PERIYAR UNIVERSITY

SALEM – 11

M.Sc., ( CA ) Syllabus for candidates admitted from the academic

year 2008 – 2009 and thereafter under Choice Based Credit System
( CBCS )

[ Semester Pattern with Continuous Internal Assessment ]

1
 BOARD OF STUDIES

1. Thiru. K. Rangasamy, Chairman

Lecturer in Mathematics ( SG ),
Government Arts College (M),
Krishnagiri – 635 001.

2. Tmt. P. Sivagami, Member

Lecturer in Mathematics ( SG ),
NKR Govt.Arts College,
Namakkal.

3. Thiru. N. Krishnakumar, Member

Lecturer in Mathematics ( SG ),
Kandaswami Kandar’s College,
Paramathy Velur – 638 182.

4. Thiru. M. Subahchandra Bosh, Member

Lecturer in Mathematics ( SG ),
Govt.Arts College (Autonomous )
Salem – 636 007.

5. Dr. C. Selvaraj, Member

Reader in Mathematics,
Periyar University,
Salem – 11.

6. Thiru. R. V. M. Rengarajan, Member

Lecturer in Mathematics,
Sengundar Arts & Science College,
Tiruchengode – 637 205.

7. Dr. Rajan, Member

Reader in Mathematics,
Erode Arts College ( Autonomous),
Erode.

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 PERIYAR UNIVERSITY, SALEM – 11
FACULTY OF SCIENCE
M.SC., DEGREE COURSE
(SEMESTER SYSTEM)
BRANCH – I(C): MATHEMATICS (Computer Applications)
( Choice Based Credit System )
REGULATIONS AND SYLLABUS
(with effect from 2008-2009 onwards)

1. Objectives of the course:

Mathematics to-day is penetrating all fields of human endeavor and it is
necessary to train the students to scope with the advanced developments in various
fields of Mathematics. The objectives of this application oriented post-graduate
course are the following:
(a) To import knowledge in advanced concepts and applications in various
branches of Mathematics.
(b) To orient the students in the application aspects of computer in solving
mathematical problems.
2. Eligibility for Admission:
A candidate who has passed B.Sc., Mathematics/ B.Sc., Mathematics
(Computer Applications) degree of this University or any of the above degree of any
other University accepted by the Syndicate as equivalent thereto, subject to such
condition as may be prescribed therefore shall be permitted to appear and qualify for
the Master of Science (M.Sc.,) Degree Examination in Mathematics (Computer
Applications) of this University after a course of study of two academic years.
3. Duration of the Course:
The course of study of Master of Science in Mathematics (Computer
Applications) shall consist of two academic years divided into four semesters. Each
semester consists of 90 working days.
4. Course of Study:
The course of study shall comprise instruction in the following subjects according to
the syllabus and books prescribed from time to time.

3
 M.Sc Mathematics (CA)
(For the candidate admitted from the year 2008 onwards)

Core Marks
Sem PaperCode Core Course Hrs Credit
Course CIE EA Total

I P08MACA01 Algebra 6 5 25 75 100

II P08MACA02 Real Analysis 6 5 25 75 100

I III P08MACA03 Differential Equations 6 5 25 75 100

IV P08MACA04 Discrete Mathematics 6 5 25 75 100
Principles of Programming and Information
V P08MACA05 Technology 6 5 25 75 100
VI P08MACA06 Numerical Analysis 6 5 25 75 100
VII P08MACA07 Complex Analysis 6 5 25 75 100
II VIII P08MACA08 Mathematical Statistics 6 5 25 75 100
IX P08MACA09 C++ Programming and Data Structure 6 5 25 75 100

X P08MACAP01 C++ Programming and data structures Practical 4 4 40 60 100

XI P08MACA10 General Topology 6 5 25 75 100
XII P08MACA11 Differential Geometry 6 5 25 75 100
III XIII P08MACA12 Optimization Techniques 6 5 25 75 100
XIV P08MACA13 Graph Theory 6 5 25 75 100
XV P08MACA14 Functional Analysis 6 5 25 75 100
XVI P08MACA15 Measure Theory and Integrations 6 5 25 75 100
XVII P08MACA16 Java Programming 6 5 25 75 100
IV XVIII P08MACAP02 Java Programming Practical 6 4 40 60 100
XIX Elective (To be chosen from the list) 6 5 25 75 100
XX P08MACA03 Project 6 6 100 100
Total 90 2000

PaperCode Elective

P08MACAE01 Fuzzy sets and their applications

Sem
P08MACAE02 Number Theory

P08MACAE03 Database Technology

P08MACAE04 Fluid Dynamics

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5. Examinations:
The examination shall be of THREE HOURS duration for each paper at the
end of each semester. The candidate failing in any subject(s) will be permitted to
appear for each failed subjects(s) in the subsequent examination.
Practical examinations for PG course should be conducted at the end of the
even semester only.
At the end of fourth semester viva-voce will be conducted on the basis of the
Dissertation/ Project report submitted by the student. The viva-voce will be conducted
by one internal and one external examiner.
6. Question paper pattern:
Question paper pattern for Theory Examination
Time: Three Hours Maximum Marks: 75
Part – A (5x5 = 25 Marks)
Answer ALL questions
Two questions from each unit with internal choice
Part – B (5 x 10 = 50 Marks)
Answer ALL questions.
Two questions from each unit with internal choice
#########
Question paper pattern from Practical Examination
Time: 3 Hours Maximum Marks: 100
Passing Minimum: 50 Marks (Aggregate of examination and Record)
Practical Examination: 60 Marks
CIA: 40 Marks
(No passing minimum for records)
There will be one question with or without subsections to be asked for the
practical examination. Every question should be chosen from the question bank
prepared by the examiner(s). Every fourth student should get a new question i.e. each
question may be used for at most three students.

