b.sc., mathematics (honours) syllabus - christ university mathematics honours... · differential...

(Under Section 3 of the UGC Act, 1956)

B.Sc., Mathematics (Honours)

Syllabus

Ban ga lor e , Ka rn a t ak a , In d i a , 2 0 1 1

ii

Contents 1 COURSE OBJECTIVE AND METHODOLOGY ............................................................................................. 1

1.1 COURSE OBJECTIVE ............................................................................................................... 1

1.2 METHODOLOGY ...................................................................................................................... 2

2 PAPER OBJECTIVES ....................................................................................................................................... 3

2.1 B.Sc., MATHEMATICS (Honours): ........................................................................................... 3

2.1.1 MAT 131: INTRODUCTORY ALGEBRA: ........................................................................ 3

2.1.2 MAT 231: CALCULUS: ...................................................................................................... 3

2.1.3 MAT 331: DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS: .......................... 3

2.1.4 MAT 431: ANALYTICAL GEOMETRY AND VECTOR CALCULUS: .......................... 3

2.1.5 MAT 531: ALGEBRA: ......................................................................................................... 3

2.1.6 MAT 532: INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING: ................... 4

2.1.7 MAT 533: INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY: ... 4

2.1.8 MAT 534: PROGRAMMING IN C: .................................................................................... 4

2.1.9 MAT 535: GRAPH THEORY: ............................................................................................. 4

2.1.10 MAT 536: NUMBER THEORY: ....................................................................................... 4

2.1.11 MAT 631: REAL AND COMPLEX ANALYSIS: ............................................................. 5

2.1.12 MAT 632: NUMERICAL METHODS:.............................................................................. 5

2.1.13 MAT 633: ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL

MODELLING: ............................................................................................................................... 5

2.1.14 MAT 634: INTRODUCTION TO MATHEMATICAL PACKAGES: .............................. 5

2.1.15 MAT 635: OPERATIONS RESEARCH: ........................................................................... 6

2.1.16 MAT 636: MECHANICS: .................................................................................................. 6

2.2 CERTIFICATE COURSES: ........................................................................................................ 6

2.2.1 MAT 101: FOUNDATION OF MATHEMATICS: ............................................................. 6

2.2.2 MAT 201: QUANTITATIVE TECHNIQUES FOR MANAGERS: .................................... 6

2.2.3 MAT 301: INTRODUCTION TO MATHEMATICA: ........................................................ 7

2.2.4 MAT 401: QUANTITATIVE APTITUDE FOR COMPETITIVE EXAMINATIONS: ..... 7

3 COURSE STRUCTURE .................................................................................................................................... 7

3.1 B.Sc MATHEMATICS:............................................................................................................... 7

3.2 CERTIFICATE COURSES ......................................................................................................... 8

iii

4 SYLLABI FOR REGULAR PAPERS ................................................................................................................ 9

4.1 MAT 131: INTRODUCTORY ALGEBRA ................................................................................. 9

4.2 MAT 231: CALCULUS ............................................................................................................. 11

4.3 MAT 331: DIFFERENTIAL EQUATIONS AND APPLICATIONS ....................................... 13

4.4 MAT 431: ANALYTICAL GEOMETRY AND VECTOR CALCULUS ................................. 15

4.5 MAT 531: ALGEBRA ............................................................................................................... 17

4.6 MAT 532: INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING .......................... 19

4.7 MAT 533: INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY ......... 21

4.8 MAT 534: PROGRAMMING IN C ........................................................................................... 23

4.9 MAT 535: GRAPH THEORY ................................................................................................... 25

4.10 MAT 536: NUMBER THEORY .............................................................................................. 27

4.11 MAT 631: REAL AND COMPLEX ANALYSIS ................................................................... 29

4.12 MAT 632: NUMERICAL METHODS .................................................................................... 31

4.13 MAT 633: ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL

MODELING ..................................................................................................................................... 33

4.14 MAT 634: INTRODUCTION TO MATHEMATICAL PACKAGES .................................... 35

4.15 MAT 635: OPERATIONS RESEARCH ................................................................................. 37

4.16 MAT 636: MECHANICS......................................................................................................... 39

5 SYLLABI FOR CERTIFICATE COURSES .................................................................................................... 41

5.1 MAT 101: FOUNDATIONS OF MATHEMATICS ................................................................. 41

5.2 MAT 201: QUANTITATIVE TECHNIQUES FOR MANAGERS .......................................... 42

5.3 MAT 301: INTRODUCTION TO MATHEMATICA ............................................................... 43

5.4 MAT 401: QUANTITATIVE APTITUDE FOR COMPETITIVE EXAMINATIONS ............ 44

1

COURSE OBJECTIVE AND METHODOLOGY

1.1 COURSE OBJECTIVE

An educational institution that does not lead to research and specialization will

remain on the way side of the higher education missing the golden opportunities

for pushing farther the frontiers of knowledge and opening up new vistas of

scientific endeavor to the young. Keeping the above in mind it has been

proposed to continue with triple main system with mathematics as one of the

core subjects. The B.Sc. course aims at to fulfill the following broad

objectives:

1. Developing a respectable intellectual level seeking to expose the various

concepts in mathematics.

2. To enhance the students reasoning, analytical and problem solving skills

3. To cultivate a mathematicians habit of thought and reasoning.

4. To enlighten the student that the mathematical ideas are relevant for

oneself no matter what his/her interests are.

