nehru memorial college (autonomous), puthanampatti-621007 b.sc. mathematics … i.pdf · ·...

Nehru Memorial College (Autonomous), Puthanampatti-621007

B.sc. Mathematics- Course Structure under CBCS

(For candidates admitted from 2011-2012 onwards)

Part Sem Course Title Hours Credits Internal External Total

I

I

Tamil 6 3 25 75 100

II English 6 3 25 75 100

III CC1 Major 5 4 25 75 100

CC2 Major 4 4 25 75 100

AC1 Allied 4 4 25 75 100

AC2 Allied 3 - - - -

IV VE 2 2 - 100 100

I

II

Tamil 6 3 25 75 100

II English 6 3 25 75 100

III CC3 Major 6 5 25 75 100

AC2 Allied 3 4 25 75 100

AC3 Allied 5 4 25 75 100

IV EVNS 2 2 - 100 100

SKBC1 2 2 - 100 100

I

III

Tamil 6 3 25 75 100

II English 6 3 25 75 100

IIII CC4 Major 6 5 25 75 100

AC4 Allied 5 4 25 75 100

AC5 Allied 5 4 25 75 100

IV SKBC2 2 2 - 100 100

I

IV

Tamil 6 3 25 75 100

II English 6 3 25 75 100

III CC5 Major 6 5 25 75 100

CC6 Major 5 4 25 75 100

AC6 Allied 5 4 25 75 100

IV SKBC3 2 2 - 100 100

III

V

CC7 Major 5 4 25 75 100

CC8 Major 5 4 25 75 100

CC9 Major 5 4 25 75 100

CC10 Major 6 5 25 75 100

MBEC1A/B Elective 5 5 25 75 100

IV NMEC 4 4 - 100 100

III

VI

CC11 Major 5 5 25 75 100

CC12 Major 5 5 25 75 100

CC13 Major 5 4 25 75 100

CC14 Major 6 5 25 75 100

MBEC2A/B Elective 5 5 25 75 100

IV Comph 4 4 - 100 100

V Extension

Activities

- 1 - - -

Total 180 140 750 2950 3700

Major Based Elective Courses: Non – Major Elective Course

1. Numerical Methods / Astronomy

2. Operations Research / Mathematical Modeling Quantitative aptitude

Code Course Title Hours/Week Semester Credits

CC1 Calculus 5 1 4

Objective: On successful completion of course the students will gain knowledge

about

differentiation, the evolutes and envelopes, different types of integrations,

proper

and improper integration.

Unit 1 Successive Differentiation – Leibnit’z theorem and its applications - Increasing

and decreasing functions – Maxima and Minima of two variables

Unit 2

Pedal Equation- Curvature – Radius of curvature in cartesian and polar

coordinates – Centre of curvature – Evolutes and Involutes

Unit 3

Integration by parts – Definite Integrals – Reduction formulae

Unit 4

Double Integrals – Changing the order of Integration – Triple Integrals

Unit5

Beta and Gamma functions – Relationship between them – Evaluation of integrals

Text Book(s)

1.S.Narayanan, T.K.Manicavachagom Pillay, “Differential Calculus”, Volume I,

S.V.Publications,2000 (Units1,2)

2.S.Narayanan, T.K.Manicavachagom Pillay, “Integral Calculus, Volume II,

S.V.Publications , 2000 (Units3,4,5)

Unit1: Ch3,Ch8 Unit2: Ch10 Unit3: Ch1(11-15.1)

Unit 4: Ch5 Unit5: Ch7(2-5)

References 1. S.Arumugam , A.Thangapandi Isaac “Calculus”, Volume I New Gamma

Publications,1991

2. A. Singaravelu, “ Differential Calculus and Trigonometry” , AR Publications ,2003


CC2

Trigonometry &

Analytical

Geometry

4 I 4

Objective: On successful completion of the paper the students will understood the

concepts of

trigonometry, conics and spheres.

Unit 1

Expansions of sin(nx), cos(nx), tan(nx), sinn(x), cos

n(x) – Expansions of sin(x),

cos(x) and tan(x) in powers of x.

Unit 2

Hyperbolic functions – Relationship between hyperbolic functions and circular

functions – Inverse hyperbolic functions

Unit 3

Logarithm of complex numbers – Factorization

Unit 4 Polar equation of conics – Properties – Equation of a chord – Tangents and

normals – Simple problems

Unit 5

Sphere – Standard Equations – Length of Tangent from any point – Sphere

passing

through a given circle – Intersection of two spheres – Tangent plane

Text Book(s)

1. S. Arumugam, A.Thangapandi Isaac “Theory of Equations and Trigonometry”,

New Gamma Publications, 2006 ( Units1,2,3)

2. T.Natarajan,T.K. Manicavachagom Pillay, ”Analytical Geometry PartI -Two

Dimensions”, S.V Publication,2005 (Unit 4)

3. Shanthi Narayanan. P.K.Mittal, “Analytical Solid Geometry”, S.Chand &

Company

Ltd 2007 (Unit5)

Unit1: Ch6 Unit2:Ch7 Unit3:Ch8,Ch9 (9-9.86)

Unit4: Ch9 (Page99-102) Unit5:Ch4 (5,6.1,7,8)

References

1.P.Durai Pandiyan, Laxmi Duraipandian, D.Muhilan, “Analytical Geometry of Three

Dimensions”,Emerald Publishers, 2003.

2. A. Singaravelu., “Differential Calculus and Trigonometry”, AR Publication, 2003


CC3 Algebra 6 II 5

Objective: On successful completion of the paper the students will understood

the concepts of Theory of equation , Theory of Numbers, Matrices and

inequalities

Unit 1 Relation between roots & coefficients – Symmetric functions – Sum of

the rth

powers of the Roots – Two methods - Transfomations of

Equations – Diminishing, Increasing & multiplying the roots by a constant

– Forming equations with the given roots.