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7. Dissertation:
(a) Topic:
The topic of the dissertation shall be assigned to the candidate before the
beginning of third semester and a copy of the same should be submitted to the
University for approval.
(b) No. of copies of project/dissertation;
The students should prepare three copies of dissertation and submit the same
for the evaluation by Examiners. After evaluation one copy is to be retained in the
college library and one copy is to be submitted to the University (Registrar) and one
copy can be held by the student.
Format to be followed:
The formats/certificate for project/dissertation to be submitted by the students
is given below:
Format for the preparation of project work:
(a) Title page
(b) Bonafide Certificate
(c) Acknowledgement
(d) Table of contents
CONTENTS
Chapter No. TITLE Page No.
1. Introduction
2. Title of the Chapters
3. Conclusion
4. References

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Format of the Title Page:
TITLE OF THE PROJECT/DISSERTATION
Project/Dissertation Submitted in part fulfillment of the requirement for the Degree of
Master of Science in MATHEMATICS to the Periyar University, Salem – 636 011
By
Student’s Name :
Register Number :
College :
Year :

Format of the Certificate:

CERTIFICATE
This is to certify that the dissertation entitled ……………….. submitted in part
fulfillment of the requirement of the degree of Master of Science in Mathematics
(Computer Applications) to the Periyar University, Salem is a record of bonafide
research work carried out by ……………… under my supervision and guidance and
that no part of the dissertation has been submitted for the award of any degree,
diploma, fellowship or other similar titles or prizes and that the work has not been
published in part or full in any scientific or popular journals or magazines

Date:
Place: Signature of the Guide

Signature of the Head of the Department

7
Guidelines for approval of PG guides for guiding students in their research for
submitting project / dissertation:
A person seeking for recognition, as guide should have:
(a) A Ph.D. degree or M.Phil/ M.A. / M.Sc., degree with first class / second class
and
(b) Should have 3 years of active teaching / research experience
8. Passing Minimum
The candidate shall be declared to have passed the examination if the
candidate secures not less than 50% marks (i.e. 38 marks) in the University
examination in each paper and not less than 50% marks (i.e. 12 marks) in the
Continuous Internal Assessment
For the Practical paper, a minimum of 50 marks out of 100 marks in the
University examination and the record notebook taken together is necessary for a
pass. There is no passing minimum for the record notebook. However submission of
record notebook is a must.
For the Project work and viva-voce a candidate should secure 50% of the
marks for pass. The candidate should attend viva-voce examination to secure a pass in
that paper.
Candidate who does not obtain the required minimum marks for a pass in a
paper Project Report shall be required to appear and pass the same at a subsequent
appearance.
9. Classification of Successful Candidates
Candidates who secure not less than 60% of the aggregate marks in the whole
examination shall be declared to have passed the examination in First Class.
All other successful candidate shall be declared to have passed in the Second
Class.
Candidates who obtain 75%of the marks in the aggregate shall be deemed to
have passed the examination in the First Class with Distinction provided they pass
all the examinations prescribed for the course at the first appearance.
Candidates who pass all the examinations prescribed for the course in the first
instance and within a period of two academic years from the year of admission to the
course only are eligible for University Ranking.
10. Maximum Duration for the completion of the PG Programme:

8
 The maximum duration for completion of the PG Programme shall not exceed
eight semesters.
11. Commencement of this Regulation:
These regulations shall take effect from the academic year 2008-09, that is, for
students who are admitted to the first year of the course during the academic year
2008-09 and thereafter.
12. Transitory Provision:
Candidates who were admitted to the PG course of study before 2008-2009
shall be permitted to appear for the examinations under those regulations for a period
of three years, that is, up to and inclusive of the examination of April / May 2011.
Thereafter, they will be permitted to appear for the examination only under the
regulations then in force.

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 CORE COURSE – I P08MACA01
Algebra
Unit I:
Another counting principle, Sylows theorem, Direct product, Finite abelian
groups(Chapter 2 Sections 2.11 to 2.14)
Unit II:
Ring theory: Polynomial rings – rings over rational field; rings over commutative
ring(Chapter 3 Sections3.9 to 3.11)
Unit III:
Vector spaces and modules vectorspaces – Dual spaces – Inner product spaces;
modules. (Chapter 4 Sections 4.3 to 4.5)
Unit IV:
Field theory: Extension field – roots of polynomials; more about roots(Chapter 5
Sections 5.1, 5.3 and 5 .5)
Unit V:
Galois Theory: Elements of Galois theory – Solvability by radicals. Galois groups
over the rational (Chapter 5 Section 5.6, 5.7 and 5.8)
Text book:
I.N Herstein : Topics in Algebra 2nd Edition John Wiley and Sons New York 2003.
Reference:
1.S.Lang Algebra 3rd Edition Addison Wesley, Mass 1993.
2. John B.Fraleigh – A first course in abstract Algebra - Addison Wesley Mass 1982.
3. M.Artin Algebra Prentice Hall of India New Delhi 1991.

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 CORE COURSE – II P08MACA02
Real Analysis
Unit I:
Functions of bounded variations: Introduction, Properties of monotonic
functions, functions of bounded variation, Total Variation, Additive property of total
variation, Total variation on [a,x], Functions of b.v. expressed as the difference of
increasing functions. Continuous function of b.v(6.1 to 6.8)
Unit II:
The Riemann-Stieltjes Integral: Introduction Notation, The definition of R.S
Integral, Linear properties, Integration by points, change of variable in R.S Integral,
Reduction of a R.I, Euler’s Summation formula, Monotonically increasing
integrations, upper and lower integrals, additive and linearity property of upper and
lower integral, Riemarri’s Condtion (7.1 to 7.13)
Unit III:
Sequence of functions: Power series, Multiplication of power series, The
substations theorem, The Taylor’s series generated by a function, Bensteiri’s
Theorem, The binomial series, Abel’s limit theorem, Tauber’s Theorem (9.14 to 9.16
; 9.19 to 9.23)
Unit IV:
The Lebergue Integral: Introduction, The integral of a step function,
Monotonic sequence of step functions, Upper functions and their integrals, The class
of L.I function on a general interval, Basic properties of L.I Lebergue Integration and
sets of measure zero. The Levi motor convergence theorems, The Lebessgue
Dominated convergence Theorem (10.1 to 10.4 ; 10.6 to 10.10)
Unit V:
Fourier Series and Fourier Integrals: Introduction Orthogonal System of
functions, The theorem on best approximation, The F.S of a fum relative to an
orthonormal system. Properties of F.C, The Riesz Fircher theorem The Rieman-
Lebergue lemma, The Dirichlet intergns, An integral representation for the partial
sums of F.S Riemann’s localization theorem, Ceraro summabiltity of F.S
Consequences of Fejor’s theorem, the Weiostrass approximation theorem (11.1 to
11.2 except 11.7, 11.12)

11
Text Book
Tom M. Apostal, Mathematical Analysis 2nd edition Narason Publishing
House Delhi, Bombay, Madras.
Reference Book
R.Goldberg, Methods of Real Analysis Oxford & IBH Publishing Co. Pvt Ltd
New Delhi & Kolkata.