5. To cultivate a research culture in young minds.

6. Development of students’ competence by evolving a learner centered

curriculum.

7. To encourage the students to uphold scientific integrity and objectivity in

professional endeavors.

8. To pursue higher studies in top notch institutions.

The course curriculum is intensive and extensive and includes 16 core

papers covering all major topics in mathematics. Students who opt for

Mathematics Honours programme will have to follow three major syllabi of

PCM or PME or CMS or CME combinations in the first four semesters. There

will be one mathematics paper in each of the first four semesters and six papers

in each of the fifth and sixth semesters. Each of the sixteen papers will carry

100 marks. In each paper the minimum marks for pass will be 40. Courses like

“Foundations of Mathematics”, “Introduction to Mathematica”, “Quantitative

2

methods for managers” and “Quantitative aptitude for competitive

examinations” are offered as certificate courses.

After completing three years of honours degree course, students can opt

for higher studies; get into the institutions like ISRO, NAL etc or IT oriented

service sections.

1.2 METHODOLOGY

In order to realize the objectives, a methodology based on the combination of

the following will be adopted: Case studies, Debates, Project work, Team

teaching, Reflective diary writing, Seminars, Field visits, Information and

communications technology.

3

2

PAPER OBJECTIVES

2.1 B.Sc., MATHEMATICS (Honours):

2.1.1 MAT 131: INTRODUCTORY ALGEBRA:

This paper emphasizes general techniques of problem solving and explores the

creation of mathematical patters. It aims at introducing a course that initiates the

students into the world of Discrete Mathematics. It includes the topic like

Mathematical Logic, Set Theory, Relations, Functions, Mathematical Induction,

Recursive relations and Matrices.

2.1.2 MAT 231: CALCULUS:

This paper aims at enabling the students to know various concepts and

principles of differential and integral calculus. Sound Knowledge of calculus is

essential for the students of mathematics for the better perceptions of the

subject and its development.

2.1.3 MAT 331: DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS:

This paper enables the students to know the beauty of an important branch of

mathematics, viz. Differential Equations and its applications in Physics.

2.1.4 MAT 431: ANALYTICAL GEOMETRY AND VECTOR CALCULUS:

Three Dimensional Geometry is one of the fundamental areas of Mathematics.

The course is designed to lay a strong foundation of Geometry and Vector

Calculus.

2.1.5 MAT 531: ALGEBRA:

This paper aims at developing the ability to write the mathematical proofs. It

helps the students to understand and appreciate the beauty of the abstract nature

4

of mathematics and also to develop a solid foundation of theoretical

mathematics.

2.1.6 MAT 532: INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING:

This paper aims at providing a solid foundation upon the fundamental theories

and transformations of Fourier Transforms and Laplace Transforms. It also

covers the introduction to linear programming techniques.

2.1.7 MAT 533: INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY:

Differential geometry is the study of geometrical objects using Calculus. This

paper aims at increasing the students understanding in differential geometry due

to its connection and significance to other areas of Mathematics. It helps

students in understanding some of the fundamental concepts in differential

geometry through curves and surfaces in R3

2.1.8 MAT 534: PROGRAMMING IN C:

The objective of this paper is to help students learn various aspects of C

programming and make them skilled in C programming. Also helps to evaluate

critically the C programs written by others.

2.1.9 MAT 535: GRAPH THEORY:

This paper aims at imparting in the minds of the students the fundamental

concepts in graph theory. Also helps in appreciating the application of the

subject in a variety of fields, to learn, to understand and to construct

mathematical proofs involving graphs.

2.1.10 MAT 536: NUMBER THEORY:

The objective of the paper is to help the students to learn long and interesting

history of Number Theory and its problems that have attracted many of the

greatest mathematicians. Consequently the study of number theory is an

5

excellent introduction to the development and the achievement of Mathematics.

With its discrete precise nature is an ideal topic which helps the students to

perform Numerical Experiments and Calculations; also to explore its wide

spread applications in Cryptography.

2.1.11 MAT 631: REAL AND COMPLEX ANALYSIS:

This paper enables the students to understand the basic techniques and theories

of real and complex analysis, two traditionally separated subjects.

2.1.12 MAT 632: NUMERICAL METHODS:

This paper will help the students to have an in depth knowledge of various

advanced numerical methods and some interpolation techniques.

2.1.13 MAT 633: ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL

MODELLING:

Mathematical modeling is a mathematical tool for solving real world problems.

In this paper, students study a problem-solving process and learn how to

identify a problem, construct or select appropriate models, find solutions and

implement the model. Emphasis lies on model construction in order to promote

student creativity and demonstrate the link between theoretical mathematics and

real world applications.

2.1.14 MAT 634: INTRODUCTION TO MATHEMATICAL PACKAGES:

This paper gives a comprehensive introduction to the basic commands and

operations in MATLAB. It aims at introducing the students to write the script

files and function files and effective use them in implementing the built in

features of 2-D ploting and 3-D ploting. Also aims at introducing the

programming with applications.

6

2.1.15 MAT 635: OPERATIONS RESEARCH:

As Operations Research (OR) applications continue to grow and flourish in a

number of decision making fields, a number of applications of linear

programming are covered in this paper. This skill-based paper aims at imparting

theoretical knowledge of optimization techniques which are widely used in the

industry to optimize available resources.

