department of mathematics -...

B.Sc.,Mathematics 284

DEPARTMENT OF MATHEMATICS

Programme Specific Outcomes

1 Help the students to enhance their knowledge in soft skills

and Computing skills.

2 Enable the students to equip knowledge in various

concepts involved in algebra, differential equations and

graph theory.

3 Enable the students to acquire knowledge in C

programming.

4 Students are trained in an effective manner to attend the

competitive exams in order to brighten their future.

5 Facilitate students to acquire a flair knowledge in discrete

mathematics, real analysis and solve problems efficiently.


NEW SYLLABUS UNDER CBCS PATTERN (w.e.f. 2014-15)

B.Sc. MATHEMATICS – PROGRAMME STRUCTURE

Sem

Course

Cr.

Hrs./

Week

Marks

Total Part Subject

Code

Name Int. Ext.

I

I 411T Tamil/other languages – I 3 6 25 75 100

II 412E English – I 3 6 25 75 100

III

4BMA1C1 Core – I – Differential Calculus

and Trigonometry

4 6 25 75 100

4BMA1C2 Core – II – Theory of Equations,

Theory of Numbers and

Inequalities

4 6 25 75 100

Allied – I(Theory only) (or)

Allied – I(Theory cum Practical)

5

4

5

3

25

15

75

60

100

75

Allied Practical - I -- 2* -- -- --

IV

4NME1A /

4NME1B /

4NME1C

(1) Non-Major Elective – I –

(a)jkpo; nkhopapd; mbg;gilfs;/

(b) ,f;fhy ,yf;fpak; /

(c) Communicative English

2 1 25 75 100

Total (Allied Theory Only) 21 30 -- --

600

Total(Allied Theory cum Practical) 20 575

II

I 421T Tamil/other languages – II 3 6 25 75 100

II 422E English – II 3 6 25 75 100

III

4BMA2C1 Core – III – Integral Calculus and

Fourier Series

4 6 25 75 100

4BMA2C2 Core – IV – Analytical Geometry

of 3D and Vector Calculus

4 5 25 75 100

Allied– II(Theory) (or)

Allied –II(Theory cum Practical)

5

4

5

3

25

15

75

60

100

75


Allied Practical - I 2 2 20 30 50

IV 4BES2 (3) Environmental Studies 2 2 25 75 100

Total (Allied Theory Only) 21 30 -- -- 600


III

I 431T Tamil /other languages – III 3 6 25 75 100

II 432E English – III 3 6 25 75 100

III

4BMA3C1 Core – V – Modern Algebra 4 5 25 75 100

4BMA3C2 Core – VI – Differential Equations

and its Applications

4 5 25 75 100

Allied – III (Theory only) (or)

Allied–III(Theory cum Practical)

5

4

5

3

25

15

75

60

100

75

Allied Practical - II -- 2* -- -- --


IV

4NME3A /

4NME3B /

4NME3C

(1) Non-major Elective – II – (a)

,yf;fpaKk; nkhopg; gad;ghLk;/

(b) goe;jkpo; ,yf;fpaq;fSk;

,yf;fpa tuyhWk; /

(c)Effective Employability Skills

2 1 25 75 100

4SBS3A1/

4SBS3A2

(2) Skill Based Subjects – I 2 2 25 75 100

V 4BEA3 Extension activities 1 -- 100 -- 100

Total (Allied Theory Only) 24 30

--

--

800


IV

I 441T Tamil /other language – IV 3 6 25 75 100

II 442E English – IV 3 6 25 75 100

III

4BMA4C1 Core –VII – Sequences and Series 4 5 25 75 100

4BMA4C2 Core – VIII –Linear Algebra 4 4 25 75 100

Allied – III (Theory only) (or)

Allied–III(Theory cum Practical)

5

4

5

3

25

15

75

60

100

75

Allied Practical - II 2 2 20 30 50

IV

4SBS4B1/

4SBS4B2

(2) Skill Based Subjects – II 2 2 25 75 100

4BVE4/

4BMY4/

4BWS4

(4) Value Education /

Manavalakalai Yoga /

Women’s Studies

2 2 25 75 100

Total (Allied Theory Only) 23 30 -- --

700


V III

4BMA5C1 Core – IX – Modern Analysis 4 6 25 75 100

4BMA5C2 Core – X – Mathematical Statistics 4 5 25 75 100

4BMA5C3 Core – XI – Statics 4 5 25 75 100


4BMA5C4 Core –XII– Linear Programming 4 5 25 75 100

4BMAE1A/

4BMAE1B

Elective – I – Graph Theory (or)

Programming in C with Lab

5 5 25 75 100

IV

4SBS5A3/

4SBS5A4/

4SBS5A5



Total 25 30 -- -- 700

VI

III

4BMA6C1 Core – XIII – Complex Analysis 4 6 25 75 100

4BMA6C2 Core –XIV– Operations Research 4 5 25 75 100

4BMA6C3 Core –XV- Dynamics 4 5 25 75 100

4BMAE2A/

4BMAE2B

Elective – II – Discrete

Mathematics (or) Fuzzy Algebra

5 5 25 75 100

4BMAE3A/

4BMAE3B

Elective – III – Numerical

Analysis (or) M.S.Office with Lab

5 5 25 75 100

IV

4SBS6B3/

4SBS6B4/

4SBS6B5



Total 26 30 -- -- 700

Grand Total 140 180 -- -- 4100

* University Examinations will be held in the Even Semesters.

I YEAR – I SEMESTER

Part - II English Name of the Subject(412E): Prose and Communication Skills

Course Description

Students will be exposed to prose, and poetry works of great writers and poets, provided they will

learn Grammar and composition to enhance the skill of LSRW.

Course Objectives

Students completing the course will be able to

a. Speak and write in English for Global competency.

b. Will be able to analyze literary works(prose and poetry).

c. They will also be exposed to basic literary genres of prose and poetry.

d. Grammar, reading and writing exercises will make the student to read any text and understand it

and make them to think beyond the text.

e. Compositions give space for more writing skills. They will help the student to write essays, and

reports. Thereby they will be able to differentiate objective and subjective writing.

Course Outcome (COs)

a. The core objectives of the above prescribed texts are :

1. Critical thinking, to analyse, evaluate, and synthesis the information he has gathered in from

the lecture.

2. Communication, to effectively interpret and express his ideas through written and spoken.

3. To inculcate Social Responsibility about civic responsibility, and adjust with regional, national

and global communities.


COURSE CODE: 4BMA1C1

CORE COURSE – I – DIFFERENTIAL CALCULUS AND TRIGONOMETRY

Course description: This course is intended to develop practical skills in differential calculus and

trigonometry.

Course Objective: On completion of this course the learner will

1. know to find higer derivatives and expand the given function and to find the max and min of a

function of two variables.

2. have knowledge about sub tangent, sub - normal, polar sub tangent, polar sub - normal and

asymptotes.

3. know about envelope, curvature and evolute of a curve.

4. know De - Movire’s theorem and its applications.

5. expose to hyperbolic function and inverse hyperbolic function.

Course outcome: students will be able to

1. find the nth derivative of a given function and find the max and min of a function of two variables.

2. find sub tangent, sub - normal, polar sub tangent, polar sub - normal and asymptotes of a given

curve.

3. evaluate envelope, circle, radius and centre of curvature and evolute of a curve and polar equation.

4. expand sin nError! Reference source not found., cos nError! Reference source not found., tan

nError! Reference source not found. and expand sin Error! Reference source not found., cos

Error! Reference source not found., tan Error! Reference source not found. and find the

expansion of sinnError! Reference source not found. , cosnError! Reference source not found..

5. do problems in hyperbolic function and inverse hyperbolic function.

Text Books 1. Calculus Vol. 1 by Narayanan and Manickavsagam pillai

2. Trigonometry by Narayanan and Manickavasagam Pillai

Reference Books: Advanced Calculus Vol.I by S. Arumugam and others



CORE COURSE II – THEORY OF EQUATIONS, THEORY OF NUMBERS AND INEQUALITIES

Description of Course:

This is an introductory course in Number Theory for students interested in mathematics and the teaching of

mathematics. The course begins with the basic notions of integers and sequences, divisibility, and

mathematical induction. It also covers standard topics such as Prime Numbers; the Fundamental Theorem

of Arithmetic; Euclidean Algorithm; the Diophantine Equations; Congruence Equations and their

Applications (e.g. Fermat’s Little Theorem); Multiplicative Functions (e.g. Euler’s Phi Function);

Application to Encryption and Decryption of Text; The Law of Quadratic Reciprocity.

Course Objectives:

To present a rigorous development of Number Theory using axioms, definitions, examples, theorems and

their proofs.

Student Learning Outcomes: Students will be able to:

1) effectively express the concepts and results of Number Theory.

2) construct mathematical proofs of statements and find counterexamples to false statements in Number

Theory.

3) collect and use numerical data to form conjectures about the integers.

4) understand the logic and methods behind the major proofs in Number Theory.

5) work effectively as part of a group to solve challenging problems in Number Theory.

Text Book

1. Set theory and theory of equations by S.Arumugam and Issac.

2. Algebra by Narayanan and T.K. Manickavasagam Pillai.

Reference Book

Theory of Equations, Theory of Numbers and Inequalities by Dr. M.K. Venkataraman and Mrs.Manaroma Sridhar


Allied -I Core: Properties of Matter, Thermal Physics and Optics (4BPHA1)

Aim and objective:

To introduce the concept of elastic moduli.

To give the exposure of Moment of inertia.

To understand the concept of viscosity and Bernoulli’s theorem.

To make the students to learn about the conduction, convection and Radiation.

To understand the concept of Thermodynamic laws.

To enable the students to learn about the interference, diffraction and polarization.

Course outcomes:

Acquire the knowledge in different elastic moduli of the materials.

Ability to understand the application of Poiseuille’s formula and Bernoulli’s equation.

Thorough knowledge in stream lined motion and turbulent motion.

Enable to calculate the thermal conductivity of the bad conductor using Lee’s disc method.

Practice to derive the Rayleigh jeans law and Wien’s laws from Planck’s law.

Arrive the Carnot’s cycle condition for heat engine and cold engine.

Thorough knowledge in fundamental principles of thermodynamics.

Application of interference, diffraction and polarization.


I YEAR – II SEMESTER

Part -II English Name of the Subject(422E): Prose Extensive Reading and Communication Skills

Course Description

Students will be exposed to prose and short stories of great writers, provided they will learn

Grammar and composition to enhance the skill of LSRW.

Course Objectives

The core objectives of the above prescribed texts are :

1. Critical thinking, to analyse, evaluate, and synthesis the information he has gathered in

from the lecture.


3. To inculcate Social Responsibility about civic responsibility, and adjust with regional,

national and global communities.

Course Outcome:


a. Speak and write in English for Global competency.

b. Will be able to analyze literary works (prose and short stories).

c. They will also be exposed to basic literary genres of prose and short stories

d. Grammar, reading and writing exercises will make the student to read any text and understand it and

make them to think beyond the text.

e. Compositions give space for more writing skills. They will help the student to write essays, and




CORE COURSE III – INTEGRAL CALCULUS AND FOURIER SERIES

Course Description: This course in calculus is intended to develop practical skills in integral calculus and

Fourier series. As well, it is intended to illustrate various applications of calculus to technical problems.

Methods of algebraic integration will be introduced, with both definite and indefinite integrals being

determined for a variety of functions. The use of tables of integrals for finding solutions for difficult

integrals will be introduced. Various applications of integration will be studied including Fourier series.

And in particular about,

Definite Integrals and their properties, the Fundamental Theorems of Calculus, substitution, integration

by parts, other methods of integration, numerical techniques.

Reduction formula for Sinnx, cosnx, tannx, sinmxcosnx – Bernoulli’s formula

Beta and Gamma Integrals – Properties and Problems

Fourier series – Expansion of even and odd functions – half range series

Double integrals – change of variables – Jacobean – Triple integrals

Course Objectives: Integral Calculus and Fourier series is primarily concerned with developing the

students’ understanding of the concepts of calculus and providing experience with its methods and

applications. The course emphasizes a multi representational approach to calculus, with concepts, results,

and problems being expressed geometrically, numerically, analytically, and verbally. The connections

among these representations are also important

to introduce the basics of multivariable calculus and Integral Transformers and their applications.

Understand the meaning of integration and fourier series

to make the students understand the basic concepts of multiple integrals, vector calculus, and Fourier

transformers, Fourier series and their applications in various engineering problems.

To introduce improper integrals and specially to Beta and Gamma Functions

Course Outcome: Upon successful completion of this course, the student will have reliably demonstrated

the ability to:

Calculate definite integral values using Beta and Gamma Functions

define the basic concepts and principles of differential and integral calculus of real functions and

sequences and series

interpret the geometric meaning of differential and integral calculus

apply the concept and principles of differential and integral calculus to solve geometric and

physical problems. organize solving of complex problems by combining the acquired mathematical

concepts and principles

Apply integration to determine volumes, areas, and averages and to produce Fourier series.

Know how to derive a Fourier series of a given periodic function by evaluating Fourier coefficients.

Text Book

1. Calculus: Volume 2 by Narayanan and Manicka vasagampillai

2. Calculus Vol.3 (2004) by Narayanan and Manickavsagam pillai

Reference Book: Fourier series by S.Arumugam and Issac.



CORE COURSE IV – ANALYTICAL GEOMETRY OF 3D AND VECTOR CALCULUS

Course Description: This is a beginning course in plane analytic geometry emphasizing the

correspondence between geometric curves and algebraic equations. The course assumes a sound

background in analytical geometry, and vector calculus. The Geometry course includes,

Analysis of plane, solid, coordinate geometry, logic and proof, parallel lines and polygons,

perimeter and area analysis, volume and surface area analysis,

Analysis of Intersection of two lines, coplanar lines Shortest distance, distance between two

skew lines, Equation of a sphere Tangent line and tangent plane, section of a sphere problems.