Unit 2

Theory of Numbers – Prime & Composite numbers – divisors of a given

number N – Euler’s function and its value – The highest power of a prime

p contained

in N! .

Unit 3

Congruences – Fermat’s, Wilson’s & Lagrange’s Theorems – Their

applications.

Unit4

Rank of Matrix – Consistency – Eigen values, Eigen vectors – Cayley

Hamilton’s Theorem (statement only)-Symmetric, Skew Symmetric,

Orthogonal, Hermitian, Skew Hermitian,Orthogonal & Unitary Matrices .

Unit 5

Elementary Principles of inequalities-Geometric and Arithmetic means-

Wierstrass’ inequalities -Cauchy inequality.

Text Book(s)

1. T.K.Manicavachagom Pillay, T. Natarajan, K.S.Ganapathy,“Algebra”,

S.V.Publications, 1992, Volumes I & II (Units1,2,4,5)

2. S.Arumugam, A.Thangapandi Issac, “Modern Algebra”, New Gamma Publishers,

1997(Unit3)

Unit 1 :Ch 6( 11 to 14) Unit 2:Ch6( 15 to 18, 20,24) Unit 3 :Ch7(

7.2,7.5,7.6,7.7)

Unit 4 :Ch5( 1 to 10) Unit 5 :Ch5( 12 to 18)

References

1. A.Singaravelu,”Classical Algebra”,Meenakshi Agency,2000

2.S.Arumugam, S.Ramaa,”Classical Algebra”,New Gamma Publisher,2000

Code Course Title Hrs/week Semester Credit

CC4 Sequences and

Series

6 III 5

Objective: On successful completion of this course the students will gain knowledge

about the convergence of sequences and series.

Unit 1 Sequences and their limits - Limit Theorems – Monotone Sequences –

Subsequences and Bolzano – Weirstrass Theorem – The Cauchy Criterion –

Properly Divergent sequences.

Unit 2

Infinite series, its convergence and sum – A necessary condition for the

convergence of an infinite series - Cauchy’s convergence Criterion –

Convergence of positive term series – Geometric series ∑rn - Comparison series -

Comparison Test- D’ Alamberts’ ratio Test – Cauchy’s nth

Root Test.

Unit 3

Raabe’s Test - Logarithmic Test - Cauchy’s Condensation Test – Absolute

Convergence and Conditional Convergence – Alternating Series- Leibnitz’s

Theorem.

Unit4

Binomial Theorem for a rational index – Exponential, Logarithmic series

`(statements only) – Summation of series based on Binomial, Exponential and

Logarithmic series – Approximation (Using Binomial Theorem only).

Unit 5

Sum of n terms of a given series – Summation by difference series – Recurring

series – Sum of n terms of a given recurring series.

Text Book(s)

1. Robert G. Bartle, Donald R. Sherber,” Introduction to Real Analysis”,

Wiley India Third Edition, 2007 (Unit1)

2. Shanti Narayan and M.D.Raisinghania,”Elements of Real Analysis”,S.Chand

Revised Edition 2007(Units 2,3)

3. T.K. Manicavachagom Pillay. T.Natarajan, K.S. Ganapathy, “Algebra”,

S.Viswanathan Publisher,2007 Volume I(Units 4,5)

Unit 1: Ch 3 (3.1, 3.2, 3.3,3.4,3.5:- 3.5.1- 3.5.6 & 3.6) Unit 2: Ch 6 (6.1 -6.12)

Unit 3: Ch 6 (6.13,6.14,6.20) Unit 4: Ch 3 (5,6,10,14) and Ch 4 (2,3,5,7,9,11)

Unit 5: Ch 5

References

1. K.Singal and AshaRani Singal, ” A First course in Real Analysis”,

S.Chand Publishers,2007.

2. S.Arumugam, A.Thangapandi Isaac, ”Sequences and Series”,

New Gamma Publishing Hourse,1999.

3. P.N. Arora and Ranjit Singh, ”First Course in Real Analysis”,

S.Chand Publishers,Third Edition,1981.

Objective: On successful completion of the course the students will gain the

knowledge about the method of solving Differential Equations.

Unit 1 Linear equations – Exact differential equations – Integrating factor - Necessary

and Sufficient Condition – Equations solvable for x,y,p and Clairaut’s equation.

Unit 2 Second order linear equations with constant coefficients and with

variable coefficients - Linear equations reducible to homogeneous linear form –

Variation of parameters – Total differential equation - Condition of Inegrability.

Unit 3 Classification of Integrals – General, Particular, Complete and Singular integrals

- Formation of partial differential equation – Four standard forms – Lagrange’s

Equation - Charpit’s Method.

Unit 4 Higher order homogeneous and non_ homogeneous partial differential equations

with constant coefficients – Particular integrals of F(D,D’) = f(x,y) where f(x,y) =

eax+by

, sin(ax+by), cos(ax+by) ,xr.y

r and e

ax +by h(x,y).

Unit 5 Definition of Laplace Transform - Laplace Transform of standard functions –

Inverse transforms-Solution of ordinary differential equations and simultaneous

equations - Convolution theorem.

Text Book(s)

1.S.Narayanan, T.K.ManicavachagomPillay, “Differential equations”,

S.V.Publications, 1996

( Units1,2,3,5)

2.P.Kandasamy, K.Thilagavaty and K.Gunavathy, “ EngineeringMathematics”,

S.Chand & Company Ltd,1997(Unit4)

Unit 1: Ch 2 (4,6) and Ch 4 Unit 2: Ch 5 (1 -6) and Ch 9

Unit 3: Ch 12 (2,3,4,5.1-5.4,6) Unit 4: Ch 2 (2.17-2.23) Unit 5:Ch 9

References

1. S.Arumugam and A. Thangapandi Isaac,”Differential Equations and its

Applications” ,New Gamma Publication, 2003

2.P.R.Vittal,“Differential equations& Laplace Transforms” Margam Publication,2004.