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 CORE COURSE – III P08MACA03
Differential Equations
Unit I:
General Solution of Homogeneous Equation:
The general solution of the Homogenous Equation – The use of known solution to
find another – The method of variation of parameter – Power series solutions.
(Chapter 3 : Sections 15,16,17,19) (Chapter 5: Sections 26,27)
Unit II:
Power Series Solutions:
Regular – Singular Points – Gauss’s Hyper geometric equation – The point at infinity
– Legendre Polynomial – Bessel functions – Properties of Legendre’s Polynomials –
Bessel Functions. (Chapter 5 : Sections 28-31) (Chapter 6 : Sections 32-35)
Unit III:
Existence and Uniqueness:
Linear systems of first order equations – Homogenous equations with constant
coefficients – The exact and uniqueness of solutions of initial value problem for first
order ordinary differential equation. The method of successive approximations –
Picard’s theorem. (Chapter 7 : Sections 37-38) (Chapter 11: Sections 55,56)
Unit IV:
First order partial differential equations:
Partial differential equations of first order in two independent variables – Formulation
– Solution – Integral surfaces passing through a curve – Surfaces orthogonal to a
given system – Compactibility – Classification of solutions of first order equation –
Solutions of non –linear equation – Charpits Method – Jacobi Method.
(Chapter 1 : Sections 1.1 – 1.9)
Unit V:
Second Order Partial Differential Equations:
Origin of second order partial differential equations – Linear partial differential
equations – Method of solving of second order partial differential equations –
Canonical forms – Adjoint operator.(Chapter 2 : Sections 2.1 - 2.6)

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Text Books:
1. G.F.Simmons – Differential Equations with Application and Historical Notes
– TataMcGraw Hill, New Delhi,1984. (For Units I to III)
2. J.N. Sharma and K.Singh, Partial Differential Equations for Engineers and
Scientist, Narosha Publishing House, New Delhi, 2000 (For Units IV and V)
References:
1. I.N. Sneddon, Elements of Partial Differential Equations, McGraw Hill, New
Delhi,1983.
2. Shepley L.Ross, Differential Equations, John Wiley & Sons, New York,1984.
3. D. Somasundaram, Ordinary Differential Equations, Narosa Publishing House,
Chennai – 2002.

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 CORE COURSE – IV P08MACA04
Discrete Mathematics
Unit I:
Theory of inference:
Consistency of premises validity using truth table – Consistency of premises –
Predicates – 15e statement function, Variables and quantifiers – Predicate formulae –
Free and bound variables – Theory of inference for the predicate calculus (Chapter 1:
Sections 1- 4.1, 1 - 4.2, 1 - 5.1, 1 - 5.2,1 - 5.3, 1 - 5.4, 1 - 6.4)
Unit II:
Set Theory:
Functions – Definition and introduction – Composition of functions – Inverse
functions – Binary and n-ary Operations – Characteristic function of a set – Hashing
functions – Peuno axioms and mathematical induction – Cardinality. (Chapter 2: 2 -
4.1, 2 - 4.2, 2 – 4.3, 2 – 4.4,2 – 4.5, 2 – 4.6, 2 – 5.1, 2 – 5.2)
Unit III:
Algebraic Structures:
Groups: Definition and Examples – Subgroups and homomorphism - Cosets and
Lagrange’s Theorem – Normal subgroups – Algebraic systems with Two Binary
Operations.(Chapter 3 : Sections 3 – 5.1, 3 – 5.2, 3 – 5.3, 3 – 5.4, 3 – 5.5)
Unit IV:
Lattices and Boolean algebra:
Lattices as Algebraic Systems – Sub lattices, direct product and homomorphism –
Boolean Algebra Definition and examples – Sub Algebra. Direct Product and
homomorphism – Boolean functions, Boolean forms and free Boolean Algebras –
Values of Boolean expression and Boolean functions. (Chapter 4: Sections 4 – 1.3, 4
– 1.4, 4 – 2.2, 4 – 3.4, 4 – 3.2)
Unit V:
Graph Theory:
Basic definitions – Paths – Rechability and Connectedness – Matrix representation of
Graphs – Trees – Finite state machine: Introductory special circuits – Equivalence of
finite state machines (Chapter 5: 5 – 1.1, 5 - 1.2, 5 – 1.3, 5 – 1.4)(Chapter 4: Sections
4 – 6.1, 4 – 6.2)

15
Text Book:
1. J.P. Trembley and R.Manohar, Discrete Mathematical Structures applications
to Computer Science Tata McGraw Hills New Delhi, 1997.
References:
1. James C.Abbott, Sets, Lattices and Boolean algebra, Allya and Bacon Boston,
1969.
2. H.G.Flegg Boolean Algebra and its applications. John Wiley and Sons Inc.
NewYork, 1974.

16
 CORE COURSE – V P08MACA05
Principles of Programming and Information Technology
Unit I:
Constants – Variables – Data Types – Operators – Declaration – I/O – Decision
making – Branching and Looping – Arrays – Strings.
Unit II:
The C Pre Processor – Pointers – Functions – Files.
Unit III:
Components of Computers – types of Computer – Memory types and devices –
Processors – High level languages – Translators. Software: Definition – Types of
Software tools. Operating System : Definition – Needs of Operating System – History
of Operating System – Classification of Operating System. Software Engineering:
Definition – Need for Software Engineering – Testing – Types.
Unit IV:
Data Communication and networking : Types of Communication – Need of network –
Transmission media – Network Topologies – LAN Transmission Control –
Protocol/Internet Protocol (E-Mail HTML, Web Page, WWW, FTP). Multimedia –
Definition – Software Engineering Component – Hardware Component – Application.
Unit V:
WAP – WAP Transmission model – Application. Blue tooth – Application. GPS –
Application – Data mining – E Commerce – Fuzzy System.(Basic Concepts Only)
References:
1. Ansi C – E Balagurusamy.
2. Introduction to IT – ITL Education Solution Ltd.
3. Computer Science and Information Technology – S. Khandare
4. Fundamentals of Computer Science – R. Rajaraman.
5. Computer Network – Andrew Techenbaum
6. Multimedia – Making it work toy Vaughan
7. Software Engineering – Roger Pressman.
8. Information Technology – Leon and Leon.