Includes vector-valued functions, gradient, curl, divergence, vector identities, problems vector

fields, line and surface integrals partial derivatives, and the theorems of Green, Gauss, and

Stokes, vector operators and the extension of the calculus to the vectors in 3-D space.

Course Objectives: This course is intended to expose the students to,

Solve Bisector planes, Perpendicular distance from a point to a plane – Problems.

Evaluate angle between a line and a plane, length of perpendicular from a point to a line –

Shortest distance, distance between two skew lines

Demonstrate Vectors, gradient, curl, divergence, vector identities, and problems.

Solve Line integral, surface integral, volume integral.

Prove Green's Theorem, Stokes theorem, Gauss's Theorem. Statements and verification

Course Outcome: At the end of the course, a student who has studied and learned the material

should be able to:

Solve problems involving lengths and distances in the plane, including midpoint and point-

of-division formulas.

Demonstrate understanding of the notions of slope and inclination of lines, including angles

between lines, parallel lines, and perpendicular lines.

Recognize the relationship between equations in two variables and graphs in the plane and

use the equations to find pertinent information such as points of intersection, and intercepts.

Text Books

1. Analytical Geometry 3D and Vector Calculus by T.K. Manickavasagampillai and others.

2. Analytical Geometry 3D and Vector Calculus by Dr.S.Arumugam & Issac

Reference Books

Analytical Geometry 3D and Vector Calculus by M.K. Venkataraman & Manorama Sridhar


Allied Physics Practical (4BPHAP1)

Aim and objective:

To determine the young’s modulus of the given material.

To find the thickness of the thin wire using Air wedge.

To calibrate the given ammeter and voltmeter.

To find the number of lines per meter and wavelength of the mercury spectrum.

To verify the logic gates using discrete components and ICs.

To find the thermal conductivity of the bad conductor using Lees disc method.

Course outcomes:

Ability to determine the Youngs modulus of different mateials.

Able to calibrate the given ammeter and voltmeter using potentiometer.

Acquire the knowledge of interference fringes and measure the bandwidth.

Ability to construct the logic gates by using discrete components and ICs.

Capable of producing line spectra and measure the diffraction angle by using spectrometer.


Allied physics- II

ELECTRICITY, ELECTRONICS, ATOMIC AND NUCLEAR PHYSICS - 4BPHA2

The paper titled “Electricity, Electronics, Atomic and Nuclear Physics” is the allied paper for the

B.Sc., (Maths) and B.Sc.,(Chemistry) major students. Mathematics major students will study this allied

paper in the second semester whereas Chemistry major students will study this allied paper in the fourth

semester. This paper has four credits. The students will be examined for 60 marks externally and 15 marks

for internally.

Objectives:

The objectives of the paper “Electricity, Electronics, Atomic and Nuclear Physics” are

To be familiar with basic definitions in electricity

To be familiar with basic concepts of electromagnetism

To be familiar with various atoms model and related phenomenon

To understand the basic concepts in digital and analog electronics

Learning Outcomes

After course completion the students will have the following learning outcomes

Enable to understand the concepts of electricity and current flow related bridges

Enable to understand the concepts of magnetic fields

Thorough knowledge in the basic concepts of electromagnetic induction

Application of interference, diffraction and polarization experiments


Part - IV Name of the Subject: (4BES2) Environmental Studies.

Course Description

The course Explore the basics of environmental studies and the unique interdisciplinary methods used

to address the most challenging environmental problems. This segment will give to the students a brief

overview of types of issues and the solutions examined within environmental studies.

Course Objective:

Creating the awareness about environmental problems among to the students.

Imparting basic knowledge about the environment and its allied problems.

Examine the Renewable and Non renewable resources.

Motivating students to participate in environment.

Environmental Study to learn the importance of Eco-system.

Mention the causes and effect of pollution.


Developing an attitude of students for the environment.

Study the importance of Plantation. The Environmental Studies Program actively cultivates in our students for environmental issues. Acquiring skills to help the concerned individuals in identifying and solving environmental

problems.

Striving to attain harmony with Nature.

Texts Prescribe

1. K.C.Agarwal, Environmental Biology.

2. Bharucha Erach, The Biodiversity of India.

3. T.G.Miller, Environmental Science.

4. P.E.Odurm, Fundamental of Ecology.

5. R.E.Hawlinks, Encyclopedia of India Natural History.


II YEAR – III SEMESTER

Name of the Subject (432E)Poetry Drama and Communication Skills

Course Description

Prose, Poetry and Grammar Works are taught to students. Students will learn grammar and

composition to enhance the skill of LSRW.

Course Objectives

Texts Prescribed

a. Fragrant Thoughts in Flowery Words Ed. By the board of Editors

b. Modern English - A Book of Grammar Usage and Composition

by N.Krishnaswamy, Macmillan publisher

The core Objectives are:

a) Speak and Write in English

b) to analyse literary works

c) They will be exposed to basic literary genres of prose and poetry

Course Outcome

After completing the course, Students will be able to

a) Grammar, Reading and Writing exercises will make the students read any text

b) Composition practice will help the student to write essays



CORE COURSE V – MODERN ALGEBRA

Course Description: In this course, we will study algebraic structures that are fundamental to almost all

branches of mathematics and to other fields of study such as physics, chemistry, and computer science.

Modern Algebra covers group theory, including finite groups, subgroups, cyclic groups, permutation

groups, group isomorphism, and cosets, and introduces rings and fields, including integral domains,

polynomial rings, unique factorization domains and Euclidean domains. This course will also focus on

understanding and writing proofs.

Course Objective:

● Present the relationships between abstract algebraic structures with familiar numbers systems such as

the integers and real numbers.

● Present concepts of and the relationships between operations satisfying various properties (e.g.

commutative property).

● Present concepts and properties of various algebraic structures.

● Use results from elementary group theory to solve contemporary problems;

● Explain from elementary principles why certain algebraic facts are true.

Course Outcomes: ○ Students will have a working knowledge of important mathematical concepts in abstract algebra such as

definition of a group, order of a finite group and order of an element.

○ Students will be knowledgeable of different types of subgroups such as normal subgroups, cyclic

subgroups and understand the structure and characteristics of these subgroups.

○ Students will be introduced to and have knowledge of many mathematical concepts studied in abstract

mathematics such as permutation groups, factor groups and Abelian groups.

○ Students will gain experience and confidence in proving theorems. A blended teaching method will be

used requiring the students to prove theorems give the student the experience, knowledge, and

confidence to move forward in the study of mathematics.

○ Analyze and demonstrate examples of subgroups, normal subgroups and quotient groups,

○ Analyze and demonstrate examples of ideals and quotient rings,

○ Use the concepts of isomorphism and homomorphism for groups and rings

Text Book: Modem Algebra by Arumugam & others.



CORE COURSE VI – DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS

Course Description:

This course provides an introduction to topics involving

ordinary differential equations. Emphasis is placed on the development of abstract concepts and

applications for first-order and linear higher-order differential equations,.

Exact differential equations –Clairaut's equation – Second and higher order linear Differential equations

with constant Coefficients. Homogeneous linear Equations with variable coefficients

Method of reduction and variation of parameters –Necessary and Sufficient condition of integrability of

Pdx+Qdy +Rdz = 0 – Rules for solving it.

Partial Differential Equations – Formation of P.D.E. by the elimination of constants –Lagrange’s

method – Charpit’s method.

Laplace Transforms and Inverse Laplace Transforms –

Course Objectives: learning differential equations is certainly one of the goals of this course, the purpose of

this module is to provide participants with the skills, knowledge and attitudes required to solve differential

equations

Identify essential characteristics of ordinary differential equations.

Explore the use of differential equations as models in various applications

classify differential equations by order, linearity, and homogeneity • solve first order linear

differential equations • solve linear equations with constant coefficients • use separation of variables

to solve differential equations • solve exact differential equations • use variation of parameters to

solve differential equations

Laplace transforms and their inverses to solve differential equations • solve systems of linear

differential equations using matrix techniques and eigenvalues • use numerical methods to solve

differential equations

Course Outcome - On completion of this module the learner should be able to:

Find general solutions to first-order, second-order, and higher-order homogeneous and

nonhomogeneous differential equations by manual and technology-based methods.

Determine solutions to first order exact differential equations,Clairaut's equation.

Determine solutions to second order linear homogeneous differential equations with constant

coefficients.

Determine solutions to second order linear non-homogeneous differential equations with constant

coefficients

Determine solutions to Partial Differential Equations – Formation of P.D.E. by the elimination of

constants –Lagrange’s method – Charpit’s method

Select and apply appropriate methods to solve differential equations; variation of parameters,

LaPlace and inverse LaPlace transforms

Text Book

Differential Equations by T.K.Manivasagam and Narayanan

Reference Book

Differential Equations and Laplace Transforms by Dr. M.K. Venkataraman & Mrs. Manorama Sridhar


ALLIED COURSE III

COURSE CODE: 4BCEA3

PROGRAMMING IN C (THEORY & LAB)

Course Description

This C programming course provides a comprehensive introduction to the ANSI C language,

emphasizing portability and structured design. Comprehensive examples are integrated throughout to

reinforce learning.

Course Objectives

Students will be exposed to C Programming language. They will learn syntax and semantics in C

language. Students are introduced to fundamental data types, flow control, and standard function libraries.

Thorough treatment is given to the topics of string and character manipulation, dynamic memory allocation,

standard I/O, macro definition, and the C runtime library. The course explains the use of structures, unions,

and pointers. Structured programming constructs and various functions are also covered. Emphasis is given

to the processing of command line arguments and environment variables so students will be able to write

flexible, user-friendly programs. They will also learn to solve problems using various programming logic

and various file types.

Texts Prescribed

The first book is the prescribed text book and the next one is given as reference.

1. Programming in ANSI C – E.Balagurusamy Tata McGrawHill Publishing Company Ltd, New Delhi

2. Programming with C – K.R.Venugopal, Sudeep.R Prasad Tata McGrawHill Publishing Company

Ltd, New Delhi.

Lectures enable the students to learn new material relevant to computational thinking. Practical classes

enable the students to put into practice learning from lectures and strengthen their understanding through

application. Students are assessed by formative and summative assessment and examinations.

Course Outcomes(COs)


CO1. Develop their skill in C programming language.

CO2. Understand the basic concepts of program development statements and its syntax.


CO3. Understand the various types of arrays.

CO4. Know about the various types of Functions and String handling mechanisms.

CO5. Really Understand the Concepts of structures and Unions.

CO6. Illustrates the various operations performed on different types of data files.

Part - IV Course code : 4 SBS 3A1

COMPETITIVE EXAMINATIONS SKILLS

COURSE DESCRIPTION:

Students are expected to develop the skill of creativity, numerical ability to have

a better job.

COURSE OBJECTIVE:

STUDENTS COMPLETING THE COURSE WILL BE ABLE TO:

1. Develop the art of speaking to have a fluency in language

2. Know the various type of inductive reasoning to develop the individual memory.

3. Developing the verbal skill of an individual.

4. Analyze the various test of an individual.

5. Prompt thought to have a overall development in an individual.

6. Understanding Analytical Method which are essential for the development of an

individual.

Text prescribed:

1. Ajay raj – intelligence Tests.

2. Competition success Review.

The above two books are prescribed texts for first two semesters.


Course code:4 NME 3C EFFECTIVE EMPLOYABILITY SKILLS

COURSE DESCRIPTION:

Students will be exposed to have employment which are the basics of life to

have income which lead to higher standard of living.

COURSE OBJECTIVE:

Students completing the course will be able to,

1. Fill the job application form while they are approaching for the job without

others help.

2. Know the frequently asked question in the interview.

3. The rules to be followed while facing the interview.

4. Steps to be followed in group discussion with the management.

5. Leadership qualities that are needed for the growth of inculcating the

characteristics of the leader.

COURSE OUTCOME (COS)

THE PRESCRIBED TEXTS ARE:

1. D.K.Sarma – you of your career.

2. IndianJaycees- Skills Series.

The above two books are prescribed texts for first two semester. The course objectives

of the above prescribed text are,

1. Critical thinking about how to face the interview.

2. Analytical skill to develop the art to face the interview.


II YEAR – IV SEMESTER

Name of the Course: Shakespeare and English for Competitive Examinations(442E)

Course Description To enable the learners become proficient users of English involving all the skills, so that the students

confidentially face competitive examinations and come out successfully.

Objectives

1. To impart specific training necessary for writing competitive examinations.

2. To facilitate effective communication in English.

3. To familiarize the learners with the use of technology for writing the exams

4.To make the students understand and relish the great works of Shakespeare.

Course Outcomes

Abilities Developed:

1. Usage of appropriate vocabulary in appropriate contexts, identifying unnecessary words and sentence

structure, critical analysis, summarizing skills and identifying the tone.

2. Fluency in English, precise and correct use of English language, building confidence in handling English

language.

Text Prescribed:

1. Twelfth Night - Shakespeare

2. English for Competitive Examination- R.P. Bhatnagar.



CORE COURSE VII – SEQUENCES AND SERIES

Course Description: This course will introduce students to a variety of new techniques of infinite series,

and to sequences and series. Students will be expected both to become proficient with basic skills and to

demonstrate an understanding of the underlying principles of the subject.

Sequences:, Convergence, divergence. Oscillation, Monotonic and bounded sequences, subsequence and

Cauchy sequence. algebra of limits. Behaviour of Geometric sequence.

