the use of If, If else, For, Do While and select case statements.

UNIT III:Using working with files:

Identifies file system controls, types of file and Reading a files. Identifies Random access file, operations of files. Identifies the accessing object’s properties.

Using menus in visual basic applications: Recalls how to Create Menus and adding tool bar in your Application.

UNIT IV:Multiple forms:

Understanding MDI form features of an MDI form Understanding to Active form property, Active child property. Understanding the common dialog box, Rich text box, Changing the color of the selected text

UNIT V:Database programming with visual basic:

Understanding Database Working with Visual Data Manager. Recalls data control, bound control and database grid control. Understanding Jet database engine and its functions. Introducing SQL and working with Data Access Object Model.



MAJOR ELECTIVE 3–DYNAMICS

SPECIFIC OUTCOMES OF LEARNING No of Hours:5

No of Credits:5 CODE:U08MA6MET03

UNIT: I- Recalls the definition of force, momentum and Newton’s laws of motion.- Recalls the derivation of motion of a particle on a rough horizontal plane, up a rough inclined plane.- Determines the different types of motion of connected particles.- Determines the solution of the given problem using laws of motion.

UNIT II:- Recalls the definitions connected with projectiles.- Determine the maximum horizontal range, directions of projection with a horizontal range and range

on an inclined plane.- Determines velocity of the projectile in magnitude and direction at the end of time‘t’.- Determines solution to the given problems using motion of projectiles on a horizontal plane.

UNIT III:

- Determines the range, greatest distance, maximum range of the projectile on an inclined plane.- Recalls directions of projections on an inclined plane. - Determines the solution of the given problems using motion of projectiles on an inclined plane.

UNIT I V:

- Recalls the definition of the impulse of force, impulsive force, coefficient of elasticity, fundamental laws of impact.

- Recalls the derivation of the impact of a smooth sphere on a fixed smooth plane, direct impact of two smooth spheres, laws of kinetic smooth spheres, oblique impact of two smooth spheres.

- Determines the solution of the given problem using impact of two bodies, collision of elastic bodies.

UNIT V:- Recalls the definition of harmonic motion in a straight line.

- Determines the general solution of the simple harmonic motion equation.- Recalls the composition of two simple harmonic motions.- Determines the solution of the given problem using simple harmonic motion.


DEPARTMENT OF MATHEMATICSNME 2- ART OF PROGRAMMING


No. of hours :2 Code : U08MA6NMT02No. of credits :2

UNIT : I1. Recalls the definition and various symbols of flow chart.2. Develop flow charts of specified work.

UNIT : II1. Recalls the definition of algorithms.2. Write specified algorithms.

UNIT : III1. Recalls the definition of constants , variable, arithmetic operators,intger and real expressions.2. Recalls the various intrinsic functions.3. Identifies FORTRAN constants & variable , real and integer expressions.4. Recalls precedence of operators in expressions.5. Translates mathematical expressions into arithmetic expressions.

UNIT : IV1. Recalls comment statement , I/O statements and Assignment statement.2. Recalls relational operators , BLOCK IF construct.3. Identifies loops in programs.

4. Recalls rules regarding BLOCK DO LOOP.

UNIT : V1. Define & manipulates arrays.2. Identifies elementary Format specifications for READ and PRINT statements3. Develops mentioned programs.

s.o.l even sem

Documents

given equation

definitions of vector

equation of plane

unit iv vector integration

u08ma2mct03 unit

equation of skew lines

vector differentiation

vector identities