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 CORE COURSE – VI P08MACA06
Numerical Analysis
Unit I :
Numerical Solutions to ordinary differential equation:
Numerical solutions to ordinary differential equation – Power series solution –
Pointwise method – Solution by Taylor’s series – Taylor’s series method for
simultaneous first order differential equations – Taylor’s series method for Higher
order Differential equations – Predictor – Corrector methods – Milne’s method –
Adam – Bashforth method (Chapter 11: Sections 11.1 to 11.6 and Sections 11.8 to
11.20)
Unit II :
Picard and Euler Methods:
Picard’s Method of successive approximations – Picard’s method for simultaneous
first order differential equations – Picard’s method for simultaneous second order
differential equations – Euler’s Method – Improved Euler’s method – Modified
Euler’s Method. (Chapter 11: Sections 11.7 to 11.12)
Unit III :
Runge – Kutta Method:
Runge’s method – Runge-Kutta methods – Higher order Runge-Kutta methods-
Runge-Kutta methods for simultaneous first order differential equations – Runge-
Kutta methods for simultaneous second order differential equations. (Chapter 11:
Sections 11.13 to 11.17)
Unit IV :
Numerical solutions to partial differential equations:
Introduction Difference Quotients – Geometrical representation of partial differential
quotients – Classifications of partial differential equations – Elliptic equation –
Solution to Laplace’s equation by Liebmann’s iteration process. (Chapter 12: Sections
12.1 to 12.6)

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Unit V :
Numerical Solutions to partial differential equations (contd.)
Poisson equation – its solution – Parabolic equations – Bender – Schmidt method –
Crank – Nicholson method – Hyperbolic equation – Solution to partial differential
equation by Relaxation method. (Chapter 12: Sections 12.7 to 12.10)
Text Book:
V.N Vedamurthy and Ch. S.N.Iyengar; Numerical Methods, Vikas
Publishing House Pvt Ltd., 1998.

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 CORE COURSE – VII P08MACA07
Complex Analysis
Unit I:
Power series expansions:
Weiestrass’s theorem – The Taylor series – The Laurent’s series, partial fractions –
Infinite products – Canonical products. (Chapter 5 : Sections 1 and 2.1,2.2, & 2.3)
Unit II:
Entire functions:
Jenson’s formula – Hadamards theorem Normal Families: Equicontinuity – Normality
and compactness – Arzela’s theorem – familier of analytic functions – The classical
definition (Chapter 5 : Sections 3 and 5)
Unit III:
Conformal mapping:
The Riemann mappping theorem, conformal mapping of polygons. A closure look at
harmonic functions.(Chapter 6 : Sections 1,2 & 3)
Unit IV:
Elliptic functions :
Simply periodic functions, Representation by exponentials – The Fourier development
– Functions of finite order. Doubly periodic functions : The period module –
Unimodular transformation the canonical basis – General properties of elliptic
functions (Chapter 7 : Sections 1 & 2)
Unit V:
The Weiestrass’s theorem :
The Weiestrass’s function – The functions (z) and σ(z). The differential equation –
Problems (Chapter 7 : Sections 3.1,3.2,& 3.3)
Text book:
L.V.Ahlfors, Complex Analysis, 3rd Edition, McGraw Hill Indian Edition, New Delhi,
1979.
Reference:
1. J.B.Conway, Functions of one complex variable, Narosa publishing house,
New Delhi, 1980
2. S. Ponnusamy, Foundations of Complex Analysis , Narosa Publishing house,
New Delhi , 2004.

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 CORE COURSE – VIII P08MACA08
Mathematical Statistics
Unit I:
Probability and Random Variables:
Probability – Axioms – Combinatorics, Probability on finite sample spaces –
Conditional probability and Baye’s theorem - Independence of events – Random
variables – Probability distribution of a random variable – Discrete and continuous
random variables – Function of a random variable. (Chapter 1: Sections 1.3 to 1.6 and
Chapter 2: Sections 2.2 to 2.5)
Unit II:
Moments and Generating Functions:
Moments of a distribution function – Generating functions – Some moment
inequalities. (Chapter 3: Sections 3.2 to 3.4)
Unit III:
Multiple Random Variables:
Multiple random variables – Independent random variables – Functions of several
random variables. (Chapter 4: Sections 4.2 to 4.4)
Unit IV:
Multiple Random Variables (Contd.):
Covariance, Correlation and moments – Conditional expectation – Some discrete
distributions – Some continuous distributions. (Chapter 4: Sections 4.5 and 4.6 and
Chapter 5: Sections 5.2 to 5.3)
Unit V:
Limit Theorems:
Modes of convergence – Weak law of large numbers – Strong law of large numbers –
Central limit theorems. (Chapter 6: Sections 6.2 to 6.4 and 6.6)

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Text Book:
V.K. Rohatgi and Statistics, John Wiley Pvt. Singapore, 2001.
Reference:
1. G.G. Roussas, A First Course in Mathematical Statistics, Addition Wesley
Publ. Co. Mass, 1973.
2. M. Fisz, Probability Theory and Mathematical Statistics, John Wiley, New
York, 1963.
3. E.J. Dudewisg and S.N. Mishra, Modern Mathematical Statistics, John Wiley,
New York, 1988.

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 CORE COURSE – IX P08MACA09
Programming in C++ and Data Structures
Unit I:
Principles of OOP – Tokens – Expressions, Control Structures – Functions – Classes
and Objects – Constructors and Destructors.
Unit II:
Operator overloading and type conversion – Inheritance – Pointers, Virtual Functions
and Polymorphism – Managing console I/O Operations – Working with files.
Unit III:
Definitions of a Data Structure – Primitive and composite data types – Arrays –
Operations on Arrays – Application stock – Infix – Postfix – Conversion – Recursive
maze problem.
Unit IV:
Queues – Operations on Queues – Application – Circular Queues – Single linked list
– Operations – Applications – Representation of a polynomial – Polynomial addition
– Doubly linked list – Operations – Applications – Ordering of books in library.
Unit V:
Trees – Graphs – Binary Trees – Conversion of Forest Binary Trees – Tree Traversals
– Graph definition – Types of Graphs – Hashing – Tables and Hashing function –
Transversal short path – Dijikstra’s Algorithm.
Text Books:
E. Balagurusamy, Object Oriented Programming in C++, Tata McGraw Hill
Publishing co. Ltd., New Delhi, 1999.(For Units I and II).
E. Horowitz and Sahani, Fundamentals of Computer Algorithm, CBS Publishers, New
Delhi, 1984. (For Units III, IV, and V)
References:
1. S.B. Lipman and J.Lafer, C++ Primer, Addition Wesley, Mass., 1998.
2. L. Sarat, Data Processing Logic, McGraw Hill, Singapore, 1985.
3. D. Ravichandran, Object Oriented Programming with C++, Tata McGraw Hill
Publishing Co.Ltd., New Delhi, 1998.

23
 CORE COURSE – X P08MACAP01
Practical in C++
1. Arrays
1.1. Operations on Arrays
1.2. Linear Search
1.3. Binary Search
2. Sorting
2.1. Bubble Sort
2.2. Selection Sort
2.3. Insertion Sort
2.4. Shell Sort
2.5. Quick Sort
2.6. Heap Sort
3. Stacks and Queues
3.1. Operations on Stack
3.2. Operations on Queue
3.3. Operations on Priority Queue
3.4. Operations on Circular Queue
4. Linked Lists
4.1. Singly Linked List
4.2. Doubly Linked List
4.3. Double-ended List
5. Recursion
5.1. Towers of Honoi
5.2. Merge Sort
6. Binary Tree Traversal

24
Text Books:
1. E. Balagurusamy, Object Oriented Programming in C++, Tata McGraw Hill
Publishing co. Ltd., New Delhi, 1999
2. E. Horowitz and Sahani, Fundamentals of Computer Algorithm, CBS
Publishers, New Delhi, 1984
References:
1. S.B. Lipman and J.Lafer, C++ Primer, Addition Wesley, Mass., 1998.
2. L. Sarat, Data Processing Logic, McGraw Hill, Singapore, 1985.
3. D. Ravichandran, Object Oriented Programming with C++, Tata McGraw Hill
Publishing Co.Ltd., New Delhi, 1998.