Infinite series: Series of positive terms cauchy’s general principle of convergence, comparison test ,

Harmonic series 1/np

Kummer’s test, Raabe’s test ,D’ Alembert’s ratio test, cauchy’s root test ,Gauss test and Problems

Cauchy condensation test, cauchy’s integral test Alternating series,Absolute convergence ,conditionally

convergence ,Leibnitz’s test and Problems

Course Objectives: The aim of this course is to develop an understanding of convergence in its simplest

setting. And also to learn about

the difference between a sequence and a series in the mathematical context.

The convergence/divergence of a series so we will give the basic ideas and definitions in this

section.

Using the Integral Test, Comparison Test ,Limit Comparison Tests, Alternating Series Test, Ratio

Test and Root Test to determine if a series converges or diverges.

A brief discussion on absolute convergence and how it differs from convergence.

A set of general guidelines to use when deciding which test to use.

Course outcomes: By learning this course students will be able to

Evaluate the limit of a sequence

Evaluate the limit of an infinite series

Determine the monotonic and bounded sequences.

Test the convergence of an infinite series

Represent a function as a power series

Represent a function as a infinite series

Use series in application problems

Text Book: Sequences and Series by S.Arumugam and Issac.

Reference Book: Algebra Vol.1 by T.K.Manikavasagampillai and Others.



CORE COURSE VIII – LINEAR ALGEBRA

Course Description: This course covers matrix theory and linear algebra, emphasizing topics useful in

other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the

properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social

sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of

the most widely taught subjects in college-level mathematics

Course Objective: ● Understand real vector spaces and subspaces and apply their properties. Understand linear

independence and dependence.

● Find basis and dimension of a vector space, and understand change of basis.

● Compute linear transformations, kernel and range, and inverse linear transformations, and find matrices

of general linear transformations.

● Find the dimension of spaces such as those associated with matrices and linear transformations.

● Find eigenvalues and eigenvectors and use them in applications.

● Compute inner products on a real vector space and compute angle and orthogonality in inner product

spaces.

Course Outcomes: ● Use computational techniques and algebraic skills essential for the study of systems of linear equations,

matrix algebra, vector spaces, eigenvalues and eigenvectors, orthogonality and diagonalization.

● Use visualization, spatial reasoning, as well as geometric properties and strategies to model, solve

problems, and view solutions, especially in R2 and R3 , as well as conceptually extend these results to

higher dimensions.

● Critically analyze and construct mathematical arguments that relate to the study of introductory linear

algebra.

● Communicate and understand mathematical statements, ideas and results, both verbally and in writing,

with the correct use of mathematical definitions, terminology and symbolism.

● Work collaboratively with peers and instructors to acquire mathematical understanding and to formulate

and solve problems and present solutions.

Text Book: Algebra by S. Arumugam and Issac.

Reference Book: Modern Algebra by T.K. Manicavachagom Pillay and Narayanan


II YEAR – III/IV SEMESTER

COURSE CODE : 4BCEAP2 Allied Practical – II - PROGRAMMING IN C AND C++ LAB

(for allied course III & IV)

Course Description

This C and C++ programming lab course provides hands on training in ANSI C language. Comprehensive

hands on exercises are integrated throughout to reinforce learning and develop real competency. The C and

C++ Lab course provides hands on training to students. The list of program are integrated throughout to

reinforce learning and develop real competency.

Course Objectives

This course objective is to write, compile, debug and execute C and C++ programs, to formulate

problems and implement algorithms and to effectively choose programming components that efficiently

solve computing. The list of C Programs are to find the is odd or even , sum of digits, Armstrong number,

Prime number, perfect number, palindrome, simple and compound interest , sorted array, Counting

positive, negative and zeros.

Students will be exposed to C++ Programming language. They will learn syntax and semantics of

statements in C++ computer programming language. They will also learn to solve problems in Object

oriented ways i.e., bottom approach.

The list of C++ programs are to evaluate STD, Farenheit to Celsius, Sum of digits using constructor,

employee paybill, adding and multiplying complex numbers using operator over loading, student mark list,

to find volume using inline function and to apply Multiple inheritance and Hierarchical inheritance.

Students come with their developed programs to their lab session. They have to enter, compile, link

and execute two programs in their lab session. They have to correct the syntax error, logical errors, input

errors and output errors. Students are assessed by formative and summative assessment and examinations.


Upon successful completion of this lab Course, student will be able to


CO1. Use Arrays and Functions in programs.

CO2. Use pointers, structures and files handling.

CO3. Develop their skill in executing C programs.

CO4. Construct the flowchart to solve mathematical and scientific problems.

CO5. Use the features of C++ using object oriented programming.

CO6. Use encapsulation and inheritance.

CO7. Develope programs in C++ Using polymorphism.

CO8. Use the advanced features of C++ specifically stream I/O and operator overloading.

CO9. Design and test programs to solve mathematical and scientific problems using object oriented

concepts.

COURSE CODE: 4BCEA4

ALLIED COURSE IV PROGRAMMING IN C++ (THEORY & LAB)

Course Description

Students will be exposed to C++ Programming language. The C++ programming course provides an

accelerated introduction to the most essential syntactical components of the C and C++ language, focus on

object-oriented programming with C++. Comprehensive examples are integrated throughout to reinforce

learning and develop real competency.

Course Objectives

Students will learn syntax and semantics of statements in C++ language. The course begins by

introducing the built in data types, fundamental control constructs, and rich expression operator repertoire

common to both C and C+. The central concepts of C++ syntax and style are taught in the context of using

object-oriented methods to achieve reusability, adaptability and reliability. Emphasis is placed on the

features of C++ that support abstract data types, inheritance, and polymorphism. Students will learn to

apply the process of data abstraction and class design. Practical aspects of C++ programming including

efficiency, performance, testing, and reliability considerations are stressed throughout. They will also learn

to solve problems in using object oriented approach.

Texts Prescribed : The first book given below is the prescribed text book and the next two books are

given for reference.

1. Mastering C++ – K.R.Venugopal, T.Ravishankar, RajKumar, Tata Mc Graw-Hill Publishing

Company Limited, New Delhi 2006.

2. Object Oriented Program in C++ – Nabajyoti barkakati, A prentice Hall of India Private Limited,

New Delhi 1997.

3. Balagurusamy, Object Oriented Programming with C++, Tata McGraw Hill, New Delhi.





Course Outcomes(COs) Students completing the course will be able to

CO1. Explain the top-down and bottom-up programming approach and apply bottom up

approach to solve real world problems.

CO2. Explain the difference between static and dynamic binding.

CO3. Describe the concept of inheritance, overloading, constructors and apply real world

problems.

CO4. Discuss the generic data type for the data type independent programming which relates it

to reusability.

CO5. Explain to design of handling large data set using File I/O.

CO6. Develop their skill in C++ programming language.

III YEAR – V SEMESTER


CORE COURSE IX – MODERN ANALYSIS

Course Description: The course will cover the topics contained in the five units of the syllabus.

Several additional topics will also be covered and the presentation will not necessarily follow the

text. Attendance is required and the exams will be over the lectures and homework. The course

topics include:

countable and uncountable sets inequalities of holder and minkowski-

metric space and subspace

Completeness intersection theorem-baire category theorem.

Continuity uniform continuity

Connectedness and continuity - intermediate value theorem.

Characterization for compactness - continuity and compactness.

Course Objectives This course is intended to expose you to the basic ideas of Modern Analysis. In

particular to learn about

basic properties of the field of real numbers.

the series of real numbers and convergence.

Open and Closed Sets of Real Numbers Compact, Perfect and Connected Sets The Intermediate

Value Theorem

Definitions, theorems, techniques etc… these are your mathematical tools and as a bare

minimum you have to know what they are.

continuity of a function and uniform continuity of a function

To prove various theorems about continuous functions and emphasize the proofs’ development

Course Outcome: After completion of course, the students will be able to

Define and recognize the basic properties of the field of real numbers

Improve and outline the logical thinking.

prove a basic set theoretic statement

prove a theorem about continuous functions

Give the definition of concepts related to metric spaces, such as continuity, compactness,

completeness and connectedness

Understand and perform simple proofs

apply critical thinking skills to solve problems that can be modeled mathematically.

Text Book : Modern Analysis by S. Arumugam and Issac

Reference Book : Modern Analysis by A.R.Vasishta


Part - IV

Course code: 4 SBS 4B2 EMERGENCY AND MEDICAL LAB SKILLS

COURSE STRUCTURE: The course is designed to provide understanding about

different types of emergencies and the required medical skills to be given to the people

being affected.

COURSE OBJECTIVES:

1. To prepare the students to rise to the occasion of emergencies.

2. To provide the medical lab skills to those people affected by natural and other

situations.

COURSE OUTCOMES:

1. provide knowledge and skills to rescue people affected by fractures fire Snake

bite road and bite and heat stroke and those people affected by the diseases like

diarrhoea and dysentery.

2. Introduces the traffic rules and precautions to be followed during the Travels

along the roads.

3. Introduces the basic knowledge about medical lab tests for the human beings

4. Use knowledge about treating different types of diseases by using locally

available Herbals.

5. The project work given to the students main provide them chances to learn


about different types of diseases and the methods of curing Dum by using native

treatments.

REFERENCE BOOKS

1. Muthu,R.S., and Meera Ravishankar(2013), First Aid, Sura books Private Limited,

Chennai.

2. Rama Rao, Handbook of First Aid, Sura books Private Limited, Chennai.

Course code: 4 BMY4 MANAVALAKALAI YOGA COURSE DESCRIPTION:

It provides a thorough arena for meditation, yoga and physical exercise which

leads to holistic health that totally transforms a person.

COURSE OBJECTIVES:

STUDENTS COMPLETING THE COURSE WILL BE ABLE TO

1. Understand the health concepts and the different aspects of physical body.

2. Have the basic knowledge on simplified physical exercise and asanas.

3. Introspect and improve the behaviour of an individual.

4. Understand how to improve concentration and focus.

5. Improve intellectual sharpness.

COURSE OUTCOME:

1. To enhance soft skills and develop the ability for an efficient management in

their field chosen.

2. Inculcates the social responsibility, to realize the enduring values of peace, Non-

Violence and hormone to revitalize human society for restoring its sanity and

strength.

TEXT PRESCRIBED:

1. Value education – World Community Service Center, Veathethery

publishing house


Course code:4 BWS4 WOMEN STUDIES

COURSE DESCRIPTION:

The students will be exposed to gender identity, gender equality, role

of gender in different aspects, capacity of women and the various schemes

and programmes implemented for women empowerment.

COURSE OBJECTIVES:


1. Explain the concepts of socialisation and internalisation and gain knowledge on

gender ideology.

2. Understand the role of women in various capacity and how she balances both

work and family efficiently.

3. Explain the different indexes such as HDI, GDI, GEM and participation of women

in decision making and the political arena.

4. Explain physical and biological differences of gender in sports and the mental

ability of women in handling emotions.

5. Understand the different policies, welfare schemes and programmes introduced

by the central and state government.

6. Explain the concepts, levels and tools of women empowerment.

COURSE OUTCOME:


Inculcates social responsibility by imparting the role of women to the

stakeholders and play active role in empowering women to have a balanced

development.

TEXT PRESCRIBED:

a. Complete outlook of women in various dimensions. – women in perspective:

Essays on Gender issues by Shoma A. Chaterji, Vitasta Publishing Pvt.Ltd.

b. Gender sensitization – Gender Socialization and the Making of Gender in

the Indian Context by susithkumar chattotathyay, SAGE Publication pvt.Ltd.

III YEAR – V SEMESTER

Part-III Name of the Subject (4BMA5C1) Modern Analysis

Course Description: The course will cover the topics contained in the five units of the syllabus.

Several additional topics will also be covered and the presentation will not necessarily follow the

text. Attendance is required and the exams will be over the lectures and homework. The course

topics include:











Open and Closed Sets of Real Numbers Compact, Perfect and Connected Sets The

Intermediate Value Theorem

Definitions, theorems, techniques etc… these are your mathematical tools and as a bare

minimum you have to know what they are.


To prove various theorems about continuous functions and emphasize the proofs’

development

Course Outcome After completion of course, the students will be able to










Text Book

Modern Analysis by S. Arumugam and Issac

Reference Book

Modern Analysis by A.R.Vasishta


CORE COURSE X – MATHEMATICAL STATISTICS

Course description: This course is an introduction to probability density function, probability distribution,

test of signification, analysis of varience and Latin square design.


1. know about p.d.f of a random variable, expectation and moment generating function of variable.

2. have knowledge in binomial, poisson, normal distribution.

3. know the methods to test the hypoyhesis for large samples.

4. know the methods to test the hypoyhesis for small samples.

5. expose to chi-square distribution, analysis of variance.


1. evaluate p.d.f of a discrete and continuous random variable, expectation and moment generating

function of discrete and continuous of variable.

2. do problems using binomial, poisson, normal distribution.

3. test the null hypoyhesis for large samples.

4. test the null hypoyhesis for small samples.

5. do problems in analysis of variance: one way classification, two way classification and the Latin

square.

Text book: Statistics - S.Arumugam and Issac.



CORE COURSE XI - STATICS

Course Description: The course covers the following topics; statics of particles: forces in plane, forces in

space, equilibrium, moment of a force, moment of a couple, equivalent systems of forces on rigid bodies,

equilibrium in two dimensions, equilibrium in three dimensions, distributed forces: centroids and center of

gravity, analysis of structures: trusses, frames and machines, internal forces in beams and cables, friction,

moments of inertia of areas, moments of inertia of masses, method of virtual work.

Course Objectives: 1) To provide definition of force and moment vectors and give necessary vector algebra

2) To explain the concept of equilibrium of particles and rigid bodies in plane and 3D space

3) To give information about support types and to give ability to calculate support reactions

4) To explain the equilibrium of structures and internal forces in trusses, and frames

5) To give information about distributed loads

6) To provide information on moment of inertia

7) To explain virtual work concept.