2.1.16 MAT 636: MECHANICS:

This paper helps the students to develop an ability to apply fundamental

knowledge of mathematics and science. It aims at analyzing and interpretation

of mechanical laws and theorems. It also helps the students to identify,

formulate, and solve problems involving mechanics and to appreciate the

application of mechanics in various fields.

2.2 CERTIFICATE COURSES:

2.2.1 MAT 101: FOUNDATION OF MATHEMATICS:

This course is designed as a foundation course in Mathematics for those who

have not been exposed to any Mathematics course earlier. This enables the

students to improve their analytical, reasoning and problem solving skills.

Topics included are Set Theory, Theory of Equations, Matrices, Determinants,

Differential Calculus and Integral Calculus.

2.2.2 MAT 201: QUANTITATIVE TECHNIQUES FOR MANAGERS:

This skill based paper aims at imparting theoretical knowledge of optimization

techniques. These techniques are widely used in the industry to optimize

available resources. This will help the student to apply the mathematical

techniques to real life situations.

7

2.2.3 MAT 301: INTRODUCTION TO MATHEMATICA:

This paper can be used by students in Mathematics as an introduction to the

fundamental ideas of MATHEMATICA PACKAGE and as a foundation for the

development of more advanced concepts in MATHEMATICA. Study of this

paper promotes the development of Basic Programming skills in Mathematica.

2.2.4 MAT 401: QUANTITATIVE APTITUDE FOR COMPETITIVE EXAMINATIONS:

The quantitative aptitude occupies a very important place in any business

school entrance examination. This skill based paper aims at imparting the

aptitude knowledge required for competitive examination and provides a well-

knitted path to success. This knowledge acquisition will help the students to

over come the hurdles of competitive examinations like CAT, MAT, XAT,

JMET, GMAT, SWAT, etc.,

3

COURSE STRUCTURE

3.1 B.Sc MATHEMATICS:

Semester Paper Code Title of the Paper Hrs /

Week Marks Credit

I MAT 131 INTRODUCTORY ALGEBRA 6 100 4

II MAT 231 CALCULUS 6 100 4

III MAT 331 DIFFERENTIAL EQUATIONS AND ITS

APPLICATIONS 6 100 4

IV MAT 431 ANALYTICAL GEOMETRY AND VECTOR

CALCULUS 6 100 4

V

MAT 531 ALGEBRA 5 100 4

MAT 532 INTEGRAL TRANSFORMS AND LINEAR

PROGRAMMING 5 100 4

8

MAT 533 INTRODUCTION TO TOPOLOGY AND

DIFFERENTIAL GEOMETRY 5 100 4

MAT 534 PROGRAMMIN IN C 5 100 4

MAT 535 GRAPH THEORY 5 100 4

MAT 536 NUMBER THEORY 5 100 4

VI

MAT 631 REAL AND COMPLEX ANALYSIS 5 100 4

MAT 632 NUMERICAL METHODS 5 100 4

MAT 633 ORDINARY DIFFERENTIAL EQUATIONS

AND MATHEMATICAL MODELLING 5 100 4

MAT 634 INTRODUCTION TO MATHEMATICAL

PACKAGES 5 100 4

MAT 635 OPERATIONS RESEARCH 5 100 4

MAT 636 MECHANICS 5 100 4

3.2 CERTIFICATE COURSES

Semester Subject Code Paper Name Hrs /

Week Credit

I MAT 101 FOUNDATIONS OF MATHEMATICS 4 2

II MAT 201 QUANTITATIVE TECHNIQUES FOR

MANAGERS 4 2

III MAT 301 INTRODUCTION TO MATHEMATICA 4 2

IV MAT 401 QUANTITATIVE APTITUDE FOR

COMPETITIVE EXAMINATIONS. 4 2

9

4 SYLLABI FOR REGULAR PAPERS

4.1 MAT 131: INTRODUCTORY ALGEBRA

CHRIST UNIVERSITY DEPARTMENT OF MATHEMATICS

B.Sc Mathematics (Honours) – I Semester

MAT 131: INTRODUCTORY ALGEBRA

UNIT I: MATHEMATICAL LOGIC: (15 Hrs)

Propositions and Truth values – Connectives, their truth values – Tautology and contradiction – Logical

equivalence – Standard Theorems – Problems on Negation – Converse, Inverse and Contrapostive of

Propositions – open sentences – Quantifiers – Logical implications involving quantifiers – Rules of inferences.

UNIT II: SETS, RELATIONS AND FUNCTIONS: (25 Hrs)

Sets :– Axiom of extension – sub sets and empty set – Venn diagrams – Unordered pairs and Singletons –

Intersections – Unions – complements – power sets – Union and intersection of subsets – Ordered pairs –

Cartesian product of sets. Relations : - Properties of special binary relations - equivalence relations - ordering

relations - Hasse Diagram. Functions : - Types of functions – composition of functions – invertible functions

– inverse of compositions ( Standard theorems and related problems ).

UNIT III : MATHEMATICAL INDUCTION AND RECURCIVE RELATION (15 Hrs)

Mathematical induction – induction principle - related examples – Recursive Definitions – Fibonacci Sequence

– Lucas sequence – Eulerian numbers – Ackermann’s numbers – Other recursive definitions – Union and

intersection of n sets – conjunction and disjunction of n-proposition – well formed formulae.