25
 CORE COURSE – XI P08MACA10
Topology
Unit I:
Topological spaces:
Topological spaces - Basic for a topology – The order topology - The product
topology on XxY – The subspace topology – Closed sets and limit points. (Chapter 2:
sections 12 to 17)
Unit II:
Continuous functions :
Continuous functions – The product topology – The metric topology. (Chapter 2:
Sections 18 to 21)
Unit III:
Connectedness:
Connected spaces – Connected subspaces of the real line – Components and local
connectedness. (Chapter 3: Sections 23 to 25)
Unit IV:
Compactness:
Compact spaces – Compact subspace of the real line –Limit point compactness –
Local compactness. (Chapter 3: Sections 26 to 29)
Unit V:
Countability and Separation axioms:
The countability axioms – The separation axioms – Normal spaces – The Urysohns
lemma – The Urysohns metrization theorem – The Tietz extension theorem. (Chapter
4: Sections 30 to 35)
Text Book:
James R.Munkres – Topology, 2nd edition, Prentice Hall of India Ltd., New Delhi,
2005
References:
1. J. Dugundji, Topology, Prentice Hall of India, New Delhi,1975.
2. G.F.Simmons, Introduction to Topology and Modern Analysis, McGraw Hill
Book Co.New York 1963.
3. S.T. Hu, Elements of General Topology, Holden Day, Inc. New York, 1965.

26
 CORE COURSE – XII P08MACA11
Differential Geometry
Unit I:
Theory of Space Curves:
Theory of space curves – Representation of space curves – Unique parametric
representation of a space curve – Arc-length – Tangent and oscuating plane –
Principle normal and binormal – Curvature and torsion – Behaviour of a curve near
one of its points – The curvature and torsion of a curve as the intersection of two
surfaces. (Chapter 1 : Sections 1.1 to 1.9)
Unit II:
Theory of Space Curves (Contd.):
Contact between curves and surfaces – Osculating circle and osculating sphere –
Locus of centre of spherical curvature – Tangent surfaces – Involutes and Evolutes –
Intrinsic equations of space curves – Fundamental Existence Theorem – Helices.
(Chapter 1 : Sections 1.10 to 1.13 and 1.16 to 1.18)
Unit III:
Local Intrinsic properties of surface:
Definition of a surface – Nature of points on a surface – Representation of a surface –
Curves on surfaces – Tangent plane and surface normal – The general surfaces of
revolution – Helicoids – Metric on a surface – Direction coefficients on a surface
(Chapter 2 : Sections 2.1 to 2.10)
Unit IV:
Local Intrinsic properties of surface and geodesic on a surface:
Families of curves – Orthogonal trajectories – Double family of curves – Isometric
correspondence – Intrinsic properties – Geodesics and their differential equations –
Canonical geodesic equations – Geodesics on surface of revolution.
(Chapter 2: Sections 2.11 to 2.15 and Chapter 3: Sections 3.1 to 3.4)
Unit V:
Geodesic on a surface:
Normal property of Geodesics – Differential equations of geodesics using normal
property – Existence theorems – Geodesic parallels – Geodesic curvature – Gauss
Bonnet Theorems – Gaussian curvature – Surface of constant curvature
(Chapter 3: Sections 3.5 to 3.8 and Sections 3.10 to 3.13)

27
Text Book:
D. Somasundaram, Differential Geometry, Narosa Publ. House, Chennai, 2005
References:
1. T. Willmore, An Introduction to Differential Geometry, Clarendan Press,
Oxford, 1959.
2. D.T Struik, Lectures on Classical Differential Geometry, Addison – Wesely,
Mass. 1950.
3. J.A. Thorpe, Elementary Topics in Differential Geometry, Springer – Verlag,
New York, 1979.

28
 CORE COURSE – XIII P08MACA12
Optimization Techniques
Unit I:
Integer linear programming:
Introduction – Illustrative applications integer programming solution algorithms:
Branch and Bound (B & B) algorithm – zero – One implicit enumeration algorithm –
Cutting plane Algorithm. (Sections 9.1,9.2,9.3.1.,9.3.2,9.3.3)
Unit II:
Deterministic dynamic programming:
Introduction – Recursive nature of computations in DP – Forward and backward
recursion – Selected DP applications cargo – Loading model – Work force size model
– Equipment replacement model – Investment model – Inventory models. (Sections
10.1,10.2,10.3,10.4.1,10.4.2,10.4.3,10.4.4,10.4.5)
Unit III:
Decision analysis and games:
Decision environment – Decision making under certainty (Analytical Hierarchy
approach) Decision making under risk – Expected value criterion – Variations of the
expected value criterion – Decision under uncertainty Game theory – optimal solution
of two – Person Zero – Sum games – Solution of mixed strategy games (Sections
14.1,14.2,114.3.1,14.3.2,14.4,14.5.1,14.5.2)
Unit IV:
Simulation modeling:
What is simulation – Monte carlo simulation – Types of simulation – Elements of
discrete event simulation – Generic definition of events – Sampling from probability
distributions. Methods for gathering statistical observations – Sub interval method –
Replication method – Regenerative (Cycle) method – Simulation languages (Sections
18.1,18.2,18.3,18.4.1,18.4.2,18.5,18.6,18.7.1,18.7.2,18.7.3,18.8)

29
Unit V:
Nonlinear programming algorithms:
Unconstrained non linear algorithms – Direct search method – Gradient method
Constrained algorithms: Separable programming – Quadratic programming –
Geometric programming – Stochastic programming – Linear combinations method –
SUMT algorithm (Sections : 21.1.1, 21.1.2, 21.2.1, 21.2.2, 21.2.3, 21.2.4, 21.2.5,
21.2.6)

Text Book:
Operations Research An Introduction 6th edison by Hamdy A. Taha,
University of Arkansas Fayetteville.
Reference:
1. F.S. Hillier and G.J. Lieberman Introduction to Operation Research 4th edition,
Mc Graw Hill Book Company, New York, 1989.
2. Philips D.T.Ravindra A. and Solbery.J. Operations Research, Principles and
Practice John Wiley and Sons, New York.
3. B.E.Gillett, Operations research – A Computer Oriented Algorithmic
Approach,TMH Edition, New Delhi, 1976.