Course Material: Text Book is Statics (17thedition) by Dr. M.K.Venkataraman, Agasthiyar Publications,

Tiruchirapalli, 17th Edition, July 2014.



CORE COURSE XII - LINEAR PROGRAMMING

Course Description: Operations Research is the study of scientific approaches to decision-making.

Through mathematical modeling, it seeks to design, improve and operate complex systems in the best

possible way. And also, introduce the students to the advanced methods for large-scale transportation and

assignment problems. The goal of this course is to teach to formulate, analyze, and solve mathematical

models that represent real-world problems.

Course Objective:

● Formulate a real-world problem as a mathematical programming model

● Understand the theoretical workings of the simplex method for linear programming and perform

iterations of it by hand

● Understand the relationship between a linear program and its dual, including strong duality and

complementary slackness

● Solve specialized linear programming problems like the transportation and assignment problems

● To introduce the students to the use of basic methodology for the solution of linear Programs.

Course Outcomes: ● explain the meaning of operations research

● know the various techniques of operations research;

● select an optimum solution with profit maximization;

● Identify and develop operational research models from the verbal description of the real system.

● Understand the mathematical tools that are needed to solve optimisation problems. Use mathematical

software to solve the proposed models.

Develop a report that describes the model and the solving technique, analyse the results and propose

recommendations in language understandable to the decision-making processes in Management

Engineering.

Text Book Operations Research by Kanti Swarup, P.K. Gupta & Man Mohan

Reference Books

1. Operations Research by Hamdy A. Taha

2. Linear Programming by M.K. Venkataraman


COURSE CODE: 4BMAE1A

ELECTIVE COURSE I (A) – GRAPH THEORY

Course Description: The course covers basic theory and applications of combinatory and graph theory.

Combinatory is a study of different enumeration techniques of finite but large sets. Topics that will be

studied include principle of inclusion and exclusion, generating functions and methods to solve difference

equations. Graph theory is a study of graphs, trees and networks. Topics that will be discussed include Euler

formula, Hamilton paths, planar graphs and coloring problem; the use of trees in sorting and prefix codes;

useful algorithms on networks such as shortest path algorithm, minimal spanning tree algorithm and min-

flow max-cut algorithm. Course Objectives: The successful student will know the definitions of relevant

vocabulary from graph theory and combinatory, and know the statements and proofs of many of the

important theorems in the subject, and be able to perform related calculations.

Course Objectives: The successful student will know the definitions of relevant vocabulary from graph

theory and combinatory, and know the statements and proofs of many of the important theorems in the

subject, and be able to perform related calculations.Goals of the Course:

• gain an understanding of the fundamental concepts of graph theory,

• gain an understanding of when a graph is a useful mathematical tool to solve problems in mathematics, the

sciences and the environment,

• develop the ability to write a logical and coherent proof, including proof by contradiction and induction,

• introduce topics suitable for a senior thesis (and see ones that have been),

• develop a desire for further study in related areas, including combinatorics and computer science.

Text Books

1. Invitation to graph Theory: Dr. S Arumugam and others

2. A first course in Graph Theory: S.A. Choudam. (For directed graph)

Reference Graph Theory – Bondy Mur


Part - IV Course code:4 SBS A4

HERITAGE AND TOURISM

COURSE DESCRIPTION:

This course covers the Importance of Tourism and inter-linkage factors between

Heritage and tourism.

COURSE OBJECTIVES:

1. To illustrate the complexity of “heritage” and heritage tourism;

2. Students will learn the tourist places in regional, state level and national level

3. To outline the challenges of conserving, managing and marketing heritage

tourism;

4. Inculcate and mindset creation to go around the tourist places to enrich their

knowledge on cultural and linguistic integration.

5. Speak and write other Indian languages for national competency, for that

tourism will motivate the students.

6. Will be able to get new innovative ideas to promote tourism by attracting even

foreign tourists.

COURSE OUTCOME:

This course will bring national integration through tourism. Students will turn into

broad minded humans and social reforms, also economic development will be

enhanced.

TEXTS PRESCRIBED:

A. Bhatia, A. K – Tourism Development Principles and Practices, Sterling Publishers


(P) Ltd., New Delhi)

B. Ananand M. M – Tourism and Hotel Industry in India Sterling Publishers (P)

Ltd., New Delhi

c. Acharya Ram – Tourism and Cultural Heritage Rosa Publications: Jaipur, 1986)

These texts will pave the way for critical understanding of the relationships between

culture, heritage and tourism;

COURSE

CODE

COURSE TITLE COURSE

HOURS

COURSE

CREDIT

COURSE

EVALUATION

4 SBS 5A5 MARKETTING AND

SALES MANAGEMENT

2 HOURS PER

WEEK 2

INT EXT TOT

25 75 100

COURSE DESCRIPTION:

This course is meant to be an introduction to a career in sales. Despite the “sales” focus, students can find

significant value in the sales techniques for many other elements of their lives, from leadership and management to

career-building concepts such as interviews.

COURSE OBJECTIVES

1. Recognize the key drivers of change in selling and sales management.

2. Understand the best practices in selling that lead to exceeding customer expectations.

3. Explain the historical basis for stereotypical views of selling in society.

4. Identify and explain key success factors for salesperson performance.

5. Discuss and give examples of different types of selling jobs.

6. List and explain the role of various participants in an organizational buying center.

COURSE OUTCOME:

This course is designed to provide students with an understanding of the processes involved in personal selling and

sales management.

TEXTS PRESCRIBED:

1. Chunawalla, S. A., Sales Management, 5th Edition (2007), Himalaya Publishing House

2. Havaldar, Krishna; Sales And Distribution Management, 1st Edition (2006), Tata Mcgraw Hill

3. Perreault, Jr., William; Mccarthy, E. Jerome, Basic Marketing, 15th Edition, 2006,

Tata Mcgraw Hill

These texts will enrich knowledge on marketing sales management besides students could learn many


marketing and sales management techniques


III YEAR – VI SEMESTER


CORE COURSE XIII – COMPLEX ANALYSIS

Course Description: This course is an introductory course on Complex Analysis. It is designed for

students in Mathematics disciplines. It may, however, be useful to students in engineering and other related

fields. It introduces students to the complex numbers system and varieties of operations, analyses and

problems that may arise within the context. It also equips the students with mathematical techniques and

skills to handles such cases. Topics to be covered in this course includes: Introduction to complex number

system, Limits and Continuity of Complex variable functions, Derivation of the Cauchy –Riemann”s

Equation, Analytic functions. Harmonic functions, Bilinear transformation, Conformal mapping, Contour

Integrals, Convergence of a sequences and series of function of Complex variable. Complex numbers, the

topology of the complex plane, the extended complex plane and its representation using the sphere.

Complex functions and their mapping properties, their limits, continuity and differentiability, analytic

functions, analytic branches of a multiple valued function. Complex integration, Cauchy's theorems,

Cauchy's integral formulae. Power series, Taylor's series, zeroes of analytic functions, Rouche's theorem,

and open mapping theorem. Mobius transformations and their properties. Isolated singularities and their

classification, Laurent’s series, Cauchy’s residue theorem, the argument principle

Course Learning Outcomes: Demonstrate understanding of the basic concepts underlying complex

analysis. Demonstrate familiarity with a range of examples of these concepts. Prove basic results in

complex analysis. Apply the methods of complex analysis to evaluate definite integrals and infinite series.

Demonstrate understanding and appreciation of deeper aspects of complex analysis such as the Riemann

Mapping theorem.

Objectives: Demonstrate skills in communicating mathematics orally and in writing.

Upon successful completion of this course, the student will be able to:

justify the need for a Complex Number System and explain how is related to other existing number

systems

define a function of complex variable and carry out basic mathematical operations with complex

numbers.

know the condition(s) for a complex variable function to be analytic and/or harmonic

State and prove the Cauchy Riemann Equation and use it to show that a function is analytic.

define singularities of a function, know the different types of singularities, and be able to determine the

points of singularities of a function.

explain the concept of transformation in a complex space (linear and non-linear) and sketch associated

diagrams.

understand the concept of sequences and series with respect to the complex numbers system and

establish whether a given series/ sequences is convergent/ divergent at a specified point or interval.

Text Book: Complex Analysis by S. Arumugam & Issac

Reference Book

1. Complex Analysis by Dr. N. Sridharan

2. Complex Analysis by S.Narayanan & T.K.Manickavasagam Pillai



CORE COURSE XIV – OPERATIONS RESEARCH

Course Description: Operations research (OR) has many applications in science, engineering, economics,

and industry and thus the ability to solve OR problems is crucial for both researchers and practitioners.

Being able to solve the real life problems and obtaining the right solution requires understanding and

modeling the problem correctly and applying appropriate optimization tools and skills to solve the

mathematical model. The goal of this course is to teach to formulate, analyze, and solve mathematical

models that represent real-world problems.

Course Objective: The objectives of this course are to:

● introduce students to the techniques of operations research in mining operations

● provide students with basic skills and knowledge of operations research and its application in mineral

industry

● introduce students to practical application of operations research in big mining projects

● And, the subject learning will emphasize the mathematical procedures of nonlinear programming search

techniques, probabilistic models in operations research.

● Students successfully completing this course are expected to be able to apply a variety of operations

research techniques for solving nonlinear programming problems; to have a good command of

probabilistic operations research methods and dynamic programming techniques; and to be familiar

with computer software for solving nonlinear programming problems.

Course Outcomes:

formulate and solve problems as networks and graphs.

solve the problems using special solution algorithms.

use CPM and PERT techniques, to plan, schedule, and control project activities.

set up decision models and use some solution methods for nonlinear optimization problems.

Formulate and analyses the general nonlinear programming problems.

use some solution methods for solving the nonlinear optimization problems.

propose the best strategy using decision making methods under uncertainty and game theory and to

solve the zero-sum two- person games

Text Book: Operations Research by

1. Kanti Swarup, P.K.Gupta & Man mohan

2. Sultan Chand & Sons, New Delhi, Nineth Edition Chapters 1,17, 18,19, 20 and 21

Reference Books 1. Hamdy A Taha: Operations Research

2. Sundaresan & others Operations Research



CORE COURSE XV – DYNAMICS

Course Description: Dynamics is the study of motion and force systems on bodies in motion. The course

will be an overview of the application of Newton's Laws to rectilinear and curvilinear motion problems.

Plane motion, work/energy, impulse/ momentum, force analysis, and mechanical vibration will be studied

as well as motivation to understand and analyze linkages.

Student Learning Outcomes: On successful completion of this course the student will have reliably

demonstrated the ability to:

1. Apply analytical skills to solve problems involving motion, force and energy

2. Determine the specific effect of forces on the motion of an element by applying the laws of motion and

conservation of energy and momentum.

3. Use dynamics theory in the solution of various engineering problems

Course Material: Text Book is Dynamics (18th edition) byDr. M.K.Venkataraman, Agasthiyar

Publications, Tiruchirapalli, 2017

Text Book: M.K.Venkataraman, Dynamics, Agasthiar Publications.


COURSE CODE: 4BMAE2B

ELELCTIVE COURSE II (B) – FUZZY ALGEBRA

Course Description: To master the various fundamental concepts of fuzzy logic. This will help the students

to get sufficient knowledge on Fuzzy sets. This course introduces students to the basic concepts of

Extension principle for Fuzzy sets.

Operations on Fuzzy sets– Fuzzy complements fuzzy morphisms

Fuzzy numbers Fuzzy relations – Binary fuzzy relations – Fuzzy equivalence relations.

Course Objectives: Provide an understanding of the basic mathematical elements of the theory of fuzzy

sets.

Be able to understand basic knowledge of fuzzy sets and fuzzy logic

Be able to apply basic knowledge of eextension principle for Fuzzy sets.

Be able to apply basic fuzzy inference and approximate reasoning

Be able to understand the basic notion of fuzzy rule base

Be able to apply basic fuzzy complement

Be able to apply basic fuzzy relations and inverse relations.

Be able to understand the basic notion of fuzzy numbers.

Course Outcome:

Upon successful completion of this course, the student will be able to

Understand how fuzzy sets model ambiguity.

Manipulate fuzzy membership functions for simple operations.

Be familiar with the nature and use of fuzzy relations.

Perform linguistic analysis using fuzzy sets.

Develop and simulate simple fuzzy numbers

Familiar with a wide variety of areas in which fuzzy sets may be applied.

Text Book George J.Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic, Prentice Hall of India, New Delhi,

2004.

References 1. H.J. Zimmermann, Fuzzy Set Theory and its Applications, Allied Publishers Limited, New

Delhi, 1991



ELECTIVE COURSE III (A) – NUMERICAL ANALYSIS

Course description: This course introduces the theory and application of numerical methods and

techniques to interpolate, to evaluate derivatives and integrals from the given data and also to solve

difference equation and differential equation.


1. be introduced to the operators Error! Reference source not found. and E, factorial polynomial and

difference of polynomial.

2. learn Newton’s forward and backward formulas, Newton’s divided difference formula and etc… to

interpolate. Also successive approximation.

3. expose to numerical differentions and integration.

4. accure knowledge in summation of series and difference equation.

5. know to solve differential equations by Euler, Taylor and Runge –Kutta methods.


1. prove the relations between the numerical operators and find the difference of a given polynomials.

2. interpolate using the learnt formulae.

3. find derivatives and integrales from the given data without knowing the function.

4. sum the given series, solve difference equation and differential equation using numerical methods.

5. solve differential equations by Euler, Taylor and Runge –Kutta methods.

Text Book: Numerical Analysis – S.Arumugam & Issac

Reference: Numerical methods in Science and Engineering – M.K.Venkatraman


Part-IV Course code:4SBS6B3

BASIC INTERNET AND OFFICE AUTOMATION LAB COURSE DESCRIPTION

Students will get fundamentals of knowledge in MS-Word, MS-Excel, a

preparation of power point slides, Internet browsing and application of tools in social

science.