3. M.D. Rani Singhal “Advanced differential equation”, S.Chand&company Ltd,1999.


CC5 Differential Equations

and Laplace Transform

6 IV 5

Code Course Title

Hrs/week Semester Credit

CC6 VectorCalculus,

Fourier Series& Transforms.

5 IV 4

Objective:On successful completion of this course the students will gain the

knowledge about vector differentiation, vector integration, Fourier series and

Fourier transforms.

Unit 1 Introduction –Scalar and vector point function – Differentiation of vectors –

Differential operators-Directional Derivative –Gradient-Divergence - Curl and

Laplace operator

Unit 2

Introduction – Line ,Surface and Volume Integrals –. Gauss and Stoke’s

Theorems (statements only)– Verifications of these theorems

Unit 3 Differential Operators – Differential of length – Fundamental trial of mutually

orthogonal

unit vectors through any point – Differential operators in terms of orthogonal

curvilinear

co-ordinates –Special curvilinear systems – Spherical polar and cylindrical polar

systems.

Unit 4 Definition of Fourier series – Fourier series expansion of periodic functions of

period2п and 2a-Odd and Even functions – Half range series – Change of

Integrals

Unit 5

Fourier transforms-Integral formula-Fourier Integral theorem-Properties of

Fourier transforms-cosine and sine transforms and their properties-Parsaval’s

identity-convolution theorem.

Text Book(s)

1.P.R.Vittal,V.Malini, “VectorAnalysis”, Margham Publication,2003,(Units1,2)

2.Shanthi Narayanan,”Vector Analysis”, S.Chand Company Ltd,2005(Unit3)

3.S.Narayanan, T.K.Manicavachagom Pillay, “Calculus”, S. Viswanathan

Publishers,1991 Volume I (Units 4,5)

Unit 1: Ch 1 Unit 2: Ch 2 Unit 3: Ch 2

Unit 4: Ch 10(10.18 - 10.22) Unit 5: Ch 13(13.1 - 13.6)

References

1. Jain and Iyangar, “Advanced Engineering Mathematics” Second Edition , Narosa

Publishing House, 2006.

2. A. Singaravelu , “Text Book of Engineering Mathematics” A.R. Publications,1999.

3. Murray R.Spiegel, “Vector Analysis”, McGraw-Hill Book Company.

Code Course Title


Allied IV Probability and

Statistics I

5 III 4

Objective:On successful completion of the paper the students should have understood

the concepts of data interpretation , correlation ,regression, index numbers

and time

series.

Unit 1

Definition of statistics - Types of data- Methods of collecting data - Bar diagram,

Histogram, Ogive, Pie diagram.

Unit 2

Measures of skewness, Karl Pearson’s and Bowley’s coefficients of skewness,

Limits for Bowley’s coefficient - Kurtosis – Karl Pearson’s measures of Kurtosis.

Unit 3

Definition of Correlation - Karl Pearson’s coefficient of correlation- Rank

correlation- Spearman’s rank correlation coefficient- Definition of Regression-

Two lines of Regression- Coefficient of Regression.

.Unit 4

Definition and uses of index numbers- Methods of Constructing Index numbers-

Unweighted aggregate method -Weighted aggregate method- Simple and

Weighted average price relative method.

Unit 5

Definition of Time series and its components- Measurement of Trend- Semi

average method- Curve fitting by the method of least squares.

Text Book: S.C. Gupta ,” Fundamental of Statistics” ,Himalaya Publishing House , April 2004.

Unit 1: Ch 1(1.2), Ch 2( 2.2- 2.) and Ch 4(4.1, 4.2, 4.3: 4.3.1- 4.3.4, 4.4: 4.4.1 - 4.4.3)

Unit 2: Ch 7 (7.2:7.2.1 - 7.2.5, 7.3, 7.4, 7.5, 7.6)

Unit 3: Ch 8 ( 8.1-8.4, 8.7) and Ch 9( 9.1- 9.4)

Unit 4: Ch 10(10.1-10.5)

Unit 5: Ch 11(11.1-11.4, 11.5-11.5.1,11.5.2,11.5.3)

Reference Books: 1. S.C. Gupta and V.K. Kapoor , “Fundamentals of Mathematical Statistics

“,2004.

2. S.P.Gupta , “Statistical methods” ,1997.

3. J.K.Sharma, “Business Statistics” ,Pearson Education, 2004.

Code Course Title


Allied V Probability and

Statistics I

5 III 4

Objective:On successful completion of the paper the students should have understood

the concepts of data interpretation , correlation ,regression, index numbers

and time

series.

Unit 1

Definition of statistics - Types of data- Methods of collecting data - Bar diagram,

Histogram, Ogive, Pie diagram.

Unit 2

Measures of skewness, Karl Pearson’s and Bowley’s coefficients of skewness,

Limits for Bowley’s coefficient - Kurtosis – Karl Pearson’s measures of Kurtosis.

Unit 3

Definition of Correlation - Karl Pearson’s coefficient of correlation- Rank

correlation- Spearman’s rank correlation coefficient- Definition of Regression-

Two lines of Regression- Coefficient of Regression.

.Unit 4

Definition and uses of index numbers- Methods of Constructing Index numbers-

Unweighted aggregate method -Weighted aggregate method- Simple and

Weighted average price relative method.

Unit 5

Definition of Time series and its components- Measurement of Trend- Semi

average method- Curve fitting by the method of least squares.