30
 CORE COURSE – XIV P08MACA13
Graph Theory
Unit I:
Graphs and Subgraphs:
Graphs and simple graphs – Graph isomorphism – Incidence and Adjacency Matrices
– Subgraphs – Vertex degrees – Paths and connection – Cycles – Application – The
shortest path problem.(Chapter 1 : Sections 1.1 to 1.8)
Unit II:
Trees and Connectivity:
Trees – Cut edges and bonds – Cut vertices – Cayley’s formula - Application –
Connector problem – Connectivity – Blocks – Application – Reliable Communication
Networks. (Chapter 2: Sections 2.1 to 2.5 and Chapter 3: Sections 3.1 to 3.3)
Unit III:
Euler Tours and Matchings:
Euler Tours – Hamilton cycles – Application – Chinese Postman Problem – Traveling
salesman problem - Matchings – Matching and coverings in Bipartite Graphs –
Perfect Matchings – Applications – Personal Assignment Problem – Optimal
Assignment Problem. (Chapter 4: Sections 4.1 to 4.4 and Chapter 5: Sections 5.1 to
5.5)
Unit IV:
Edge Colouring and Independent sets:
Edge Colouring – Edge Chromatic Number – Vizings Theorem – Application –
Timetabling Problem – Independents sets – Ramsey’s Theorem – Turan’s Theorem.
(Chapter 6: Sections 6.1 to 6.3 and Chapter 7: Sections 7.1 to 7.3)
Unit V:
Vertex Colourings:
Vertex Colourings – Chromatic Number – Brook Theorem – Hajos conjecture –
Chromatic Polynomials – Girth and Chromatic Number – A storage problem.
(Chapter 8 : Sections 8.1 to 8.6)

31
Text Book:
J.A.Bondy and U.S.R. Murty, Graph Theory with Applications, North Holland, New
York, 1982.
References:
1. Narasing Deo, Graph Theory with Application to Engineering and Computer
Science, Prentice Hall of India, New Delhi. 2003.
2. F. Harary, Graph Theory, Addison – Wesely Pub. Co. The Mass. 1969.
3. L. R.. Foulds, Graph Theory Application, Narosa Publ. House, Chennai, 1933.

32
 CORE COURSE – XV P08MACA14
Functional Analysis
Unit I:
Banach Spaces:
Banach Spaces – Definition and examples – Continuous linear transformations –
Hahn Banach theorem (Chapter 9 : Sections 46 to 48)
Unit II:
Banach Spaces and Hilbert Spaces:
The natural embedding of N in N** - Open mapping theorem – Conjugate of an
operator – Hilbert space – Definition and properties. (Chapter 9 : Sections 49 to 51,
Chapter 10 : Sections 52)
Unit III:
Hilbert Spaces:
Orthogonal complements – Orthonormal sets – Conjugate space H* - Adjust of an
operator (Chapter 10 : Sections 53 to 56)
Unit IV:
Operations on Hilbert Spaces:
Self adjoint operator – Normal and Unitary operators – Projections.(Chapter 10:
Sections 57 to 59)
Unit V:
Banach Algebras:
Banach Algebras – Definition and examples – Regular and simple elements –
Topological divisors of zero – Spectrum – The formula for the spectral radius – The
radical and semi simplicity. (Chapter 12 : Sections 64 to 69)

33
Text Book:
1. G.F.Simmons, Introduction to Topology and Modern Analysis, McGraw
Hill Inter. Book Co. New York 1963.
References:
1. W. Rudin, Functional Analysis, Tata McGraw Hill Publ. Co. New Delhi,
1973.
2. H.C. Goffman and G.Fedrick, First Course in Functional Analysis, Prentice
Hall of India , New Delhi 1987.
3. D. Somasundaram, Functional Analysis S. Viswanathan Pvt.Ltd.,
Chennai,1994.

34
 CORE COURSE – XVI P08MACA15
Measure Theory and Integration
Unit I:
Lebesgue Measure:
Lebesgue Measure – Introduction – Outer measure – Measurable sets and Lebesgue
measure – Measurable functions – Little Woods’ Three Principle. (Chapter 3:
Sections 1 to 3, 5 and 6)
Unit II:
Lebesgue Integral:
Lebesgue integral – The Riemann integral – Lebesgue integral of bounded functions
over a set of finite measure – The integral of a nonnegative function – The general
Lebesgue integral.(Chapter 4: Sections 1 to 4)
Unit III:
Differentiation and Integration:
Differentiation and Integration – Differentiation of monotone functions – Functions of
bounded variation – Differentiation of an integral – Absolute continuity. (Chapter 5:
Sections 1 to 4)
Unit IV :
General Measure and Integration:
General Measure and Integration – Measure spaces – Measurable functions –
integration – Signed Measure – The Radon – Nikodym theorem. (Chapter 11:
Sections 1 to 3, 5 and 6)
Unit V:
Measure and Outer Measure
Measure and outer measure – outer measure and measurability – The Extension
theorem – Product measures. (Chapter 12: Sections 1, 2 and 4)

35
Text Book:
H.L.Royden, Real Analysis, Mc Millian Publ. Co. New York 1993.
Reference:
1. G. de Barra, Measure Theory and integration, Wiley Eastern Ltd, 1981.
2. P.K. Jain and V.P. Gupta, Lebesgue Measure and Integration, New Age Int.
(P) Ltd., NewDelhi, 2000.
3. Walter Rudin, Real and Complex Analysis, Tata McGraw Hill Publ. Co. Ltd.,
New Delhi, 1966.

36
 CORE COURSE – XVII P08MACA16
Java Programming

Unit I:
Java Tokens – Java statements – Constants – Variables – Data types.
[Chapters 3 and 4]
Unit II:
Operators – Expressions – Decision making and Branching [Chapters 5,6, and 7]
Unit III:
Classes – Objects – Methods – Arrays – Strings – Vectors – Multiple Inheritance
[Chapter 8,9 and 10]
Unit IV:
Multithreaded Programming – Managing errors and Exceptions. [Chapters 12 and 13]
Unit V:
Applet Programming. [Chapter 14]

Text Book:
E. Balagurusamy, Programming with Java – A primer, Tata McGraw Hill
Publishing Company Limited, New Delhi, 1998.

References:
1. Mitchell Waite and Robert Lafore, Data Structures and Algorithms in Java,
Techmedia (Indian Edition), New Delhi, 1999.
2. Adam Drozdek, Data Structures and Algorithms in Java, (Brown/Cole), Vikas
Publishing House, New Delhi, 2001.