OBJECTIVES OF THE COURSE:

1. MS-Word is introduced in the syllabus to help the students learn typing,

alignment, cut, copy, paste etc., of theoretical work

2. MS-Excel is help the students in diagrammatic and statistical representation of

data, Drafting documents, preparation of balance sheet accounts etc.,

3. MS- PowerPoint to enhance the knowledge of students in the presentations of

slides, flex, animation work etc.,

4. Internet and Browsing to give access to students in downloading reading

materials, literature etc., their subject.

5. Statistical Package for Social Science (SPSS) to apply statistical and mathematical

tools in the preparation of thesis, dissertation, project etc.,

COURSE OUTCOMES

Application of computer knowledge in economics has widened the scope of Economics.

1. Ms-Word and Excel to highly useful in the analysis, evaluation, interpretation and

presentation of statistical data collected.

2. Through the knowledge in internet browsing, students can download relevant

literature or any study material they need.

3. SPSS is highly useful, when they go for higher studies or when they undertake

research works.

4. PowerPoint presentation helps the students to effectively give the substance of a

topic in a nutshell.

TEXT BOOKS


1. V.Rajaram Fundamentals of computers, Prentice Hall of India, New Delhi.

2. P.K.Singa, Computer Fundamentals, BPB publication, New Delhi.

3. E.Balagurusamy, Programming in Basic, TataMcGraw Hill publication New Delhi.

Course code:4SBS6B4

FRUITS AND VEGETABLES PRESERVATION SKILLS

COURSE DESCRIPTION:

Provides the knowledge related to the various types of vegetables and fruits that

could be preserved, the preservation techniques available the related equipment’s and

methodology.

COURSE OBJECTIVES:

1. To improve income earning skills through fruits and vegetable

preservation.

2. To open up new areas of self-employment opportunities for the youth.

COURSE OUTCOMES

1. Introduces the principles and method available in the preservation process.

2. Provides knowledge about various types of equipment available and different

types of containers that are being used in the preservation process.

3. To introduce various methods available for the preservation of vegetables and

fruits. Also gives knowledge related to personal hygiene and the sanitary

standards to be followed in the preservation process.

4. Gives the practical knowledge of fruits and their preservation methods.

5. The project work helps the students to know the various centres that are

involved in the reservation practices. Also it helps to understand the area

specific Technology that could be applied.

REFERENCE BOOKS

1. Srivastava,R.P. and S.Kumar., fruit and vegetable preservation: principles.

2. Ranjit Singh, Fruits, National Book Trust.

3. Girdhari Lal Tandon et al., Preservation of Fruit and Vegetable Products.


------------------------------------------------------------------------------------------------------

ALAGAPPA UNIVERSITY, KARAIKUDI

NEW SYLLABUS UNDER CBCS PATTERN (w.e.f. 2017-18)

B.Sc. MATHEMATICS – PROGRAMME STRUCTURE

Sem. Part Course

Code Title of the Course Cr.

Hrs. /

Week

Max. Marks

Int. Ext. Total

I

I 711T Tamil / Other Languages – I 3 6 25 75 100

II 712E English – I 3 6 25 75 100

III

7BMA1C1 Core–I-Calculus 4 6 25 75 100

7BMA1C2 Core–II-Algebra and Trigonometry 4 6 25 75 100

Allied – I (Theory only) (or)

Allied – I (Theory cum Practical)

5

4

5

3

25

15

75

60

100

75

Allied Practical – I - 2** -- -- ---

IV 7NME1A/

7NME1B/

7NME1C

(1) Non-Major Elective – I 2 1 25 75 100

Total (Allied Theory only) 21 30 -- --

600

Total (Allied Theory cum Practical) 20 575

II

I 721T Tamil / Other Languages – II 3 6 25 75 100

II 722E English – II 3 6 25 75 100

III

7BMA2C1 Core–III-Analytical Geometry of 3D

and Vector Calculus

4 6 25 75 100

7BMA2C2 Core–IV-Sequences and Series 4 5 25 75 100

Allied – II (Theory only) (or)

Allied– II (Theory cum Practical)

5

4

5

3

25

15

75

60

100

75

Allied Practical – I 2 2 20 30 50

IV 7BES2 (3) Environmental Studies 2 2 25 75 100


Total (Allied Theory only) 21 30 -- --

600


III

I 731T Tamil / Other Languages – III 3 6 25 75 100

II 732E English – III 3 6 25 75 100

III 7BMA3C1 Core–V-Abstract Algebra 4 5 25 75 100

III 7BMA3C2 Core–VI-Differential Equations and

its Applications

4 5 25 75 100

III Allied – III (Theory only) (or)

Allied–III (Theory cum Practical)

5

4

5

3

25

15

75

60

100

75

Allied Practical – II - 2** -- -- ---

IV

7NME3A/

7NME3B/

7NME3C

(1) Non-major Elective – II

2 1 25 75 100

7SBS3A1/

7SBS3A2/

7SBS3A3

(2) Skill Based Subjects– I 2 2 25 75 100

V 7BEA3 Extension Activities 1 - 100 - 100

Total (Allied Theory only) 24 30 - -

800


IV

I 741T Tamil / Other Languages – IV 3 6 25 75 100

II 742E English – IV 3 6 25 75 100

III 7BMA4C1 Core–VII-Transform Techniques 4 5 25 75 100

III 7BMA4C2 Core–VIII-Linear Algebra 4 4 25 75 100

III Allied – IV(Theory only) (or)

Allied –IV(Theory cum Practical)

5

4

5

3

25

15

75

60

100

75

Allied Practical - II 2 2 20 30 50

7SBS4B1/

7SBS4B2/



IV

7SBS4B3

7BVE4/

7BMY4/

7BWS4

(4) Value Education /

Manavalakalai Yoga /

Women’s Studies

2

2

25

75

100

Total (Allied Theory only) 23 30 - -

700


V

III 7BMA5C1 Core–IX-Real Analysis 4 6 25 75 100

III 7BMA5C2 Core–X-Statistics I 4 5 25 75 100

III 7BMA5C3 Core–XI-Operations Research I 4 5 25 75 100

III 7BMAE1A/

7BMAE1B

Elective (I) - A) Graph Theory (or)

B) Special Functions

5 5 25 75 100

III 7BMAE2A/

7BMAE2B

Elective (II) – A) Numerical Analysis

(or) B) Combinatorics

5 5 25 75 100

IV

7SBS5A4/

7SBS5A5/

7SBS5A6/

7SBS5A7


(2) Skill Based Subjects – I 2

2 25

75

100

Total 26 30 - - 700

VI

III 7BMA6C1 Core – XII Mechanics 4 6 25 75 100

III 7BMA6C2 Core – XIII Complex Analysis 4 5 25 75 100

III 7BMA6C3 Core – XIV Statistics II 4 5 25 75 100

III 7BMA6C4 Core – XV Operations Research II 4 5 25 75 100

III 7BMAE3A/

7BMAE3B

Elective – III A) Discrete

Mathematics (or) B) Fuzzy Algebra

5 5 25 75 100

IV 7SBS6B4/

7SBS6B5/

7SBS6B6/

7SBS6B7

(2) Skill Based Subjects – II

(2) Skill Based Subjects – II

2

2

2

2

25

25

75

75

100

100


Total 25 30 - - 700

Grand Total 140 180 - - 4100

** University Examinations will be held in the Even Semesters only.

Semester -I

Part -II

Name of the Subject(712E): English for Enrichment-I

Course Description

Students will be exposed to prose, and poetry works of great writers and poets, provided they will

learn Grammar and composition to enhance the skill of LSRW.

Course Objectives The core objectives are :

1. Critical thinking, to analyze, evaluate, and synthesis the information he has gathered in from

the lecture.


3. To inculcate Social Responsibility about civic responsibility, and adjust with regional, national

and global communities.



f. Speak and write in English for Global competency.

g. Will be able to analyze literary works(prose and poetry).

h. They will also be exposed to basic literary genres of prose and poetry.

i. Grammar, reading and writing exercises will make the student to read any text and understand it

and make them to think beyond the text.

j. Compositions give space for more writing skills. They will help the student to write essays, and


Part III

Course Name : calculus

Course Code: 7BMA1C1

Course description: This course is intended to develop practical skills in

differential calculus and Integral calculus.


1. know to find higer derivatives and expand the given function and know

about envelope, curvature and evolute of a curve.

2. accure knowledge about p – r equation of curve, asymptotes and radius of

curvature in polar co – ordinates.

3. expose to definite integrals and their properties, reduction formulae and

Bernoulli’s formula.

4. know about double and triple integral and their properties, Jacobian.

5. Be familiar with Beta and Gamma functions.



1. evaluate higer derivatives and expand the given function and find

envelope, curvature and evolute of a given curve.

2. find the radius of curvature, p – r equation of curve, asymptotes and radius

of curvature in polar co – ordinates.

3. evaluate definite integrals and integrate a given function by integration by

parts and Bernoulli’s formula.

4. find double and triple integral and their properties, Jacobian.

5. do problems Beta and Gamma functions.

Text books:

Calculus vol.1 and vol.2 by Narayanan and Manickavasagam Pillai. I YEAR - I SEMESTER


CORE COURSE - II – ALGEBRA AND TRIGONOMETRY

ALGEBRA AND TRIGONOMETRY

Course Description: This course covers topics from algebra and trigonometry at a level and emphasis

appropriate for applied technology majors who will continue on with at least one semester of applied

calculus. Topics are chosen from the following: functions and their graphs, angles and triangles, systems of

linear equations with determinants, trigonometric functions, equations and identities, exponential and

logarithmic functions, and a general treatment of conic sections.

Student Learning Outcomes:

Students will be able to apply trigonometric, logarithmic, and polynomial functions to solve

problems.

Students will be able to solve problems in analytic geometry.

Students will be able to choose appropriate mathematical functions to model physical

phenomena. Students will be able to present material in a logical fashion.

Books for Reference:

1. Trigonometry by S.Narayanan, T.K.ManicavachagomPillay.

2. Algebra Volume – I by T.K.ManicavachagomPillay, T.Natarajan, KS.Ganapathy.

Allied-I

Core: Properties of Matter, Thermal Physics and Optics (7BPHA1)

Aim and objective:

To introduce the concept of elastic moduli.

To give the exposure of Moment of inertia.

To understand the concept of viscosity and Bernoulli’s theorem.

To make the students to learn about the conduction, convection and Radiation.


To understand the concept of Thermodynamic laws.

To enable the students to learn about the interference, diffraction and polarization.

Course outcomes:

Acquire the knowledge in different elastic moduli of the materials.

Ability to understand the application of Poiseuille’s formula and Bernoulli’s equation.

Thorough knowledge in stream lined motion and turbulent motion.

Enable to calculate the thermal conductivity of the bad conductor using Lee’s disc method.

Practice to derive the Rayleigh jeans law and Wien’s laws from Planck’s law.

Arrive the Carnot’s cycle condition for heat engine and cold engine.

Thorough knowledge in fundamental principles of thermodynamics.

Application of interference, diffraction and polarization.

Name of the subject (7BMA2C1) ANALYTICAL GEOMETRY OF 3D AND VECTOR CALCULUS

Course Description: This is a beginning course in plane analytic geometry emphasizing the

correspondence between geometric curves and algebraic equations. The course assumes a sound

background in analytical geometry, and vector calculus.The Geometry course includes,

Analysis of Intersection of two lines, coplanar lines Shortest distance, distance between two

skew lines, Equation of a sphere Tangent line and tangent plane, section of a sphere problems.

Analysis of plane, solid, coordinate geometry, logic and proof, parallel lines and polygons,

perimeter and area analysis, volume and surface area analysis,

Includes vector-valued functions, gradient, curl, divergence, vector identities, problems vector

fields, line and surface integrals partial derivatives, and the theorems of Green, Gauss, and

Stokes, vector operators and the extension of the calculus to the vectors in 3-D space.

Course Objectives: This course is intended to expose the students to,

Solve Bisector planes, Perpendicular distance from a point to a plane – Problems.

Evaluate angle between a line and a plane, length of perpendicular from a point to a line –

Shortest distance, distance between two skew lines

Solve Line integral, surface integral, volume integral.

Demonstrate Vectors, gradient, curl, divergence, vector identities, problems.

Prove Green's Theorem, Stokes theorem, Gauss's Theorem. Statements and verification

Course Outcome: At the end of the course, a student who has studied and learned the material

should be able to:


Recognize the relationship between equations in two variables and graphs in the plane and

use the equations to find pertinent information such as points of intersection, and intercepts.

Demonstrate understanding of the notions of slope and inclination of lines, including angles

between lines, parallel lines, and perpendicular lines.

Solve problems involving lengths and distances in the plane, including midpoint and point-

of-division formulas.

Text Books

1.Analytical Geometry 3D and Vector Calculus by T.K. Manickavasagampillai and others.

2.Analytical Geometry 3D and Vector Calculus by Dr.S.Arumugam & Issac

Reference Books

Analytical Geometry 3D and Vector Calculus by M.K. Venkataraman & Manorama Sridhar

Name of the Subject (7BMA2C2) Sequences and Series

Course Description This course will introduce students to a variety of new techniques of infinite

series, and to sequences and series. Students will be expected both to become proficient with basic

skills and to demonstrate an understanding of the underlying principles of the subject.

Sequences:, Convergence, divergence. Oscillation, Monotonic and bounded sequences,

subsequence and Cauchy sequence. algebra of limits. Behaviour of Geometric sequence.