Text Book: S.C. Gupta ,” Fundamental of Statistics” ,Himalaya Publishing House , April 2004.

Unit 1: Ch 1(1.2), Ch 2( 2.2- 2.) and Ch 4(4.1, 4.2, 4.3: 4.3.1- 4.3.4, 4.4: 4.4.1 - 4.4.3)

Unit 2: Ch 7 (7.2:7.2.1 - 7.2.5, 7.3, 7.4, 7.5, 7.6)

Unit 3: Ch 8 ( 8.1-8.4, 8.7) and Ch 9( 9.1- 9.4)

Unit 4: Ch 10(10.1-10.5)

Unit 5: Ch 11(11.1-11.4, 11.5-11.5.1,11.5.2,11.5.3)

Reference Books: 1. S.C. Gupta and V.K. Kapoor , “Fundamentals of Mathematical Statistics

“,2004.

2. S.P.Gupta , “Statistical methods” ,1997.

3. J.K.Sharma, “Business Statistics” ,Pearson Education, 2004.

Code Course Title


Allied VI Probability and

Statistics III

5 IV 4

Objective: On successful completion of the paper the students will understood

the concepts of estimation ,testing ,sampling, design of experiments.

Unit 1

Types of samples - Characteristics of Estimators- Factorization Theorem

(Statement only) - Methods of estimation- Maximum Likelihood

Estimator- Method of Moments.

Unit 2 Null &Alternative Hypotheses- Degrees of Freedom- Testing of

Hypotheses, Types of errors- Level of Significance - Critical Region-

Critical Value- Sampling of Attributes- Tests of significance for single

proportion , Difference of proportions, single mean, Difference of means,

Difference of standard deviations.

Unit 3 Definition of density function of Chi–square distribution- Constants of the

distribution- Additive property- Test of goodness of fit- Test of

Independence of attributes.

Unit 4

Student’s- t statistic - Definition of density function of student’s-t

distribution - Properties of the distribution-Test for single mean

and difference of means - Paired t –test for difference of means.

Unit 5 F – Statistic- Definition of density function of F variate- Test of Equality

of population variances- Relations between F,t,Chi-square distributions -

Analysis of Variance – One way and Two way classification.

Text Book(s)

1. S.C. Gupta and V.K.Kapoor, “Fundamentals of Mathematical Statistics”,

Educational

Publishers, 2004.(Unit1)

2. S.C.Gupta” Fundamentals of Statistics “ Himalaya Publishing House,

1992.(Unit2,3,4,5)

Unit 1 : Ch 17 (17.2-17.5,17.6 - 17.6.1, 17.6.3)

Unit 2 : Ch 16 (16.6,16.7) and Ch 17(17.1 – 17.4)

Unit 3 : Ch 18(18.1 – 18.6)

Unit 4 : Ch 19(19.1 – 19.7)

Unit 5 : Ch 19(19.10,19.11) and Ch 23( 23.2 – 23.4)

References

1. S.C.Gupta and V.K.Kapoor “ Fundamentals of Statistics”,Himalayan Publishing House

,1992.

2. S.P.Gupta “ Statistical Methods”,Sultan Chand and Co, 1997.

Part IV – No CIA –External Exam for 100 Marks

(For other than Mathematics Students)

Code Course Title


NMEC Quantitative Aptitude 4

V 4

Objective: The objective is to gain the numerical ability and accuracy in mathematical

calculations

Unit 1

Arithmetic Progression - Geometric Progression - Simple interest , compound

interest –

Types of annuities- Present value and amount of annuity.

Unit 2

Ratio – Proportion - Partnership

.

Unit 3

Percentage – Mixture -Profit and Loss .

Unit 4

Time and Work,Time and Distance, Work and Wage

Unit 5

Pipes and Cisterns. Permutations and Combinations

Text Book(s)

1. P.Navaneetham,”Business Mathematics”,Jai Publishers,Trichy21(Unit 1)

2. R.S.Aggarwal,” Quantitative Aptitude for competitive Examinations”,S.Chand

and Co.-

Seventh Revised Edition,2007.(Units 2,3,4,5)

Unit 1:Chapters 4&5 Unit 2: Chapters 10 &11 Unit3 :Chapters

12,13,20 Unit 4: Chapters 15,17 Unit 5: Chapters 16,30

References

1. Ashish Aggarwal,” Quick Arithmetic”S.Chand ,2005.

2. P.N.Arora,”Business Mathematics” Allied Publishers,1985.


CC7 Modern Algebra 5 V 4


about Groups ,Rings, Vector Spaces and linear transformations.

Unit 1

Groups-Subgroups-Normal subgroups-Cyclic groups-Abelian groups-

Factor groups

Unit 2

Rings-Subrings and ideals-Homomorphism and isomorphism of rings-Quotient

Rings-fields

Unit 3

System of Linear Equations-Vector Spaces: Definition and Examples —Vector

subspaces-Basis and Dimension of a Vector Space

Unit4

Lines and Quotient Spaces: definition of a line-Affine Spaces - Quotient Space

Unit 5

Linear Transformations: Definition- Representation of Linear Maps by Matrices-

Kernel and Image of a Linear transformation –Linear Isomorphism- Geometric

ideas and some Loose Ends-Some Special Linear Transformations

Text Book(s) 1. R.Balakrishnan, N.Ramabadhran, “Modern Algebra”, Second revised Edition,

Vikas Publishing House Pvt Ltd, 1994(Units 1,2)

2. S.Kumaresan, “Linear Algebra”, A Geometric Approach, PHI Learning

Pvt Ltd ,2010(Units 3,4,5)

Units 1 & 2 : Chapter 5 & Chapter 6

Units 3,4 & 5: Chapter 1,2 3 & 4

References

1. I.N.Herstein, “Topics in Algebra”, Vani Educational Books, 1986

2. John.B Fraleigh, “A First Course in Abstract Algebra”, 7th Edition ,2002

3. Stephen H. Friedberg, Arnold J.Insel, Lawrence E.Spence, “Linear Algebra”,

4th

Edition, PH publications, 2007


CC8 Real Analysis 5 V 4

Objective: The main objective of this paper is to provide detailed information to students

about

continuity , differentiability and integrability of real functions.