UNIT IV : MATRIX THEORY (20 Hrs)

Recapitulation of fundamentals of matrix algebra – Symmetric and skew-symmetric – Hermitian and skew

Hermitian matrices – Idempotent, Nilpotent, Orthogonal, Unitary matrices and their properties – Rank of a

matrix – Normal form – Finding the inverse of a matrix by elementary transformation – System of linear

equations and consistency - Characteristic equations – Eigen values, Eigen vectors and properties – Cayley

Hamilton theorem and its use in finding inverse and powers of a matrix.

Total Hours: (75+15)

10

TEXT BOOKS:

1. K T Lueng, Doris L C Chen, “ Elementary Set Theory – Part I”, Reprint, 2009, Hong Kong University Press,

(Chapter 2: A, B, C, D, E, F, G, H, I, J; Chapter 3: A, B )

2. D.S. Chandrasekharaiah, Discrete Mathematical Structures, 2nd

Edition, 2005, PRISM Book Pvt. Ltd. ( Sections :

2.1, 2.1.1, 2.1.2, 2.2 , 2.2.1, 2.2.3, 2.2.4, 2.3, 2.4 , 2.4.1, 3.1, 3.2, 4.1, 4.2, 4.2.1, 4.4, 4.5, 4.6, 5.1, 5.2, 5.3, 5.4 )

3. B S Vatssa, Theory of Matrices, reprint 2005, New Delhi: New Age International Publishers.

(Sections : 1.5, 3.5, 2.6, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 6.1, 6.2, 6.3, 6.4, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6 )

4. Kenneth H Rosen, Discrete Mathematics and its Applications, 5th

Edition, 1999, WCB / McGraw – Hill. ( 10.1,

10.2, 10.3, 10.4 )

Books for Reference:

1. Tremblay & Manohar, Discrete Mathematical Structures with Application to Computer Science, 5th

Edition, 2000,

Tata McGraw Hill Book Company.

2. Shanti Narayan , Text book of Matrices, 5th

edition, 1968, New Delhi, S Chand and Co.

Suggested Web links:

1. http://www.cs.columbia.edu/~zeph/3203s04/lectures.html

2. http://home.scarlet.be/math/matr.htm

3. http://www.cut-the-knot.org/induction.shtml

4. http://www.themathpage.com/

5. http://www.abstractmath.org/

6. http://mathworld.wolfram.com/DiscreteMathematics.html

FORMAT OF QUESTION PAPER MAT 131: INTRODUCTORY ALGEBRA

Part Unit and No. of subdivisions to be set in

the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 2

10 1 10 Unit II 3

Unit III 2

Unit IV 3

B

Unit I 2

9 2 18 Unit II 3

Unit III 2

Unit IV 3

C Unit I and II 5

8 6 48 Unit III and IV 5

D Unit I, II, III and IV 4 3 8 24

Total 100

11

4.2 MAT 231: CALCULUS


B.Sc Mathematics (Honours) – II Semester

MAT 231: CALCULUS

UNIT I: SUCCESSIVE AND PARTIAL DIFFERENTIATIONS (15 Hrs)

Successive differentiation – nth

derivatives of functions – Leibnitz theorem and its applications – Partial

differentiation – First and higher order derivatives – Differentiation of homogeneous functions – Euler’s theorem –

Total derivative and differential – Differentiation of implicit functions and composite functions – Jacobians.

UNIT II : DERIVATIVES OF ARCS (25 Hrs)

Polar coordinates – Angle between the radius vector and the tangent – Angle of intersection of curves

(polar form) – Polar subtangent and polar subnormal – Perpendicular from pole on the tangent – Pedal equations –

Derivative of an arc in Cartesian, parameter and polar forms – Equation of a conic in polar form – Convexity,

concavity and curvature of plane curves – Formula for radius of curvature in Cartesian, parametric, polar and pedal

forms – Centre of curvature – Evolutes and involutes – Envelopes – Asymptotes – Singular points – Cusp, node and

conjugate points. Tracing of standard Cartesian and polar curves.

UNIT III : LIMITS, CONTINUITY AND MEAN VALUE THEOREMS (15 Hrs)

Definition of the limit of a function ( - ) form – Continuity – Types of discontinuities – Properties of

continuous functions on a closed interval – Differentiability – Differentiability implies continuity – Converse not

true – Rolle’s theorem – Lagrange’s and Cauchy’s First Mean Value Theorems – Taylor’s theorem (Lagrange’s

form) – Maclaurin’s theorem and expansions – Evaluation of limits by L’Hospital’s rule.

UNIT IV: INTEGRAL CALCULUS (20 Hrs)

Integral Calculus: Recapitulation of methods of integration and Definite Integral – Reduction

Formulae – Application of Integral Calculus – Length of arcs – Surface areas and Volumes of solids of

revolutions for standard curves in Cartesian and Polar forms, Improper Integrals – beta and gamma functions –

properties – relation between beta and gamma functions.


12

TEXT BOOKS:

1. N. P. Bali, Differential Calculus, Latest edition, 2005, Laxmi Publications (P) Ltd.,.

(Sections : 3.2, 3.3, 3.4, 3.5, 3.6, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, Chapters 5, 7, 8, 9, 10, 11, 12, 13, 14, 15)

2. Shanthi Narayan, Integral Calculus, Reprint 2004, New Delhi: S Chand and Co.

(Sections : 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.10, 7.1, 7.2, 7.3, 8.1, 8.2, 8.3, 9.1, 9.2, 9.3, 9.4, 9.5 )


1. G B Thomas and R L Finney, Calculus and Analytical geometry, 10th

edition, 2000, Addison – Wesley.