Infinite series: Series of positive terms cauchy’s general principle of convergence, comparison test ,

Harmonic series 1/np

Kummer’s test, Raabe’s test ,D’ Alembert’s ratio test, cauchy’s root test ,Gauss test and Problems

Cauchy condensation test, cauchy’s integral test Alternating series,Absolute convergence

,conditionally convergence ,Leibnitz’s test and Problems

Course Objectives The aim of this course is to develop an understanding of convergence in its

simplest setting. And also to learn about

the difference between a sequence and a series in the mathematical context.

The convergence/divergence of a series so we will give the basic ideas and definitions in this

section.

Using the Integral Test, Comparison Test ,Limit Comparison Tests, Alternating Series Test,

Ratio Test and Root Test to determine if a series converges or diverges.

A brief discussion on absolute convergence and how it differs from convergence.

A set of general guidelines to use when deciding which test to use.

Course outcomes: By learning this course students will be able to


Evaluate the limit of a sequence

Evaluate the limit of an infinite series

Determine the monotonic and bounded sequences.

Test the convergence of an infinite series

Represent a function as a power series

Represent a function as a infinite series

Use series in application problems

Text Book

Sequences and Series by S.Arumugam and Issac.

Reference Book

Algebra Vol.1 by T.K.Manikavasagampillai and Others.

Allied-II

Allied Physics Practical (7BPHAP1)

Aim and objective:

To determine the young’s modulus of the given material.

To find the thickness of the thin wire using Air wedge.

To calibrate the given ammeter and voltmeter.

To find the number of lines per meter and wavelength of the mercury spectrum.

To verify the logic gates using discrete components and ICs.

To find the thermal conductivity of the bad conductor using Lees disc method.

Course outcomes:

Ability to determine the Youngs modulus of different materials.

Able to calibrate the given ammeter and voltmeter using potentiometer.

Acquire the knowledge of interference fringes and measure the bandwidth.

Ability to construct the logic gates by using discrete components and ICs.

Capable of producing line spectra and measure the diffraction angle by using spectrometer.


ELECTRICITY, ELECTRONICS, ATOMIC AND NUCLEAR PHYSICS - 7BPHA2

The paper titled “Electricity, Electronics, Atomic and Nuclear Physics” is the allied paper for the

B.Sc., (Maths) and B.Sc.,(Chemistry) major students. Mathematics major students will study this allied

paper in the second semester whereas Chemistry major students will study this allied paper in the fourth

semester. This paper has four credits. The students will be examined for 60 marks externally and 15 marks

for internally.

Objectives:

The objectives of the paper “Electricity, Electronics, Atomic and Nuclear Physics” are

To be familiar with basic definitions in electricity

To be familiar with basic concepts of electromagnetism

To be familiar with various atoms model and related phenomenon

To understand the basic concepts in digital and analog electronics

Learning Outcomes

After course completion the students will have the following learning outcomes

Enable to understand the concepts of electricity and current flow related bridges

Enable to understand the concepts of magnetic fields

Thorough knowledge in the basic concepts of electromagnetic induction

Application of interference, diffraction and polarization experiments

Part - IV Name of the Subject: (4BES2) Environmental Studies.

Course Description

The course Explore the basics of environmental studies and the unique interdisciplinary methods used

to address the most challenging environmental problems. This segment will give to the students a brief

overview of types of issues and the solutions examined within environmental studies.

Course Objective:

Creating the awareness about environmental problems among to the students.

Imparting basic knowledge about the environment and its allied problems.

Examine the Renewable and Non renewable resources.

Motivating students to participate in environment.

Environmental Study to learn the importance of Eco-system.

Mention the causes and effect of pollution.



Developing an attitude of students for the environment.

Study the importance of Plantation. The Environmental Studies Program actively cultivates in our students for environmental issues. Acquiring skills to help the concerned individuals in identifying and solving environmental

problems.

Striving to attain harmony with Nature.

Texts Prescribe

1. K.C.Agarwal, Environmental Biology.

2. Bharucha Erach, The Biodiversity of India.

3. T.G.Miller, Environmental Science.

4. P.E.Odurm, Fundamental of Ecology.

5. R.E.Hawlinks, Encyclopedia of India Natural History.

Semester-III

Part-II

Name of the Subject (732E) English for Enrichment -III

Course Description

Short Stories, One Act Play and Grammar are taught to students. Students will learn grammar and

composition to enhance the skill of LSRW.

Course Objectives

To analyse, evaluate and synthesis the things they have observed in class.

To express and communicate their thoughts effectively through written and spoken.

Texts Prescribed

c. Fragrant Thoughts in Flowery Words Ed. By the board of Editors

d. Modern English - A Book of Grammar Usage and Composition

by N.Krishnaswamy, Macmillan publishers.

Course Outcome

After completing the course, Students will be able to

a) Speak and Write in English

b) to analyse literary works

c) They will be exposed to basic literary genres of prose and poetry

d) Grammar, Reading and Writing exercises will make the students read any text

e) Composition practice will help the student to write essays


Part-III

Subject name: Absract Algebra

Subject code: 7BMA3C1

➢ Course Description:

In this course, we will study algebraic structures that are fundamental to almost all branches of

mathematics and to other fields of study such as physics, chemistry, and computer science. Modern Algebra

covers group theory, including finite groups, subgroups, cyclic groups, permutation groups, group

isomorphisms, and cosets, and introduces rings and fields, including integral domains, polynomial rings,

unique factorization domains and Euclidean domains. This course will also focus on understanding and

writing proofs.

➢ Course Objective :

○ Present the relationships between abstract algebraic structures with familiar numbers systems

such as the integers and real numbers.

○ Present concepts of and the relationships between operations satisfying various properties

(e.g. commutative property).

○ Present concepts and properties of various algebraic structures.

○ Use results from elementary group theory to solve contemporary problems;

○ Explain from elementary principles why certain algebraic facts are true.

➢ Course Outcomes :

○ Students will have a working knowledge of important mathematical concepts in abstract

algebra such as definition of a group, order of a finite group and order of an element.

○ Students will be knowledgeable of different types of subgroups such as normal subgroups,

cyclic subgroups and understand the structure and characteristics of these subgroups.

○ Students will be introduced to and have knowledge of many mathematical concepts studied

in abstract mathematics such as permutation groups, factor groups and Abelian groups.

○ Students will gain experience and confidence in proving theorems. A blended teaching

method will be used requiring the students to prove theorems give the student the experience,

knowledge, and confidence to move forward in the study of mathematics.

○ Analyze and demonstrate examples of subgroups, normal subgroups and quotient groups,

○ Analyze and demonstrate examples of ideals and quotient rings,

○ Use the concepts of isomorphism and homomorphism for groups and rings.

Name of the Subject (7BMA3C2) Differential Equation and its Application

Course Description

This course includes a variety of differential equations and their solutions with emphasis on ,

Exact differential equations –Clairaut's equation – Second and higher order linear Differential

equations with constant Coefficients. Homogeneous linear Equations with variable coefficients


Method of reduction and variation of parameters –Necessary and Sufficient condition of

integrability of Pdx+Qdy +Rdz = 0 – Rules for solving it.

ordinary differential equations. Emphasis is placed on the development of abstract concepts

and applications for first-order and linear higher-order differential equations.

Partial Differential Equations – Formation of P.D.E. by the elimination of constants –

Lagrange’s method – Charpit’s method.

Laplace Transforms and Inverse Laplace Transforms –

Course Objectives learning differential equations is certainly one of the goals of this course, the

purpose of this module is to provide participants with the skills, knowledge and attitudes required

to solve differential equations

Explore the use of differential equations as models in various applications

classify differential equations by order, linearity, and homogeneity • solve first order linear

differential equations • solve linear equations with constant coefficients • use separation of

variables to solve differential equations • solve exact differential equations • use variation of

parameters to solve differential equations

Identify essential characteristics of ordinary differential equations.

Laplace transforms and their inverses to solve differential equations • solve systems of linear

differential equations using matrix techniques and eigenvalues • use numerical methods to

solve differential equations

Course Outcome - On completion of this module the learner should be able to:

Determine solutions to second order linear homogeneous differential equations with constant

coefficients.

Determine solutions to second order linear non-homogeneous differential equations with

constant coefficients

Determine solutions to Partial Differential Equations – Formation of P.D.E. by the elimination

of constants –Lagrange’s method – Charpit’s method

Select and apply appropriate methods to solve differential equations; variation of parameters,

LaPlace and inverse LaPlace transforms

Find general solutions to first-order, second-order, and higher-order homogeneous and

nonhomogeneous differential equations by manual and technology-based methods.

Determine solutions to first order exact differential equations,Clairaut's equation.

Text Book

Differential Equations by T.K.Manivasagam and Narayanan

Reference Book

Differential Equations and Laplace Transforms by Dr. M.K. Venkataraman & Mrs. Manorama Sridhar

Allied-III COURSE CODE: 7BCEA3

ALLIED COURSE III – PROGRAMMING IN C (THEORY & LAB)

Course Description


This C programming course provides a comprehensive introduction to the ANSI C language,

emphasizing portability and structured design. Comprehensive examples are integrated throughout to

reinforce learning.

Course Objectives

Students will be exposed to C Programming language. They will learn syntax and semantics in C

language. Students are introduced to fundamental data types, flow control, and standard function libraries.

Thorough treatment is given to the topics of string and character manipulation, dynamic memory allocation,

standard I/O, macro definition, and the C runtime library. The course explains the use of structures, unions,

and pointers. Structured programming constructs and various functions are also covered. Emphasis is given

to the processing of command line arguments and environment variables so students will be able to write

flexible, user-friendly programs. They will also learn to solve problems using various programming logic

and various file types.

Texts Prescribed

The first book is the prescribed text book and the next one is given as reference.

1Programming in ANSI C – E.Balagurusamy Tata McGrawHill Publishing Company Ltd, New Delhi

2.Programming with C – K.R.Venugopal, Sudeep.R Prasad Tata McGrawHill Publishing Company Ltd,

New Delhi.






CO7. Develop their skill in C programming language.

CO8. Understand the basic concepts of program development statements and its syntax.

CO9. Understand the various types of arrays.

CO10. Know about the various types of Functions and String handling mechanisms.

CO11. Really Understand the Concepts of structures and Unions.

CO12. Illustrates the various operations performed on different types of data files.

Part - IV Course code : 7SBS3A1

COMPETITIVE EXAMINATIONS SKILLS


COURSE DESCRIPTION:

Students are expected to develop the skill of creativity, numerical ability to have

a better job.

COURSE OBJECTIVE:

STUDENTS COMPLETING THE COURSE WILL BE ABLE TO:

1.Develop the art of speaking to have a fluency in language

2.Know the various type of inductive reasoning to develop the individual memory.

3.Developing the verbal skill of an individual.

4.Analyze the various test of an individual.

5.Prompt thought to have a overall development in an individual.

6.Understanding Analytical Method which are essential for the development of an

individual.

Text prescribed:

1.Ajay raj – intelligence Tests.

2.Competition success Review.

The above two books are prescribed texts for first two semesters.

Course code:7NME3C EFFECTIVE EMPLOYABILITY SKILLS

COURSE DESCRIPTION:

Students will be exposed to have employment which are the basics of life to

have income which lead to higher standard of living.

COURSE OBJECTIVE:

Students completing the course will be able to,

1.Fill the job application form while they are approaching for the job without others

help.

2.Know the frequently asked question in the interview.

3.The rules to be followed while facing the interview.

4.Steps to be followed in group discussion with the management.


5.Leadership qualities that are needed for the growth of inculcating the

characteristics of the leader.

COURSE OUTCOME (COS)

THE PRESCRIBED TEXTS ARE:

3. D.K.Sarma – you of your career.

4. IndianJaycees- Skills Series.

The above two books are prescribed texts for first two semester. The course objectives

of the above prescribed text are,

1. Critical thinking about how to face the interview.

2. Analytical skill to develop the art to face the interview.

Semester-IV

Part –II Name of the subject (742E): English for Enrichment – IV

Course Description

Students will be exposed to Drama, Fiction and great works of Shakespeare, provided they will learn

Grammar and composition to enhance the skill of LSRW.

Course Objectives

The core objectives are :

1. To develop critical thinking among the students.

2. To analyze and synthesis the information he has observed in the class.

3. To express his ideas clearly and effectively through spoken and written.

4. To Understand Shakespeare plays through various contexts such as social,

political, historical, artistic conventions and innovations.

5. Writing about drama.

6. Speaking and listening reflectively.

7. To train and motivate them to develop their LSRW.

Course Outcomes:


1. Speak and write in English for Global competency.

2. Will be able to analyze literary works.(Drama and Fiction)

3. They will also be exposed to basic literary genres of drama , Fiction and great works

of Shakespeare.


4. Grammar, reading and writing exercises will make the student to read any text and

understand it and make them to think beyond the text.

5. Composition give space for more writing skills. They will help the student to write

essay and reports. Thereby they will be able to differentiate objective and subjective

writing.

Text Prescribed:

1. Pygmalion- G.B.Shaw

2. Swami and Friends- R.K. Narayan

3. Tales from Shakespeare Ed. By the Board of Editors, Harrows Publications, Chennai.

4. Modern English- A Book of Grammar Usages and Copsition by N. Krishnaswamy,

Macmillan Publishers.

Part-III


CORE COURSE - VII – TRANSFORM TECHNIQUES

Course Description:

1.To understand the concept of complex variables, C-R equations, harmonic functions and its conjugate and mapping in complex plane.

2.To learn the complex mapping, standard mappings, cross ratios and fixed point.

3.To learn the Laplace Transform, Inverse Laplace Transform of various functions, its application and Z-

transform.

4.To understand the concept of Fourier Series, its complex form and enhance the problem solving skill.

Course Learning Outcomes

Course Objectives

Students will be able to:

1. Understand complex variable theory, application of harmonic conjugate to get orthogonal

trajectories and analytic function.

2. Plot the image of the curve by a complex transformation from z-plane to w-plane.

3 . Expand the periodic function by using Fourier series and complex form of Fourier series.