Unit 1

The Algebraic and order properties of R – Absolute value and Real Line – The

completeness property of R – Applications of the supremum property – Intervals.

Unit 2

Definition - Limits of functions – Limit theorems – Some extensions of the limit

concept.

Unit 3 Definition - Combinations of continuous functions – Continuous functions on

Intervals – Uniform continuity – Monotone and Inverse functions.

Unit 4 The Derivative – The Mean value theorem – L’Hospital’s Rule – Taylor’s

theorem – Applications of Taylor’s theorem.

Unit 5 Definition - Riemann Integrable functions – Darboux’s theorem-Conditions for

integrability-Properties of integrable functions- Continuity and Derivability-First

Mean Value theorem–Fundamental theorem of Calculus.

Text Book(s) 1. Robert G.Bartle, Donald R.Sherbert, “Introduction to Real Analysis”, 3

rd

Edition, Wiley India,2007(Units 1,2,3,4)

2. Shanthi Narayanan, “Elements of Real Analysis”, S.Chand & Company Ltd,

2007(Unit5)

Unit 1 : Ch 2 Unit 2: Ch 4 Unit 3: Ch 5 (5.1, 5.2, 5.3, 5.4.1, 5.4.2,

5.4.3, 5.6)

Unit 4: Ch 6 (6.1, 6.2, 6.3, 6.4.1, 6.4.2, 6.4.3) Unit 5: Ch 13 (13.1-13.15)

References

1. M.K Singal, Asha Rani Singal, “A First course in Real Analysis”,S.Chand &

Co,2003.

2. Tom. M. Apostal, “Mathematical Analysis”,2ndEdition, Narosa Publishing

House,1974.

(For the candidates admitted from the academic year 2011-2012 onwards)

Objective: On successful completion of the course the students should have learnt Basics

of C,Control structures , Functions in C , OOPs Concepts, class structure, control

structures in C++ and, Functions in C++.

C Programming

Unit 1

Evaluation and Applications of C – Structures of c programs- Data types-

Declaration –Operators- Expression- Built in Function

Unit 2

Data Input & Output – Control Statement – If else – else if ladder- GOTO-Switch

–While-Do While- For-Break & Continue

Unit 3

Functions- Definition & Accessing functions- Storage classes arrays –passing

arrays to functions –Strings- String functions – String Manipulation

C++ Programming

Unit4

Principles of Object Oriented Programming:-OOP paradigam-Concepts, Benefits

of OOP-Applications of OOP- Introduction to the Basic Concepts of

C++Language-Structure of C++ program-Tokens, Keywords, Identifiers, Data

types,Variables,manipulators-Expressions-Dynamic initialization of

variables, referencevariables- operators- control structures- Functions:-Main

function- function proto-typing- Call by reference- Return by reference-constant

arguments- Inline functions- default arguments- Function overloading

Unit 5

Classes and objects- Array of objects- - Over loading unary and binary operators-

(+,-,*,/)- Inheritance- Single, multiple Hierarchial and Hybrid Inheritance.

Text Book(s)

1.E.Balagurusamy, “Programming in ANSI C “,4E, Tata McGraw-Hill Education

Pvt Ltd, 2009(Units 1,2,3)

2 . E.Balagurusamy, “Object Oriented Programming with C++”, Third Edition,

Tata McGraw-Hill Education Pvt Ltd, 2006(Units 4,5)

Unit 1: Ch 1 (1.8), 2(2.7-2.9), 3(3.2-3.16)

Unit 2 : Ch 4(4.4,4.5), 5(5.2-5.9), 6(6.2-6.4)

Unit 3 : Ch 7(7.2-7.7), 9(9.2-9.9,9.17,9.18)

Unit 4 : Ch 1(1.4,1.6,1.8), Ch 2 (2.1-2.7), Ch 3,Ch 4

Unit 5 : Ch 5, Ch 7(7.1-7.4, 7.7), Ch 8(8.1-8.8)


CC9 Programming in

C and C++ 6 V 5

References 1.Ron Gotlfried and Schaum,” Programming in C”,

Tata McGraw-Hill Publications

2.Yeshwant Kanetkar, Let Us C++, BPB Publications, 1999


CC10 C and C++ Lab 5 V 4

Objective: This course gives the practical training in Programming in C and C++.

C Programming Lab

1. Solution of a Quadratic equation

2. Sum of Series (sine, cosine, ex)

3. Ascending and Descending order of numbers using Arrays (Use it to find Largest and

Smallest Numbers)

4. Sorting of names in Alphabetical order

5. Matrix Operations (Addition, Subtraction, Multiplication – using functions)

6. Finding factorials, generating Fibnoacci numbers using recursive functions

7.Finding mean,median ,mode and standard deviation.

8.Newton- Raphson , Bisection Method of solving equations.

9.Gauss elimination method, Gauss Seidel Method of solving simultaneous equations.

10.Trapezoidal rule, Simpson’s 1/3 rule of integration.

11. Lagrange’s Method of interpolation.

12.R-K fourth order method of solving Differential equations.

C++ Programming

1. Programs implementing – OOPs Concepts, Control Structures,Looping Structures,

Arrays.