2. S. Narayanan & T. K. Manicavachogam Pillay, Calculus, Volume I & II, 1996, S. Viswanathan Pvt. Ltd.

3. Narayanan & Manicavachogam Pillay, Integral Calculus, reprint, 2004, S V Publishers.

4. Joseph Edwards, Differential Calculus, 2nd

Edition, 1956, MacMillan.

5. G K Ranganath, Text book of B.Sc., Mathematics, Revised edition, 2006, S Chand and Co.

6. Frank Ayres, Elliott Mendelson, Calculus, 5th

edition, 2009, Mc. Graw Hill.


1. http://ocw.mit.edu/courses/mathematics/

2. http://planetmath.org/encyclopedia/TopicsOnCalculus.html

3. http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2005/CourseHome/index.htm

4. http://mathworld.wolfram.com/Calculus.html

FORMAT OF QUESTION PAPER MAT 231: CALCULUS


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 2

10 1 10 Unit II 3

Unit III 2

Unit IV 3

B

Unit I 2

9 2 18 Unit II 3

Unit III 2

Unit IV 3

C Unit I and II 5



Total 100

http://www.mhprofessional.com/contributor.php?id=24688

http://www.mhprofessional.com/contributor.php?id=25079

13

4.3 MAT 331: DIFFERENTIAL EQUATIONS AND APPLICATIONS


B.Sc Mathematics (Honours) – III Semester

MAT 331: DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS

UNIT I : FIRST ORDER DIFFERENTIAL EQUATIONS (15 Hrs)

Solution of ordinary differential equations of first order and first degree – Variable separable and

reducible to variable separable forms – Homogeneous and reducible to homogeneous forms – Linear equations

and Bernoulli equations – Exact equations, equations reducible to exact form with standard integrating factors

– Clairaut’s equation – singular solution for Clairaut’s equation. Orthogonal trajectories.

UNIT II : HIGHER ORDER DIFFERENTIAL EQUATIONS (25 Hrs)

Second and higher order ordinary linear differential equations with constant coefficients –Cauchy-

Euler differential equations – Simultaneous differential equations (two variables) with constant coefficients.

Second order linear differential equations with variable coefficients by the following methods: (i) when a part

of complementary functions is given, (ii) reducing to normal form, (iii) variation of parameters and

(iv) method of undetermined co-efficient (v) by finding the first integral (exact equation) - Total and

Simultaneous differential equation.

UNIT III : PARTIAL DIFFERENTIAL EQUATIONS (20 Hrs)

Partial differential equations of first order – Lagrange’s solution – Charpit’s general method of solution –

Partial differential equations of 2nd

order – Classification of linear partial differential equation of 2nd

order –

Homogeneous and non- homogeneous equations with constant coefficients – Partial differential equations

reducible to equations with constant coefficients.

UNIT IV : APPLICATIONS OF DIFFERENTIAL EQUATIONS (15 Hrs)

Particle dynamics: Simple Harmonic motion – Projectiles: – horizontal plane - trajectory – velocity of

projection – angle of projection – Range - time of flight – greatest height - projectiles on inclined plane.

Central orbit and Central forces: – differential equation of a path – pedal equation of a differential equation –

velocity at any point of a central orbit – areal velocity – Kepler’s laws of planetary motion.


14

TEXT BOOKS:

1. Frank Ayres, Differential Equations, paperback, 1976, Schaums Outline Series. (Chapters: 1, 2, 3, 4, 5,

6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33)

2. S Narayanan, Dynamics, 16th Edition, 1986, S Chand and Co. (Chapter: 8 )

3. N.P. Bali, Dynamics - Golden Series, Latest Edition, 2004, Lakshmi Publications (p) Limited. (Chapters:5,6,7)


1. I N Sneddon, Elements of Partial Differential Equations, 3rd

Edition, 1980, Mc. Graw Hill.

2. S Narayanan & T K Manicavachogam Pillay , Differential Equations, 1981, S V Publishers Private Ltd.

3. P Duraipandian , Mechanics, 4th revised edition, 1995, S Chand and Co.

4. G K Ranganath, Text book of B.Sc, Mathematics, Revised edition, 2006, S Chand and Co.

5. G F Simmons, Differential equation with Applications and historical notes, , second edition, 2006, McGraw hill.



2. http://www.analyzemath.com/

3. http://tutorial.math.lamar.edu/classes/de/de.aspx

4. http://www.sosmath.com/diffeq/diffeq.html

5. http://www.analyzemath.com/calculus/Differential_Equations/applications.html

FORMAT OF QUESTION PAPER MAT 331: DIFFERENTIAL EQUATIONS AND APPLICATIONS


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 2

10 1 10 Unit II 3

Unit III 3

Unit IV 2

B

Unit I 2

9 2 18 Unit II 3

Unit III 3

Unit IV 2

C Unit I and II 5



Total 100

15

4.4 MAT 431: ANALYTICAL GEOMETRY AND VECTOR CALCULUS


B.Sc Mathematics (Honours) – IV Semester

MAT 431: Analytical Geometry and Vector Calculus

UNIT I: ANALYTICAL GEOMETRY(3D) - (Lines and Planes) (25 Hrs)

Direction cosines of a line – Direction ratios of the join of two points - Projection on a line – Angle

between the lines – Area of a triangle and volume of a tetrahedron with given vertices - Equation of line in

different forms – Perpendicular from a point onto a line - Equation of a plane in different forms –

Perpendicular from a point onto a plane - Angle between two planes – Line of intersection of two planes -

Plane co-axial with given planes – Planes bisecting the angle between two planes – Angle between a line and a

Plane – Co-Planarity of two lines – Shortest distance between two lines.