37
 CORE COURSE – XVIII P08MACAP02
Practical in Java
Section 1. Classes, Objects, Inheritance, Interface
1. Write a program that randomly fills a 3 by 4 array and prints the largest and
smallest values in the array.
2. Design a class to represent a bank Account, Include the following members:
Data Members: Methods:
1. Name of the Depositor 1. To assign initial values.
2. Account Number 2. To deposit an amount.
3. Type of account 3. To withdraw an amount after checking
the balance
4. Balance 4. To display the name and balance.
Write a Java program for handling 10 customers.
3. Java lacks a complex datatype. Write a complex class that represents a single
Complex number and includes methods for all the usual operation, i.e.:
addition, subtraction, multiplication, and division.
4. Create a class called Publication. Create class Tape and class Book from
Publication. Describe properties for subclasses. Create an array of publication
references to hold combination of books and tapes.
5. Assume that the test results of a batch of students are stored in 3 different
classes. ClassStudent stores the Roll number. Class test stores the marks
obtained in two subjects and Class Result contains the total marks. The Class
Result can inherit the details of marks and Roll Number of students. The
Weightage is stored in a separate interface Sports. Implement the above
multiple inheritance problem by using interface.
Section 2. Exception Handling, Multithreading and Packages
6. Write a Java program to handle different types of exceptions using try, catch
and finally statements.
7. Write a Java program to implement the behavior of threads.
a. To create and run threads.
b. To suspend and stop threads
c. To move a thread from one state to another
d. By assigning a priority for each thread.

38
 8. Create two Threads subclasses, one with a sun() that starts up, captures the
handle of the second Thread object and then calls wait(). The other class run()
should call notifyall() for the first Thread after some number of seconds have
passed, so that the first thread after some seconds have passed, so the first
thread after some number of seconds have passed, so that the first thread can
print out a message.
9. Create a thread to copy the contents of one file to another file. Write a
program to implement this thread. Create multiple threads within the program
to do multiple file copies.
10. Create three classes Protection, Derived and SamePackage all in same
package. Class Protection is a base class for the class Derived and
SamePackage is a seperate class. Class Protection has three variables each of
type private, protected and public. Write a program that shows the legal
protection modes of all the different variables.
Section 3. Applet Programming
11. Write an applet to draw the following shapes:
a. Cone
b. Cylinder
c. Cube
d. Square inside a circle
e. Circle inside a square
12. Design applet to display bar chart for the following table, which shows the
annual turnover of XYZ Company during the period 1997 to 2000.
Year : 1997 1998 1999 2000
Turnover (in Crore) : 110 150 100 180
13. Creating a Java applet, which finds palindromes in sentences. Your applet will
have two input controls; one input will be a text field for entering sentences,
the other input will be a text field or scroll bar for selecting the minimum
length a palindrome to be shown. Your applet will output the first 10
palindromes it finds in the sentence.
14. Write a program which displays a text message coming down the screen by
moving left to right and modify the above program instead of text moving
from left to right it moves top to bottom.

39
 15. Create a thread in an applet that draws an image and makes it move along the
screen.
Section 4: Awt Forms Design Using Frames
16. Create a frame with two text fields and three buttons (Cut, Copy & Paste).
Data entered in the first text field should response, according to the buttons
clicked.
17. Create a frame that contains 3 text fields and four buttons for basic arithmetic
operations. You have to enter two numbers in first two text fields. On clicking
the respective button that answer should be displayed in the last text field.
18. Create a frame with check box group containing Rectangle, Circle, Triangle,
Square. If the particular value is true then the corresponding shape should be
displayed.
19. Using AWT create a frame, which contains four-text field name, age, sex and
qualification lay out using the flow layouted manager. Run the program and
give the values of all text fields in the command line. Initially all the values of
text field should be blank. On clicking the click button all the text fields
should contain the command line inputs.
20. A car company called Maruthi is selling four models of cars. They are shown
below
Code Car Model Price
800 Maruthi 800 Rs 2.14 Lakhs
1000 Maruthi 1000 Rs 3.72 Lakhs
Esteem Maruthi Esteem Rs 3.69 Lakhs
Zen Maruthi Zen Rs 3.91 Lakhs
Design a frame with 4 buttons called 800,1000,Esteem, Zen. When we
click a button the details of a particular model must appeared in an exclusive
background color, text color and font.
Section-5: Networking, Socket and Servlets Programming
21. Practice with client-Servers and IO: Modify Data Server to watch for “Send
Text” request read a file from to “Send Data” for the “Send Text” request
read a file from disk and send it back to the client. Add a button to Data
Client interface that sends the text request when pushed. Display the text
returned by the server in the DataClient Text area.

40
22. Write a Java program to implement client-server communication using
Datagram Socket.
23. Write a program to display the address and name of local machine using
Factory Methods.
24. Write a java program to implement Cookies using getCookies(), getName()
and getValue() methods.
25. Create a server that asks for a password, the opens a file and sends the file
over the network connection. Create a client that connects to this server,
gives the appropriate password, then captures and saves the file. Test the
pair of programs on your machine using the local host (the local loop back
IP address 127.0.0.1 produced by calling InetAddress.getByName (null).

41
 ELECTIVE– I P08MACAE01
Fuzzy Sets and Their Applications
Unit I:
Fuzzy sets:
Fuzzy sets – Basic types – Basic concepts - Characteristics – Significance of the
paradigm shift – Additional properties of α - Cuts (Chapter 1: Sections 1.3 to 1.5 and
Chapter 2: Sections 2.1)
Unit II:
Fuzzy Sets Versus CRISP Sets:
Representation of Fuzzy sets – Extension principle of Fuzzy sets – Operation on
Fuzzy Sets – Types of Operation – Fuzzy complements. (Chapter 2: Sections 2.2 to
2.3 and Chapter 3: Sections 3.1 to 3.2)
Unit III:
Operations on Fuzzy Sets:
Fuzzy intersection – t-norms, Fuzzy unions – t conorms – Combinations of operations
– Aggregation operations. (Chapter 3: Sections 3.3 to 3.6)
Unit IV:
Fuzzy Arithmetic:
Fuzzy numbers – Linguistic variables – Arithmetic operation on intervals – Lattice of
Fuzzy numbers. (Chapter 4: Sections 4.1 to 4.4)
Unit V:
Constructing Fuzzy Sets:
Methods of construction: An overview – Direct methods with one expert – Direct
method with multiple experts – indirect method with multiple experts and one expert
– Construction from sample data. (Chapter 10: Sections 10.1 to 10.7)

42
Text Book:
G.J. Klir, and Bo Yuan, Fuzzy Sets and fuzzy Logic: Theory and Applications,
Prentice Hall of India Ltd., New Delhi, 2005.
References:
1. H.J. Zimmermann, Fuzzy Set Theory and its Applications, Allied Publishers,
Chennai, 1996.
2. A.Kaufman, Introduction to the Theory of Fuzzy Subsets, Academic Press,
New York, 1975.
3. V.Novak, Fuzzy Sets and Their Applications, Adam Hilger, Bristol, 1969.