2. Classes and Objects, Constructor and Destructor.

3. Constructor Overloading, Function Overloading.

4. Basics of Inheritance.


CC11 Complex

Analysis 5 VI 5

Objective: On successful completion of the paper the students will gain knowledge about

the types of singularity of a complex function,contour integrals.

Unit 1

Functions of a Complex variable –Limits-Theorems on Limits –Continuous

functions – Differentiability – Cauchy-Riemann equations – Analytic

functions –Harmonic functions.

Unit 2

Elementary transformations - Bilinear transformations – Cross ratio – fixed points

of Bilinear Transformation – Some special bilinear transformations .

Unit 3

Complex integration - definite integral – Cauchy’s Theorem –Cauchy’s integral

formula –Higher derivatives.

Unit 4

Series expansions- Taylor’s series –Laurent’s Series – Zeroes of analytic

functions – Singularities .

Unit 5

Residues – Cauchy’s Residue Theorem –Evaluation of definite integrals .

Text Book

S.Arumugam,A.Thangapandi Isaac,& A.Somasundaram, “Complex Analysis”,

New

Scitech Publications (India) Pvt Ltd, 2002.

Unit 1: Chapter 2 (Section 2.1 - 2.8 )

Unit 2 :Chapter 3 (Sections 3.1 - 3.5 )

Unit 3:Chapter 6 (Sections 6.1 -6.4 )

Unit 4:Chapter 7 (Sections 7.1 - 7.4 )

Unit 5:Chapter 8 ( Sections 8.1 - 8.3 )

References

1. T.K.Manicavachagom Pillay, Complex Analysis, S.Viswanathan Publishers Pvt

Ltd, 1994.

2.Shanthi Narayan, P.K.Mittal, “Theory of Functions of Complex Variable” S.Chand

&Company

Ltd, Revised 8th

edition 2005.


CC12 Graph Theory 5 VI 5

Objective:To introduce the basic concepts in Graph theory.

Unit 1 Introduction – Finite and Infinite graphs – Incidence and degree – Isolated

vertex, Pentant vertex, null graph – Isomorphism – Subgraphs – Walks, Paths

and Circuits – Connected graphs, Disconnected graphs and Components – Euler

graphs – Hamiltonian paths and circuits.

Unit 2

Tree-properties-Pendent vertices in a tree- Distance and Centre in a tree- Rooted

and Binary Trees – Spanning Trees – Fundamental circuits – Spanning Trees

in a weighted graph.

Unit3

Cut set – Some properties of a cut set – All cut sets in a graph – Fundamental

circuits and cut sets – planar graphs – Different representations of a planar

graph – Detection of planarity.

Unit4

Incident Matrix - Submatrices of G – Circuit Matrix- Adjacency matrix.

Unit 5

Chromatic Number Chromatic partitioning – Chromatic polynomial

Matching-Coverings - The four color problem.

Text Book

Narasingh Deo,” Graph Theory with Applications to Engineering and

Computer Science” ,Prentice Hall of India Pvt. Ltd. , 1997

Unit 1: Chapter 1 and 2 ( 1.3 to 1.5, 2.1, 2.2, 2.4 to 2.6 and 2.9)

Unit 2: Chapter 3(3.1 to 3.5, 3.7 to 3.8, 3.10)

Unit 3: Chapter 4(4.1 to 4.4, 5.2, 5.4, 5.5)

Unit 4: Chapter 7(7.1 to 7.3, 7.6, 7.8, 7.9)

Unit 5 : Chapter 8

References

1. Harary,”Graph Theory”, Narosa Publishing House,1989

2. S.Arumugam “Invitation to Graph Theory “,ScitechPublishers,2001

Course Title Hours/Week Semester Credits

CC13 Mechanics 6 VI 5

Objective: On successful completion of the course the students will gain a basic

knowledge of

the behavior of various types of forces and and the behaviour of objects in

motion.

Unit 1 Triangle of forces – Resolution of force – Parallel Forces and Moments.

Unit 2 Couples – Equilibrium of two couples – Resultant of coplanar couples – Three

coplanar forces.

Unit 3 Friction – Types of Friction – Laws of friction – Equilibrium of a body on a

rough indexed plane – Equilibrium of strings – Equation of the common catenary

– Geometrical properties – Parabolic catenary – Suspension Bridge.

Unit 4

Newton’s Laws of motion– projectiles – path of a projectile – characteristics of

the motion of a projectile – velocity of the projectile – Range on and inclined

plane – motion on the surface of a smooth inclined plane – Simple Harmonic

Motion in a straight line – composition of two simple Harmonic motions.

Unit 5 Collision of Elastic Bodies – Definitions – Fundamental Laws of Impact – Direct

and oblique of two smooth spheres – loss of Kinetic energy due to direct and

oblique impact of two smooth spheres. Motion under a central force –

Differential Equation of central orbits – Pedal equation of the central orbit –

Velocities in a central orbit – Given

the orbit to find the law of force to the pole.

Text Book(s) 1.M.K.Venkataraman,”Statics”,AgasthiarPublications,2000,(Units1,2,3)

2.M.K.Venkataraman,”Dynamics”,AgasthiarPublications, ,2006,(Units4,5)

Unit 1: Ch 1,2 and 3 Unit 2: Ch 4 and 5 Unit 3: Ch 7(1 – 12) &Ch

11

Unit 4: Ch 4 (4.1 – 4.3), Ch 6(6.1 – 6.16), Ch10 (10.1 – 10.7) and Ch 7(7.1 , 7.2)

Unit 5: Ch 8 (8.1 – 8.9) and 11 (11.5 – 11.11)

References

1. S.L.Loney ,”Elements of Statics & Dynamics”, A.I.T.B.S.Publishers, 1991

2. P.Duraipandian,Laxmi Duraipandian, Muthamizh Jayapragasam, “Mechanics”,

S.Chand&Company Ltd,2006.


about the

Mathematical logic , Lattices, Boolean Algebra, Coding Theory and

Difference

Equations.

