Post on 28-Mar-2018
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
Code Course Title Hours/Week Semester Credits
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
Code Course Title Hours/Week Semester Credits
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.
Code Course Title Hrs/week Semester Credit
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
Hrs/week Semester Credit
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
Hrs/week Semester Credit
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
Hrs/week Semester Credit
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
Hrs/week Semester Credit
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.
Code Course Title Hours/Week Semester Credits
CC7 Modern Algebra 5 V 4
Objective: On successful completion of this course the students will gain knowledge
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
Code Course Title Hours/Week Semester Credits
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)
Code Course Title Hours/Week Semester Credits
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
Code Course Title Hours/Week Semester Credits
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.
Code Course Title Hours/Week Semester Credits
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.
Code Course Title Hours/Week Semester Credits
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.
Objective: On successful completion of this course the students will gain knowledge
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
Code Course Title Hours/Week Semester Credits
CC14 Discrete Mathematics 5 VI 4
Code Course Title Hours/Week Semester Credits
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.
Code Course Title Hours/Week Semester Credits
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
Code Course Title Hours/Week Semester Credits
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.
Code Course Title Hours/Week Semester Credits
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.
Code Course Title Hours/Week Semester Credits
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
Code Course Title Hrs/week Semester Credit
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.