43
 ELECTIVE– II P08MACAE02
Number Theory
Unit I:
Divisibility and Congruence:
Divisibility – Primes - Congruence’s – Solutions of Congruence’s – Congruence’s of
Degree one. (Chapter 1: Sections 1.1 to 1.3 and Chapter 2: Sections: 2.1 to 2.3)
Unit II:
Congruence:
The function φ(n) – Congruence of higher degree – Prime power moduli – Prime
modulus – Congruence’s of degree two, prime modulus – power Residues.
(Chapter 2: Sections 2.4 to 2.9)
Unit III:
Quadratic reciprocity:
Quadratic residues – Quadratic reciprocity – The Jacobi symbol – Greatest Integer
function. (Chapter 3: Sections 3.1 to 3.3 and Chapter 4: Section 4.1)
Unit IV:
Some Functions of Number Theory:
Arithmetic functions –The Mobius inverse formula – The multiplication of arithmetic
functions. (Chapter 4: Sections 4.2 to 4.4)
Unit V:
Some Diaphantine equations:
The equation ax + by= c – positive solutions – Other linear equations – The equation
x2 + y2 = z2- The equation x4 + y4 = z4 Sums of four and five squares – Waring’s
problem – Sum of fourth powers – Sum of Two squares. (Chapter 5: Sections 5.1 to
5.10)

44
Text Book:
1. Niven and H.S Zuckerman, An Introduction to the Theory of Numbers, 3rd
edition, Wiley Eastern Ltd., New Delhi, 1989.
References:
1. D.M. Burton, Elementary Number Theory, Universal Book Stall, New Delhi
2001.
2. K.Ireland and M.Rosen, A Classical Introduction to Modern Number Theory,
Springer Verlag, New York, 1972.
3. T.M Apostol, Introduction to Analytic Number Theory Narosa Publication,
House Chennai, 1980.

45
 ELECTIVE– III P08MACAE03
Database Technology
Unit I:
Introduction DBS Application: DBS Vs File System – View of Data – Data
models – Database Languages – Database User and Administrators – Transaction
Management – DBS Structure – E-R Model: Basic Concepts – Constraints – Keys
– Design Issues – E-R Diagram – E-R Features – Design of E-R Database
Schema.
Unit II:
Relational Database Design: First Normal Form – Functional Dependencies –
Decomposition – Properties of Decomposition – Boyce-Codd Normal Form –
Third Normal Form – Fourth Normal Form.
Database – Tablespaces – Redo Logs – Control files – Programs – Database
support processes Memory structure – Oracle instance, Database Objects – Tables
– Views – Indexes – Synonyms – Grants – Roles.
Unit III:
SQL – Two types of SQL statements – SQL *Plus: Getting in – Number data type
– Character data type – Date data type – Converting from one column type to
another – Update, Delete and Alter – Joining two tables together – Formatting the
output.
Unit IV:
PL/SQL: Character set – Variables – Common data types – PL/SQL components –
Cursors – Compilation errors – Code examples. Snapshots – Functionality.
Triggers: Required system and table privileges – Types of triggers – Trigger
syntax – combining trigger types –setting inserted values – Maintaining duplicated
data – Customizing error conditions – Naming triggers – Enabling and disabling
triggers – Replacing triggers – Dropping triggers.

46
Unit V:
Procedures: Required system and table privileges – Executing procedures –
Procedures vs. function – procedures vs. packages – create procedure and function
syntax – Remote table reference – Debugging – Customizing error conditions –
naming – Create package syntax – Initializing packages – Viewing source code –
Compiling, Replacing and Dropping.
Oracle Reports: Designer – Object navigator – Setting preferences – Files –
Designer components – Sample reports

Text Books:
1. Database System Concepts, 4th Edition – Silberschatz, Korth, Sudarshan
(Unit I & II)
2. Oracle: A beginner’s Guide by Michael Abbey & Michael J.Corey (TMH)
( Unit III, IV & V)
References:
1. Essential Oracle 7 by Tom Leurs (PHI)
2. Oracle 2nd Edition – unleashed – Techmedia.

47
 ELECTIVE– IV P08MACAE04
Fluid Dynamics
Unit I:
Kinematics of Fluids in Motion:
Real fluids and ideal fluids – Velocity of a fluid at a point stream lines – path lines –
Steady and unsteady flows – Velocity potential – The velocity vector – Local and
particle rates of changes – Equations of continuity – Examples. (Chapter 2: Sections
2.1 to 2.8)
Unit II:
Equation of Motion of a fluid:
Pressure at a point in a fluid at rest – Pressure at a point in a moving fluid – Condition
at a boundary of two invicid immersible fluids. Euler’s equation of motion –
Discussion of the case of steady motion under conservative body forces. (Chapter 3:
Sections 3.1 to 3.7)
Unit III:
Some three dimensional flows:
Introduction – Sources – Sinks and doublets – Images in rigid infinite plane – Axis
symmetric flows – Stokes stream function. (Chapter 4: Sections 4.1 to 4.3 and 4.5)
Unit IV:
Some two-dimensional flows:
Two dimensional flows – Meaning of two dimensional flow – Use of cylindrical polar
co-ordinates – The stream function – Complex potential for two dimensional –
Irrational incompressible flow – Complex velocity potential for standard two
dimensional flows – Examples. (Chapter 5: Sections 5.1 to 5.6)
Unit V:
Viscous flows:
Viscous flows – Stress components in a real fluid – Relation between Cartesian
components of stress – Translation motion of fluid elements – The rate of strain
quadric and principle stresses – Further properties of the rate of strain quadric – Stress
analysis in fluid motion – Relation between stress and rate of strain – The coefficients
of viscosity and Laminar flow – The Navier – Stokes equations of motion of a viscous
fluid. (Chapter 8: Sections 8.1 to 8.9)

48
Text Book:
F. Chorlton, Text Book of Fluid Dynamic, CBS Publication New Delhi, 1985.
References:
1. G.K. Batchaelor, An Introduction to Fluid Mechanics, Foundation Books,
New Delhi,1994.
2. S.W. Yuan, Foundations of Fluid Mechanics, Prentice Hall of India Pvt.Ltd.,
New Delhi, 1976.
3. R.K. Rathy, An Introduction to Fluid Dynamics, IBH Publ. Comp. New Delhi,
1976.

49