Unit 1

Mathematical logic:Propositions-Connectives-Atomic and Compound Statements-

Tautology and Contradiction- Normal Forms- Theory of inference – Rules of

inference -Predicate Calculus: Quantifiers-Free and bound variables – Inference

Theory of Predicate Calculus .

Unit 2

Lattices- Properties of Lattices- some special Lattices- Boolean Algebra –

Principle of duality- Boolean expressions and Boolean functions.

Unit3 Mathematical Induction-Recurrence Relation and Generating Function.

Unit 4

Coding Theory:Encoders and Decoders – Group code-Hamming codes-error

correction in group codes- procedure for decoding group codes

Unit 5 Combinatorics:Introduction-Permutations and Combinations- Pascal’s Identity-

Vandermonde’s Identity- Permutations with repetition – Circular Permutation-

Pigeonhole Principle- Generalisation of the Pigeonhole Principle- Principle of

Inclusion-

Exclusion.

Text Book

1. T.Veerarajan, “Discrete Mathematics with Graph Theory and Combinatorics”,

Tata McGraw-Hill Publishing Company Ltd,2007

Unit 1: Chapter 1(Page 1- 49 ) Unit 2: Chapter 2(Page 96-108)

Unit 3:Chapter 6(Page 342-362) Unit 4: Chapter 5(Page 290- 307)

Unit 5: Chapter 6(Page 314- 337)

References

1. M.K.Venkataraman, .N.Sridharan and N.Chandrasekar, “Discrete Mathematics”

The National Publishing Company, 2000.

2. J.P. Tremblay and Manohar, “Discrete Mathematical Structures with Application

to Computer Science”, Tata McGraw-Hill,2000


CC14 Discrete Mathematics 5 VI 4


MBEC1a Numerical

Methods 5 V 5

Objective:On successful completion of this course the students will gain knowledge

about the

basic concepts in Numerical methods and their uses.

Unit1 Iterative methods – Bisection Method – False position method – Newton-

Raphson method - Solution of Simultaneous Linear Algebraic Equations- Gauss

Elimination, Gauss- Jordan , Gauss- Jacobi and Gauss- Seidel iterative methods.

Unit 2 Definition – Forward and backward differences – Newton’s formula for

interpolation – Operators – Properties and relationship among them – Missing

terms and summation of series – Montmort’s theorem.

Unit 3 Divided differences – Newton’s divided difference formula – Lagrange’s

interpolation formula – Inverse interpolation.

Unit 4

Numerical Differentiation and Integration - Trapezoidal and Simpson’s 1/3 rule –

Difference equations and Methods of solving.

Unit 5 Taylor’s series – Euler’s method – Modified Euler’s method – Runge Kutta

methods – Picard’s method of successive approximation – Predictor and Corrector

methods – Milne’s and Adam’s Bashforth Methods.

Text Book P.Kandasamy, K.Thilagavathy, K.Gunavathi, “Numerical Methods”,S.Chand

Company Ltd, Revised edition,2005.

Unit 1: Ch 3(3.1 to 3.4), 4(4.1, 4,2, 4.7 to 4.9)

Unit 2: Ch 5(5.1 to 5.8)

Unit 3: Ch 8(8.1 to 8.3, 8.8)

Unit 4: Ch 9(9.2, 9.3, 9.9, 9.13)

Unit 5: Ch11(11.5, 11.8, 11.9, 11.11-11.13, 11.16-11.18)

References

1. S.Narayanan, S.Viswanathan, “ Numerical Analysis”,1994.

2. S.S.Sastry, “Introductory Methods of Numerical Analysis” PHI,1995.


MBEC1b Astronomy 5 V 5

Objective: To introduce the exciting world of astronomy to the students.

Unit 1

Celestial sphere and diurnal motion-Celestial coordinates-Siderel time

Unit 2

Morning and Evening stars-circumpolar stars-Zones of Earth-Perpetual day-

Twilight

Unit3

Refraction-Laws of Refraction-Tangent formula-Horizontal Refraction-Geocentric

parallax

Unit 4

Kepler’s laws- Anomalies- Kepler’s equations- Calendar

Unit 5

Moon – sidereal and synodic minths- Elongation-Phase of moon-Eclipses –Umbra

and penumbra-Lunar and solar eclipses- Maximum and minimum number of eclipses in a

year.

Text Book

Kumaravel.S and Susheela Kumaravel, “Astronomy” , S.K.V Publication,

8th edition,1993

Unit1: Sec:39-79 Unit 2:Sec :80-90,106-116 Unit

3:Sec:117-144

Unit 4:Sec:146-162,173-178 Unit 5: Sec:229-241 , 256-275


MBEC1c Fuzzy theory 5 V 5

Objective: To become familiar with the fundamental concepts of fuzzy set theory and

fuzzy logic.

Unit 1

Definitions – Different types of Fuzzy sets – Properties of Fuzzy sets- Other

important

operations- General Properties of Fuzzy Vs Crisp

Unit 2

Introduction – Some important Theorems- Extension principle for Fuzzy sets-

Fuzzy

Compliments- Further operations on Fuzzy sets.

Unit 3

Introduction- Projection and cylindrical Fuzzy relations- Composition-Properties of

Min –

Max compositions- Binary relations on a single set- Compatibility relation.

Unit 4

Introduction- Fuzzy measures- Evidence theory – Probability measure- Possibility

and

Necessity measures.

Unit 5

Introduction – Individual decision making – Multiperson decision making-

Multicriteria

decision making-Fuzzy Ranking method- Fuzzy Linear Progamming.