UNIT II : ANALYTICAL GEOMETRY(3D) - (Spheres, Cylinders & Cone) (15 Hrs)

Equation of the sphere in its general form – Determination of the centre and radius of a sphere with the

given ends of a diameter – section of sphere by a plane – tangent plane - orthogonal spheres - Equations of

Right circular cones and right circular cylinders – Problems.

UNIT III : VECTOR DIFFERENTIAL CALCULUS, LINE AND MULTIPLE INTEGRALS (25 Hrs)

Vector Differentiation – Gradient – Divergence – Curl and Laplacian Operators – Vector identities -

Line integral and basic properties – examples on evaluation of the integrals – Definition of a double integral –

its conversion to iterated integrals – evaluation of double integral by change of order of integration and by

change of variables – surface areas as double integrals – Definition of a triple integral and evaluation – change

of variables – volume as a triple integral – Line, surface and volume integrals of vector functions

UNIT IV: INTEGRAL THEOREMS (10 Hrs)

Green’s theorem in the plane (statement and proof) – Direct consequences of the theorem – The

Divergence theorem (statement only) – Direct consequences of the theorem – The Stoke’s theorem (statement

only) – Direct consequences of the theorem.


16

TEXT BOOKS:

1. S.P. Mahajan & Ajay Aggarwal, Comprehensive Solid Geometry, 1st edition, 2000, Anmol Publications

Pvt. Limited. (Sections : 1.8, 1.15, 3.2, 3.3,3.7, 3.8, 3.9, 3.10, 3.12, 3.13, 4.2, 4.3, 5.3, 6.1, 6.2,

6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 6.10 )

2. B Spain, Vector Analysis, 2nd

Edition, 1988, Calcutta: Radha Publishing Co. ( Chapter 3 : Sections 17, 18,

19, 20, 21, Chapter 5 : Sections 32, 33, 34, 35, 36, Chapter 6 : Sections 37, 38, 39, Chapter 7 : 41, 42, 43,

Chapter 8 : Sections 44, 45, 46, 47, 48, 49, Chapter 9 : Sections 50, 51, 53, 54, 55, Chapter 10 : Sections

56, 57, 58, 59, 60, Chapter 11: section 66 )

Books for Reference: 1. Shanthi Narayan, Analytical Solid Geometry, 2004, New Delhi: S. Chand and Co. Pvt. Ltd.

2. S Narayanan & Manicavachogam Pillay, Vector Algebra and Analysis, 4th

edition, 1986, S V Publishers.

3. Raisinghania, M.D, Dass, H.K., Saxena, H.C., Simplified course in Vector Calculus, Special Indian

edition, 2002, S Chand & Co.

4. G K Ranganath, Text book of B.Sc. Mathematics, Revised edition, 2006, S Chand and Co.

Suggested Web links :


2. http://www.univie.ac.at/future.media/moe/galerie.html

3. http://mathworld.wolfram.com/AnalyticGeometry.html

4. http://www.math.gatech.edu/~harrell/calc/

FORMAT OF QUESTION PAPER MAT 431: ANALYTICAL GEOMETRY AND VECTOR CALCULUS


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 2

10 1 10 Unit II 3

Unit III 3

Unit IV 2

B

Unit I 2

9 2 18 Unit II 3

Unit III 3

Unit IV 2

C Unit I and II 5



Total 100

17

4.5 MAT 531: ALGEBRA


B.Sc Mathematics (Honours) – V Semester

MAT 531: ALGEBRA

UNIT I : GROUPS (25 Hrs)

Groups – Subgroups – Cyclic groups – Cosets – Lagrange’s theorem – Normal Subgroup – Quotient

Group – Homomorphism of groups – Fundamental Theorem of Homomorphism – Isomorphism - Cauchy’s

theorem for abelian groups – Permutation groups.

UNIT II : RINGS, INTEGRAL DOMAINS AND FIELDS (15 Hrs)

Rings – Properties – Subrings – Ideals, Principal, Prime and Maximal ideal in a commutative ring –

Homomorphism and Isomorphism of Rings –Integral domains – Fields – Properties following the definition.

UNIT III : LINEAR ALGEBRA (20 Hrs)

Vector space: Definition – Examples – Properties – Subspaces – Span of a set – Linear dependence

and independence – Dimension and Basis

Linear transformation: Definition and examples – Range and Kernel of a linear map – Rank and

Nullity – inverse of a linear transformation – consequence of Rank-nullity theorem.

Inner product space: Definition – examples – orthonormal sets – Schwarz inequality – Gram Schmidt

orthogonolization process – problems.

Total Hours:(60+15)

18

TEXT BOOKS:

1. Herstein I N, Topics in Algebra, 4th Edition, 1991, New Delhi, India: Vikas Publishing House Pvt.

Ltd. (for Unit I and II ).( Sections : 2.1 , 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.10, 3.1, 3.2, 3.3, 3.4, 3.5)

2. Krishnamoorty V K, Mainra V P, Arora J L, An Introduction to Linear Algebra, Reprint, 2003,

New Delhi: Affiliated East West Press Pvt. Ltd. (for Unit III). ( Sections: 3.1, 3.2, 3.3, 3.4, 3.5,

3.6, 4.1, 4.2, 4.3, 4.4, 4.5, 7.2.1, 7.2.2, 7.2.3, 7.2.4, 7.2.5, 7.2.6, 7.2.7, 7.2.8, 7.2.9, 7.2.10, 7.2.11,

7.2.12)


1. John B Fraleigh , A First course in Abstract Algebra, 3rd Edition, 1990, Narosa Publishing House.

2. Vashista.,A First Course in Modern Algebra.11th Edition, 1980, Krishna Prakasan Mandir.

3. R. Balakrishan, N.Ramabadran, A Textbook of Modern Algebra, 1st Edition, 1991, New Delhi:

Vikas publishing house pvt. Ltd.