4. Understand the concept of Laplace transform and inverse Laplace transform of various functions

and its application to solve ordinary differential equations.

5.Apply the concept of Z- transformation and its inverse of the given sequence.

6.Apply the concept of Correlation and Regression to the engineering problems.

The focus of this course is to familiarize the students with the concept of Fourier

transform & Fourier series.


Analyze the spectral characteristics of signals using Fourier analysis.

Classify systems based on their properties and determine the response of LTI

Identify system properties based on impulse response and Fourier analysis.

Apply transform techniques to analyze continuous-time and discrete-time

Text Books:

1. Calculus Volume III by S.Narayanan and T.K.ManicavachagomPillay, S.Viswanathan (Printers &

Publishers) Pvt. Ltd., 2014.

2. Engineering Mathematics 3rd Edition by T.Veerarajan, Tata McGraw Hill Publishing Company

Limited, New Delhi.

Book for Reference:

1. Transforms and Partial Differential Equations by Dr.A.Singaravelu, Meenakshi Agency, Chennai

Subject name: Linear Algebra



This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines.

Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of

matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences,

natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most

widely taught subjects in college-level mathematics


● Understand real vector spaces and subspaces and apply their properties. Understand linear

independence and dependence.

● Find basis and dimension of a vector space,and understand change of basis.

● Compute linear transformations, kernel and range, and inverse linear transformations, and

find matrices of general linear transformations.

● Find the dimension of spaces such as those associated with matrices and linear

transformations.

● Find eigenvalues and eigenvectors and use them in applications.

● Compute inner products on a real vector space and compute angle and orthogonality in inner

product spaces.


● Use computational techniques and algebraic skills essential for the study of systems of linear

equations, matrix algebra, vector spaces, eigenvalues and eigenvectors, orthogonality and

diagonalization.

● Use visualization, spatial reasoning, as well as geometric properties and strategies to model,

solve problems, and view solutions, especially in R2 and R3 , as well as conceptually extend

these results to higher dimensions.


● Critically analyze and construct mathematical arguments that relate to the study of

introductory linear algebra.

● Communicate and understand mathematical statements, ideas and results, both verbally and

in writing, with the correct use of mathematical definitions, terminology and symbolism

● Work collaboratively with peers and instructors to acquire mathematical understanding and

to formulate and solve problems and present solutions.

Allied-IV

I

COURSE CODE : 7BCEAP2

Allied Practical – II - PROGRAMMING IN C AND C++ LAB

(for allied course III & IV)

Course Description

This C and C++ programming lab course provides hands on training in ANSI C language. Comprehensive

hands on exercises are integrated throughout to reinforce learning and develop real competency. The C and

C++ Lab course provides hands on training to students. The list of program are integrated throughout to

reinforce learning and develop real competency.

Course Objectives

This course objective is to write, compile, debug and execute C and C++ programs, to formulate

problems and implement algorithms and to effectively choose programming components that efficiently

solve computing. The list of C Programs are to find the is odd or even , sum of digits, Armstrong number,

Prime number, perfect number, palindrome, simple and compound interest , sorted array, Counting

positive, negative and zeros.

Students will be exposed to C++ Programming language. They will learn syntax and semantics of

statements in C++ computer programming language. They will also learn to solve problems in Object

oriented ways i.e., bottom approach.

The list of C++ programs are to evaluate STD, Farenheit to Celsius, Sum of digits using constructor,

employee paybill, adding and multiplying complex numberSs using operator over loading, student mark

list, to find volume using inline function and to apply Multiple inheritance and Hierarchical inheritance.

Students come with their developed programs to their lab session. They have to enter, compile, link

and execute two programs in their lab session. They have to correct the syntax error, logical errors, input

errors and output errors. Students are assessed by formative and summative assessment and examinations.


Upon successful completion of this lab Course, student will be able to

CO10. Use Arrays and Functions in programs.


CO11. Use pointers, structures and files handling.

CO12. Develop their skill in executing C programs.

CO13. Construct the flowchart to solve mathematical and scientific problems.

CO14. Use the features of C++ using object oriented programming.

CO15. Use encapsulation and inheritance.

CO16. Develope programs in C++ Using polymorphism.

CO17. Use the advanced features of C++ specifically stream I/O and operator overloading.

CO18. Design and test programs to solve mathematical and scientific problems using object oriented

concepts.

COURSE CODE: 7BCEA4

ALLIED COURSE IV – PROGRAMMING IN C++ (THEORY & LAB)

Course Description

Students will be exposed to C++ Programming language. The C++ programming course provides an

accelerated introduction to the most essential syntactical components of the C and C++ language, focus on

object-oriented programming with C++. Comprehensive examples are integrated throughout to reinforce

learning and develop real competency.

Course Objectives

Students will learn syntax and semantics of statements in C++ language. The course begins by

introducing the built in data types, fundamental control constructs, and rich expression operator repertoire

common to both C and C+. The central concepts of C++ syntax and style are taught in the context of using

object-oriented methods to achieve reusability, adaptability and reliability. Emphasis is placed on the

features of C++ that support abstract data types, inheritance, and polymorphism. Students will learn to

apply the process of data abstraction and class design. Practical aspects of C++ programming including

efficiency, performance, testing, and reliability considerations are stressed throughout. They will also learn

to solve problems in using object oriented approach.

Texts Prescribed

The first book given below is the prescribed text book and the next two books are given for reference.

4. Mastering C++ – K.R.Venugopal, T.Ravishankar, RajKumar, Tata Mc Graw-Hill Publishing

Company Limited, New Delhi 2006.

5. Object Oriented Program in C++ – Nabajyoti barkakati, A prentice Hall of India Private Limited,

New Delhi 1997.

6. Balagurusamy, Object Oriented Programming with C++, Tata McGraw Hill, New Delhi.







CO7. Explain the top-down and bottom-up programming approach and apply bottom up

approach to solve real world problems.

CO8. Explain the difference between static and dynamic binding.

CO9. Describe the concept of inheritance, overloading, constructors and apply real world

problems.

CO10. Discuss the generic data type for the data type independent programming which relates it

to reusability.

CO11. Explain to design of handling large data set using File I/O.

CO12. Develop their skill in C++ programming language.

Part-IV

Course code: 7SBS4B2 EMERGENCY AND MEDICAL LAB SKILLS

COURSE STRUCTURE: The course is designed to provide understanding about

different types of emergencies and the required medical skills to be given to the people

being affected.

COURSE OBJECTIVES:

1.To prepare the students to rise to the occasion of emergencies.

2.To provide the medical lab skills to those people affected by natural and other

situations.

COURSE OUTCOMES:

1.provide knowledge and skills to rescue people affected by fractures fire Snake bite

road and bite and heat stroke and those people affected by the diseases like diarrhoea

and dysentery.

2.Introduces the traffic rules and precautions to be followed during the Travels along

the roads.

3.Introduces the basic knowledge about medical lab tests for the human beings


4.Use knowledge about treating different types of diseases by using locally available

Herbals.

5.The project work given to the students main provide them chances to learn about

different types of diseases and the methods of curing Dum by using native treatments.

REFERENCE BOOKS

1. Muthu,R.S., and Meera Ravishankar(2013), First Aid, Sura books Private Limited,

Chennai.

2. Rama Rao, Handbook of First Aid, Sura books Private Limited, Chennai.

Course code: 7BMY4 MANAVALAKALAI YOGA COURSE DESCRIPTION:

It provides a thorough arena for meditation, yoga and physical exercise which

leads to holistic health that totally transforms a person.

COURSE OBJECTIVES:


1.Understand the health concepts and the different aspects of physical body.

2.Have the basic knowledge on simplified physical exercise and asanas.

3.Introspect and improve the behaviour of an individual.

4.Understand how to improve concentration and focus.

5.Improve intellectual sharpness.

COURSE OUTCOME:

1.To enhance soft skills and develop the ability for an efficient management in their

field chosen.

2.Inculcates the social responsibility, to realize the enduring values of peace, Non-

Violence and hormone to revitalize human society for restoring its sanity and strength.

TEXT PRESCRIBED:


1.Value education – World Community Service Center, Veathethery publishing

house

Course code:7BWS4 WOMEN STUDIES

COURSE DESCRIPTION:

The students will be exposed to gender identity, gender equality, role

of gender in different aspects, capacity of women and the various schemes

and programmes implemented for women empowerment.

COURSE OBJECTIVES:


1. Explain the concepts of socialisation and internalisation and gain knowledge on

gender ideology.

2. Understand the role of women in various capacity and how she balances both

work and family efficiently.

3. Explain the different indexes such as HDI, GDI, GEM and participation of women

in decision making and the political arena.

4. Explain physical and biological differences of gender in sports and the mental

ability of women in handling emotions.

5. Understand the different policies, welfare schemes and programmes introduced

by the central and state government.

6. Explain the concepts, levels and tools of women empowerment.

COURSE OUTCOME:

Inculcates social responsibility by imparting the role of women to the

stakeholders and play active role in empowering women to have a balanced

development.

TEXT PRESCRIBED:


1.Complete outlook of women in various dimensions. – women in perspective: Essays

on Gender issues by Shoma A. Chaterji, Vitasta Publishing Pvt.Ltd.

2.Gender sensitization – Gender Socialization and the Making of Gender in the

Indian Context by susithkumar chattotathyay, SAGE Publication pvt.Ltd.

Semester –V

Part-III

Name of the Subject (7BMA5C1) Real Analysis

Course Description: This course covers the fundamentals of mathematical analysis. The course

topics include:









Open and Closed Sets of Real Numbers Compact, Perfect and Connected Sets The Intermediate

Value Theorem

Definitions, theorems, techniques etc… these are your mathematical tools and as a bare minimum

you have to know what they are.


To prove various theorems about continuous functions and emphasize the proofs’ development


a strong foundation in Real Analysis and the theory of integration.



Course Outcome After completion of course, the students will be able to









Text Book

Modern Analysis by S. Arumugam and Issac

Reference Book

Modern Analysis by A.R.Vasishta

Course Name : Statistics - I


Course description: This course is an introduction to central tendencies,

measures of dispersion, correlation, regression, interpolation and index numbers.


1. know the methods to find mean, mode, range, Q.D, mean division and S.D.

2. know to find moments skewness and kurtosis from the given data and to fit

the curve.

3. have knowledge about correlation and regression.

4. understand the meaning of interpolation and its usage.

5. know about index numbers and time series.



1. calculate mean, median, mode, range, Q.D, mean division and S.D from

the given data.

2. find out the co - efficient of skewness and kurtosis.

3. find whether given two variables of correlated are not and to find the line

of regression.

4. problems to find the missing data using various formulae.

5. find different types of index numbers and problems in time series.

Text book:

Statistics theory and practice by R.S.N.Pillai and Bagavathi.

Subject name: Operations Research I



Operations Research is the study of scientific approaches to decision-making. Through

mathematical modeling, it seeks to design, improve and operate complex systems in the best possible way.

And also, introduce the students to the advanced methods for large-scale transportation and assignment

problems. The goal of this course is to teach to formulate, analyze, and solve mathematical models that

represent real-world problems.


● Formulate a real-world problem as a mathematical programming model

● Understand the theoretical workings of the simplex method for linear programming and

perform iterations of it by hand

● Understand the relationship between a linear program and its dual, including strong duality

and complementary slackness

● Solve specialized linear programming problems like the transportation and assignment

problems

● To introduce the students to the use of basic methodology for the solution of linear

Programs.


● explain the meaning of operations research

● know the various techniques of operations research;

● select an optimum solution with profit maximization;


● Identify and develop operational research models from the verbal description of the real

system.

● Understand the mathematical tools that are needed to solve optimisation problems. Use

mathematical software to solve the proposed models.

● Develop a report that describes the model and the solving technique, analyse the results and

propose recommendations in language understandable to the decision-making processes in

Management Engineering.


ELECTIVE COURSE I (A) – GRAPH THEORY

Course Description: The course covers basic theory and applications of combinatory and graph theory.

Combinatory is a study of different enumeration techniques of finite but large sets. Topics that will be

studied include principle of inclusion and exclusion, generating functions and methods to solve difference

equations. Graph theory is a study of graphs, trees and networks. Topics that will be discussed include Euler

formula, Hamilton paths, planar graphs and coloring problem; the use of trees in sorting and prefix codes;

useful algorithms on networks such as shortest path algorithm, minimal spanning tree algorithm and min-

flow max-cut algorithm. Course Objectives: The successful student will know the definitions of relevant

vocabulary from graph theory and combinatory, and know the statements and proofs of many of the

important theorems in the subject, and be able to perform related calculations.

Course Objectives: The successful student will know the definitions of relevant vocabulary from graph

theory and combinatory, and know the statements and proofs of many of the important theorems in the

subject, and be able to perform related calculations.Goals of the Course:

• gain an understanding of the fundamental concepts of graph theory,

• gain an understanding of when a graph is a useful mathematical tool to solve problems in mathematics, the

sciences and the environment,

• develop the ability to write a logical and coherent proof, including proof by contradiction and induction,

• introduce topics suitable for a senior thesis (and see ones that have been),

• develop a desire for further study in related areas, including combinatorics and computer science.

Text Books

1. Invitation to graph Theory: Dr. S Arumugam and others

2. A first course in Graph Theory: S.A. Choudam. (For directed graph)

Reference Graph Theory – Bondy Mur

Course Name: Numerical analysis

Course Code: 7BMAE2A

Course description: This course introduces the theory and application of

numerical methods and techniques to solve algebraic and trancedental equations,

interpolate, to evaluate derivatives and integrals from the given data and also to

solve linear system of equations ,difference equation and differential equation.


1. be introduced to different methods to solve algebraic and trancedental

equations

2. learn Newton’s forward and backward formulas, Newton’s divided

difference formula and etc… to interpolate. Also successive

approximation.