Text Book

Pundir and Pundir,”, Fuzzy sets and their applications”, A Pragati edition,2006

Unit 1:Chapter 1(1.16-1.21) Unit 2:Chapter 2 (2.1-2.5) Unit 3:Chapter 4(4.1-

4.6)

Unit 4: Chapter 5(5.1-5.5) Unit 5:Chapter 9(9.1- 9.6)

Reference George J.Klir and Bo Yuan, “Fuzzy sets and Fuzzy logic theory and

Applications”, PHI, New Delhi 2002

Objective: This course gives emphasis to enhance student’s knowledge in Linear

Programming

Problem, Transportation Problem, Assignment Problem, Sequencing, optimal

use of

Inventory and Network scheduling with application.

Unit 1 Introduction to OR- Standard form of L.P.P - Simplex method with less

than, greater than, equality Contraints- Duality- Dual Simplex

method.

Unit 2 Mathematical Formulation– Finding IBFS – Moving towards optimality -

Degeneracy in Transportation Problem – Transportation algorithm –

Unbalanced Transportation problem – Assignment problem –

Mathematical formulation of Assignment Problem – Assignment

algorithm – A typical assignment problem – Routing problem.

Unit 3

Network and Basic concepts – Logical Sequencing – Rules of Network

construction – Critical path Analysis – Probability considerations in

PERT-Time and cost- Distinction between CPM and PERT.

Unit 4 Problem of sequencing – Processing of n Jobs through two machines –

Processing of n Jobs through k machines – Processing of 2 Jobs through k

machines – Replacement of equipment – Asset that Deteriorates gradually

– Replacement of Equipment that fails suddenly.

Unit 5

Variables in an inventory problem- Inventory control with known

demand- Purchasing model with and without shortages- Manufacturing

model with and without shortage- Inventory control with uncertain

demand- Buffer stock and safety stock model

.Text Book

Kantiswarup, P.K.Gupta, Manmohan, “Operation Research”, Sultan Chand and

Sons,1999.

Unit1:Ch1&2 Unit2:Ch3 Unit3:Ch6,7,22(22.1-22.3)

Unit4:Ch10(10.1-10.5),Ch19(19.1-19.5) Unit5:Ch18(18.1-18.10),Ch21.

References

1. R. Panneer Selvam , “Operations Research”,PHI,2003.

2. H.A. Taha, “Operations Research”, PHI,2004.


MBEC2a Operations Research 5 VI 5

Code Course Subject Hours/Week Semester Credits

MBEC2b Mathematical

Modelling 5 VI 5

Objective: To get an idea of what mathematical modelling is about.

Unit1

Mathematical modeling through ordinary differential Equations – Linear growth

and Decay models – Non-linear growth and decay models – Compartment Models

– Problems in Ordinary Differential Equations of First Order – Geometrical

Problem.

Unit 2 Mathematical modeling in Population Dynamics – Modelling of Epidemics –

Compartment models – Modelling in Economics – Models in Medicine, Arms,

Race, Battles and International Trade – Models in Dynamics.

Unit 3 Mathematical Modelling of Planetary motions - Circular motion and motion of

Satellites – Modelling through Linear Differential Equation.

Unit 4 Some simple models – Basic theory of Linear Difference equations with

constant coefficients – Economics and Finance – Population, Dynamics and

Genetics in Probability theory.

Unit 5 Situations that can be modeled through Graphs – Models in terms of Directed

graph – signed graph and weighted Digraphs.

Text Book 1. J.N.Kapur, “Mathematical Modelling”, New Age Iinternational (P) Ltd,2005

Unit 1: Ch 2 Unit 2: Ch 3 Unit 3: Ch 4

Unit 4: Ch 5 Unit 5: Ch 7

References

1. Pundir and Pundir, “Bio-Mathematics” Pragati Prakashan,Ist Edition,2006.

2.Bhupendra Singh, “Bio Mathematics”, Krishna Prakashan media, 2005.

3.J.N. Kapoor, “Mathematical Modelling in Biology and Medicine” East West

Press,

1985.


MBEC2c Number Theory 5 VI 5

Objective:The purpose of this course is an introduction to Diophantine equations,

congruences, Euler's function, and residue systems. Unit 1

Euclid’s Division lemma- Divisibility- The linear Diophantine equation-

Fundamental

theorem of Arithmetic.

Unit 2

Permutations and Combinations- Fermat’s Little Theorem- Wilson’s Theorem-

Generating

Functions

Unit 3

Basic properties of congruences – Residue Systems

Unit 4

Chinese remainder Theorem – Polynomial Congruences- Combinatorial study of

F(n)

Unit 5

Formulae for d(n) and s(n)- Multiplicative Arithmetic function- Mobius inversion

formula

Text Book

George E.Andrews , “Number Theory”, Hindustan Publishing Corporation, 1984

Unit 1:Chapter 2(2.1-2.4) Unit 2: Chapter 3(3.1-3.4) Unit 3 Chapter

4(4.1,4.2)

Unit 4: Chapter 5&6(5.3-5.4,6.1) Unit 5:Chapter

6(6.2,6.3)

Reference

K.C.Chowdhury, “A first Course in Theory of Numbers”, Asian Books Pvt. Ltd

1st edition,2004

Part IV – No CIA –External Exam for 100 Marks


Part IV Comprehensive

Course

4 VI 4

Syllabus:

All the syllabi that are included in CC1 to CC14 (Totally 14 Courses).

Objective type questions in the form

“Choose the Correct answer”

100 questions covering all the units of the 14 said courses.

nehru memorial college (autonomous), puthanampatti-621007 b.sc. mathematics … i.pdf · ·...

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