5. Michael Artin ,”Algebra”, 2nd

Edition, 1995, Prentice Hall.



2. http://www.extension.harvard.edu/openlearning/math222/

3. http://mathworld.wolfram.com/Algebra.html

4. http://www.math.niu.edu/~beachy/aaol/

5. http://planetmath.org/encyclopedia/Inverse.html

FORMAT OF QUESTION PAPER MAT 531: ALGEBRA


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 4

9 2 18 Unit II 3

Unit III 3

C Unit I 4

8 6 48 Unit II and III 6

D Unit I, II and III 4 3 8 24

Total 100

19

4.6 MAT 532: INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING



MAT 532 : INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING

UNIT I : FOURIER SERIES AND FOURIER TRANSFORMS (25 Hrs)

Introduction to integral transforms - Fourier Series of functions with period 2π and period

2L – half range cosine and sine series – Finite Fourier cosine and sine transforms – transform of

some common functions.

The Fourier Integral – Complex Fourier Transforms – Basic Properties - - Transform of the

derivative and t he derivative of the transform – Convolution theorem – Parseval’s Identity –

Fourier sine and cosine transforms – transforms for first and second order derivatives.

UNIT II : LAPLACE TRANSFORM (15 Hrs)

Laplace Transform of standard functions – Laplace transform of periodic functions – Inverse

Laplace transform– Solution of ordinary differential equation with constant coefficient using Laplace

transform.

UNIT III : LINEAR PROGRAMMING (20 Hrs)

Introduction - General form of Linear Programming Problem – Graphical Method of

solution – Simplex Method for Maximization of L.P.P. standard form – Minimization problem

in standard form – Big M method – Two phase method.

Introduction to Transportation Problem – Initial Basic Feasible solution – Moving

towards Optimality – Degeneracy in Transportation Problems – Unbalanced Transportation

Problem – Mathematical formulation of Assignment Problems – Hungarian method for solving

Assignment problem – Unbalanced Assignment problem – Travelling salesman problem –

Formulation of Travelling salesman problem as an assignment problem and solution procedure.

Total Hours:(60+15)

20

TEXT BOOKS:

1. Erwin Kreyszig, Advanced Engineering Mathematics, 8th

Edition, 2000, John Wiley & Sons, Inc.

(Sections : 5.1, 5.2, 5.3, 5.4,5.5,5.6,5.7, 5.8, 5.9, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9, 10.10,10.11).

2. S Dharani Venkata Krishnan, “ Operations Research “, 3rd

Edition, 1992, Keerthi Publishing

house (p) Ltd. (Sections : 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7.1, 2.7.2 2.7.3, 3.1, 3.2, 3.3, 3.4, 3.5,

3.6, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7).


1. Sneddon I N, Fourier Transform, 1st

edition, 1995, New York : Dover Publications.

2. Raisinghania M.D., Laplace and Fourier Transforms, 1995, New Delhi: S. Chand and Co. Ltd.

3. G K Ranganath, Text book of B.Sc., Mathematics, Revised edition, 2006, S Chand and Co.

4. G Hadley, Linear Programming, Reprint, 2002, New Delhi: Narosa Publishing House.

5. Hamdy A Taha, Operations Research – an introduction, 6th

edition, 1996, New Delhi: Prentice Hall of India.

6. V K Kapoor, Operations Research, 5th

revised edition, reprint, 1994, New Delhi: Sultan Chand & Sons.



2. http://www.fourier-series.com/

3. http://mathworld.wolfram.com/

4. http://www.princeton.edu/~rvdb

5. http://www.zweigmedia.com/RealWorld/Summary4.html

6. http://people.brunel.ac.uk/~mastjjb/jeb/or/contents.html

7. http://people.brunel.ac.uk/~mastjjb/jeb/or/lpmore.html

FORMAT OF QUESTION PAPER MAT 532: INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 4

9 2 18 Unit II 3

Unit III 3

C Unit I 4



Total 100

21

4.7 MAT 533: INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY



MAT 533: INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY

Unit I: INTRODUCTION TO TOPOLOGY (20 Hrs)

Metric Spaces – Open sets and closed sets – convergence and completeness – spaces of

continuous functions – Topological space – Definition and examples – Open base and Open

sub bases – The function algebras C(X,R), C(X,C).

Unit II: THE THEORY OF CURVE (20 Hrs)

Regular representations – regular curves – Orthogonal projections – Implicit representations of

a curve – Regular curves of class Cm

– Definition of arc length – Arc length as a parameter –

unit tangent vector - Tangent line and normal plane – curvature – principal normal unit vector

– Principal normal line and osculating plane – binormal – moving trihedron – torsion –

spherical indicatrices – Frenet Equations – The fundamental existence and uniqueness theorem.