3. expose to numerical differentions and integration.

4. accure knowledge about various methods to solve linear system of

equations

5. know to solve differential equations by Euler, Taylor and Runge –Kutta

methods.

Course outcome: students will be able tos

1. solve algebraic and trancedental equations

2.interpolate using the learnt formulae.

3.find derivatives and integrals from the given data without knowing the

function.

4. solve linear system of equations

5.solve differential equations by Euler, Taylor and Runge –Kutta methods.

Text book:

Numerical analysis - S.Arumugam and Issac.

Part IV

Course code:7SBS A4 HERITAGE AND TOURISM

COURSE DESCRIPTION:

This course covers the Importance of Tourism and inter-linkage factors between

Heritage and tourism.

COURSE OBJECTIVES:

1. To illustrate the complexity of “heritage” and heritage tourism;

2. Students will learn the tourist places in regional, state level and national level

3. To outline the challenges of conserving, managing and marketing heritage

tourism;

4. Inculcate and mindset creation to go around the tourist places to enrich their

knowledge on cultural and linguistic integration.

5. Speak and write other Indian languages for national competency, for that

tourism will motivate the students.

6. Will be able to get new innovative ideas to promote tourism by attracting even

foreign tourists.


COURSE OUTCOME:

This course will bring national integration through tourism. Students will turn into

broad minded humans and social reforms, also economic development will be

enhanced.

TEXTS PRESCRIBED:

1.Bhatia, A. K – Tourism Development Principles and Practices, Sterling Publishers

(P) Ltd., New Delhi)

2.Ananand M. M – Tourism and Hotel Industry in India Sterling Publishers (P)

Ltd., New Delhi

3.Acharya Ram – Tourism and Cultural Heritage Rosa Publications: Jaipur, 1986)

These texts will pave the way for critical understanding of the relationships between

culture, heritage and tourism;

COURSE CODE: 4SBS 5A5

COURSE TITLE: MARKETTING AND SALES MANAGEMENT

COURSE DESCRIPTION:

This course is meant to be an introduction to a career in sales. Despite the “sales” focus, students can find

significant value in the sales techniques for many other elements of their lives, from leadership and management to

career-building concepts such as interviews.

COURSE OBJECTIVES

1.Recognize the key drivers of change in selling and sales management.

2.Understand the best practices in selling that lead to exceeding customer expectations.

3.Explain the historical basis for stereotypical views of selling in society.

4.Identify and explain key success factors for salesperson performance.

5.Discuss and give examples of different types of selling jobs.

6.List and explain the role of various participants in an organizational buying center.

COURSE OUTCOME:

This course is designed to provide students with an understanding of the processes involved in personal selling and

sales management.


TEXTS PRESCRIBED:

1. Chunawalla, S. A., Sales Management, 5th Edition (2007), Himalaya Publishing House

2. Havaldar, Krishna; Sales And Distribution Management, 1st Edition (2006), Tata Mcgraw Hill

3. Perreault, Jr., William; Mccarthy, E. Jerome, Basic Marketing, 15th Edition, 2006,

Tata Mcgraw Hill

These texts will enrich knowledge on marketing sales management besides students could learn many

marketing and sales management techniques

Semester VI

Part-III 7BMA6C1 MECHANICS

Course Description The course emphasizes the proper utilization of vector algebra and free-body diagrams to solve problems in

the first course of the engineering mechanics sequence. The course begins with basic theory of engineering

mechanics, using calculus, involving the motion of particles, rigid bodies, and systems of particles. The

course covers six major areas of study: (1) vector algebra of forces and moments; (2) free-body diagrams

and equilibrium of particles and rigid bodies, (3) structural analysis of internal and external forces of

trusses, frames, and machines; (4) principles and application of friction; (5) centroids and centers of gravity;

and (6) moments of inertia.

Student Learning Outcomes When you complete this class you should be able to:

1. Define and calculate magnitude and direction of forces and moments.

2. Represent and calculate the reduction and simplification of force and moment systems.

3. Draw free-body diagrams for two- and three-dimensional force systems.

4. Calculate forces and moments acting internally or externally on an object.

5. Determine the location of the centroid and the center of mass for a system of discrete particles and

objects of arbitrary shape.

6. Calculate moments of inertia for lines, areas, and volumes.

7. Solve simple statics engineering problems using Newton’s laws.

8. Recognize current social, economic, and environmental issues where statics principles are important for

the development of engineering solutions.

Course Material: Text Book is

Statics (17thedition) by Dr. M.K.Venkataraman, Agasthiyar Publications, Tiruchirapalli, 17th Edition, July

2014.

Dynamics (18th edition) byDr. M.K.Venkataraman, Agasthiyar Publications, Tiruchirapalli, 2017


CORE COURSE XIII – COMPLEX ANALYSIS

Course Description: This course is an introductory course on Complex Analysis. It is designed for

students in Mathematics disciplines. It may, however, be useful to students in engineering and other related

fields. It introduces students to the complex numbers system and varieties of operations, analyses and

problems that may arise within the context. It also equips the students with mathematical techniques and

skills to handles such cases. Topics to be covered in this course includes: Introduction to complex number

system, Limits and Continuity of Complex variable functions, Derivation of the Cauchy –Riemann”s

Equation, Analytic functions. Harmonic functions, Bilinear transformation, Conformal mapping, Contour

Integrals, Convergence of a sequences and series of function of Complex variable. Complex numbers, the

topology of the complex plane, the extended complex plane and its representation using the sphere.


Complex functions and their mapping properties, their limits, continuity and differentiability, analytic

functions, analytic branches of a multiple valued function. Complex integration, Cauchy's theorems,

Cauchy's integral formulae. Power series, Taylor's series, zeroes of analytic functions, Rouche's theorem,

and open mapping theorem. Mobius transformations and their properties. Isolated singularities and their

classification, Laurent’s series, Cauchy’s residue theorem, the argument principle

Course Learning Outcomes: Demonstrate understanding of the basic concepts underlying complex

analysis. Demonstrate familiarity with a range of examples of these concepts. Prove basic results in

complex analysis. Apply the methods of complex analysis to evaluate definite integrals and infinite series.

Demonstrate understanding and appreciation of deeper aspects of complex analysis such as the Riemann

Mapping theorem.

Objectives: Demonstrate skills in communicating mathematics orally and in writing.

Upon successful completion of this course, the student will be able to:

justify the need for a Complex Number System and explain how is related to other existing number

systems

define a function of complex variable and carry out basic mathematical operations with complex

numbers.

know the condition(s) for a complex variable function to be analytic and/or harmonic

State and prove the Cauchy Riemann Equation and use it to show that a function is analytic.

define singularities of a function, know the different types of singularities, and be able to determine the

points of singularities of a function.

explain the concept of transformation in a complex space (linear and non-linear) and sketch associated

diagrams.

understand the concept of sequences and series with respect to the complex numbers system and

establish whether a given series/ sequences is convergent/ divergent at a specified point or interval.

Text Book: Complex Analysis by S. Arumugam & Issac

Reference Book

1.Complex Analysis by Dr. N. Sridharan

2.Complex Analysis by S.Narayanan & T.K.Manickavasagam Pillai

Course Name : Statistics - II


Course description: This course is an introduction to probability density

function, probability distribution, test of signification, analysis of varience and

Latin square design.


1. know about p.d.f of a random variable, expectation and moment generating

function of variable.

2. have knowledge in binomial, poisson, normal distribution.

3. know the methods to test the hypoyhesis for large samples.

4. know the methods to test the hypoyhesis for small samples.

5. expose to chi-square distribution, analysis of variance and test for

independence of attributes.


1. evaluate p.d.f of a discrete and continuous random variable, expectation

and moment generating function of discrete and continuous of variable.


2. do problems using binomial, poisson, normal distribution.

3. test the null hypoyhesis for large samples.

4. test the null hypoyhesis for small samples.

5. do problems in analysis of variance: one way classification, two way

classification and the Latin square test for independence of attributes.

Text book:

Statistics – S . Arumugam and Issac.

Subject name: Operations Research II :



Operations research (OR) has many applications in science, engineering, economics, and industry

and thus the ability to solve OR problems is crucial for both researchers and practitioners. Being able to

solve the real life problems and obtaining the right solution requires understanding and modeling the

problem correctly and applying appropriate optimization tools and skills to solve the mathematical model.

The goal of this course is to teach to formulate, analyze, and solve mathematical models that represent real-

world problems.


The objectives of this course are to:

● introduce students to the techniques of operations research in mining operations

● provide students with basic skills and knowledge of operations research and its application in

mineral industry

● introduce students to practical application of operations research in big mining projects

● And, the subject learning will emphasize the mathematical procedures of nonlinear programming

search techniques, probabilistic models in operations research.

● Students successfully completing this course are expected to be able to apply a variety of operations

research techniques for solving nonlinear programming problems; to have a good command of

probabilistic operations research methods and dynamic programming techniques; and to be familiar

with computer software for solving nonlinear programming problems.


● formulate and solve problems as networks and graphs.

● solve the problems using special solution algorithms.

● use CPM and PERT techniques, to plan, schedule, and control project activities.

● set up decision models and use some solution methods for nonlinear optimization problems.

● Formulate and analyse the general nonlinear programming problems.

● use some solution methods for solving the nonlinear optimization problems.

● propose the best strategy using decision making methods under uncertainty and game theory

and to solve the zero-sum two- person games.


Name of the Subject (7BMAE3B) FUZZY ALGEBRA

Course Description: This course is intended to master the students in various fundamental concepts

of fuzzy logic. This will help the students to get sufficient knowledge on Fuzzy sets. This course

introduces students to the basic concepts of

Extension principle for Fuzzy sets.

Operations on Fuzzy sets– Fuzzy complements fuzzy morphisms

Fuzzy numbers Fuzzy relations – Binary fuzzy relations – Fuzzy equivalence relations.

Course Objectives: Provide an understanding of the basic mathematical elements of the theory of

fuzzy sets.

Be able to understand the basic notion of fuzzy rule base

Be able to apply basic fuzzy complement

Be able to apply basic fuzzy relations and inverse relations.

Be able to understand the basic notion of fuzzy numbers.

Be able to understand basic knowledge of fuzzy sets and fuzzy logic

Be able to apply basic knowledge of eextension principle for Fuzzy sets.

Be able to apply basic fuzzy inference and approximate reasoning

Course Outcome:

Upon successful completion of this course, the student will be able to

Be familiar with the nature and use of fuzzy relations.

Perform linguistic analysis using fuzzy sets.

Develop and simulate simple fuzzy numbers

Familiar with a wide variety of areas in which fuzzy sets may be applied.

Understand how fuzzy sets model ambiguity.

Manipulate fuzzy membership functions for simple operations.

Text Book

1. George J.Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic, Prentice Hall of India, New Delhi,

2004.

References

1. H.J. Zimmermann, Fuzzy Set Theory and its Applications, Allied Publishers Limited, New

Delhi, 1991


Part-IV

Course code:7SBS6B3

BASIC INTERNET AND OFFICE AUTOMATION LAB COURSE DESCRIPTION

Students will get fundamentals of knowledge in MS-Word, MS-Excel, a

preparation of power point slides, Internet browsing and application of tools in social

science.

OBJECTIVES OF THE COURSE:

1. MS-Word is introduced in the syllabus to help the students learn typing,

alignment, cut, copy, paste etc., of theoretical work

2. MS-Excel is help the students in diagrammatic and statistical representation of

data, Drafting documents, preparation of balance sheet accounts etc.,

3. MS- PowerPoint to enhance the knowledge of students in the presentations of

slides, flex, animation work etc.,

4. Internet and Browsing to give access to students in downloading reading

materials, literature etc., their subject.

5. Statistical Package for Social Science (SPSS) to apply statistical and mathematical

tools in the preparation of thesis, dissertation, project etc.,

COURSE OUTCOMES

Application of computer knowledge in economics has widened the scope of Economics.

1. Ms-Word and Excel to highly useful in the analysis, evaluation, interpretation and

presentation of statistical data collected.

2. Through the knowledge in internet browsing, students can download relevant

literature or any study material they need.

3. SPSS is highly useful, when they go for higher studies or when they undertake

research works.

4. PowerPoint presentation helps the students to effectively give the substance of a

topic in a nutshell.

TEXT BOOKS

1. V.Rajaram Fundamentals of computers, Prentice Hall of India, New Delhi.

2. P.K.Singa, Computer Fundamentals, BPB publication, New Delhi.


3. E.Balagurusamy, Programming in Basic, TataMcGraw Hill publication New Delhi.

Course code:7SBS6B4

FRUITS AND VEGETABLES PRESERVATION SKILLS

COURSE DESCRIPTION:

Provides the knowledge related to the various types of vegetables and fruits that

could be preserved, the preservation techniques available the related equipment’s and

methodology.

COURSE OBJECTIVES:

1. To improve income earning skills through fruits and vegetable

preservation.

2. To open up new areas of self-employment opportunities for the youth.

COURSE OUTCOMES

1. Introduces the principles and method available in the preservation process.

2. Provides knowledge about various types of equipment available and different

types of containers that are being used in the preservation process.

3. To introduce various methods available for the preservation of vegetables and

fruits. Also gives knowledge related to personal hygiene and the sanitary

standards to be followed in the preservation process.

4. Gives the practical knowledge of fruits and their preservation methods.

5. The project work helps the students to know the various centres that are

involved in the reservation practices. Also it helps to understand the area

specific Technology that could be applied.

REFERENCE BOOKS

1. Srivastava,R.P. and S.Kumar., fruit and vegetable preservation: principles.

2. Ranjit Singh, Fruits, National Book Trust.

3. Girdhari Lal Tandon et al., Preservation of Fruit and Vegetable Products.

department of mathematics -...

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