Unit III: CONCEPT OF A SURFACE (20 Hrs)

Regular parametric representation – coordinate patches – Definition of a simple surface –

Tangent plane and Normal line – Topological properties of simple surfaces – First fundamental

form – arc length and surface area – second fundamental form – normal curvature – principal

curvatures and directions – Gaussian curvature and mean curvature.


22

Text Book:

1. G F Simmons, “Introduction To Topology and Modern Analysis”, 2004, NewDelhi: Tata Mc Graw-

Hill Publishing Company Limited.

2. Martin Lipschultz, Differential Geometry – Schaums Outline Series, 2005, New Delhi, Tata McGraw-

Hill Publishing Company Limited.

Reference Books:

1. Munkers, “Topology”, 2nd

Edition, 2006, Pearson Education Pvt. Limited.

2. Erwin Kreysizig, Differential Geometry, 1991, NewYork: Dover publications inc.

3. T J Willmore, An introduction to Differential Geometry, twenty first Indian impression, 2006,

Oxford University Press.


1. http://mathworld.wolfram.com/Topology.html

2. http://140.177.205.65/infocenter/Courseware/259/

3. http://www.trillia.com/online-math/geometry.html

4. http://www.trillia.com/online-math/geometry

5. http://www.wisdom.weizmann.ac.il/~yakov/Geometry/

6. http://people.math.gatech.edu/~ghomi/LectureNotes/index.html

FORMAT OF QUESTION PAPER

MAT 533: INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 3

9 2 18 Unit II 4

Unit III 3

C Unit I and II 6

8 6 48 Unit III 4


Total 100

23

4.8 MAT 534: PROGRAMMING IN C


B.Sc Mathematics (Honours)– V Semester

MAT 534: PROGRAMMING IN C

UNIT I: BASICS AND CONTROL STRUCTURES (20 HRS)

Basics: Algorithm and Flow chart. Introduction to C: Development of C, Features, constants and variables, data

types, operators and expressions, library functions. I/O statements: Formatted and Unformatted I / O, Scanf(),

Print(), getchar() and putchar() functions. Control Structures: Conditional and Unconditional, if, for, while and

do… while, switch, break and continue, goto statement. Lab Programs on the topics.

UNIT II: ARRAYS, FUNCTIONS AND POINTERS (20 HRS)

Arrays: one and Multi dimensional arrays, Strings and String functions. Linear and binary search. Functions:

Definition, different types, advantages, calling a function, passing parameters, call by reference and call by

value, local and global variables, recursive functions. Pointers: Declaration, operation on pointers, relationship.

Lab Programs on the topics.

UNIT III: STRUCTURE, UNION AND FILES (20 HRS)

Structure and Unions: Defining a structure, classification, union, user-defined data types, pointers to a

structure, structure as an argument to a function. Lab Programs on the topics. Files: Sequential files, file

pointers random files, processing a data file, unformatted data file, file error handling, implementation of copy

and merge commands.

LAB PROGRAMS:

1. LARGEST OF THREE NUMBERS.

2. SUM AND AVERAGE OF N NUMBERS.

3. FACTORIAL OF A NUMBER.

4. PRIME NUMBER.

5. REVERSE OF A NUMBER.

6. FIBONACCI SERIES.

7. FAHRENHEIT-TO- CELSIUS CONVERSION TABLE

8. ADDITION AND MULTIPLICATION OF TWO MATRICES.

9. READING, WRITING AND REVERSING AN INTEGER ARRAY.

10. LINEAR SEARCH

11. BINARY SEARCH.

12. PALINDROME

13. LENGTH OF A STRING.

14. STRING COPY, COMPARE, CONCATENATE.

15. PROGRAMS BASED ON FUNCTIONS

16. FUNCTIONS-CALL BY VALUE, CALL BY REFERENCE.

17. RECURSIVE FUNCTIONS.

18. STRUCTURE AND UNION- STUDENT PROFILE, LIBRARY DETAILS

19. FILE OPERATIONS

20. TO FIND THE SOLUTION OF AN EQUATION F(X)=0 USING BISECTION METHOD.


24

TEXT BOOKS:

1. KANETKAR, YASHAVANT: LET US C, 8TH EDITION, 2008, INFINITY SCIENCE PRESS.

2. GOTTFRIED, BYRON S: PROGRAMMING WITH C, 2ND

EDITION, 1996, TATA MCGRAW-HILL.

REFERENCE BOOKS:

1. BALAGURUSAMY, E: PROGRAMMING IN ANSI C, 2ND EDITION, 2008, TATA MCGRAW-HILL.

2. DEITEL, H M AND DEITEL P J: "C HOW TO PROGRAM", 2ND EDITION, 1992, PRENTICE-HALL.

Suggested Web Links:

1. http://www.cs.cf.ac.uk/Dave/C/CE.html

2. http://www.cprogramming.com/

3. http://www.howstuffworks.com/c.htm


MAT 534: PROGRAMMING IN C


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 3

9 2 18 Unit II 4

Unit III 3

C Unit I and II 6

8 6 48 Unit III 4


Total 100

25

4.9 MAT 535: GRAPH THEORY



MAT 535: GRAPH THEORY

UNIT I : GRAPHS, PATHS, CYCLES AND TREES (20 Hrs)

Introduction -Definition-Examples-Famous problems in graph theory- Paths Cycles-

Connectivity-Eulerian graphs-Hamiltonian graphs-Trees-Elementary properties of trees-

counting trees- Shortest path algorithms- Algorithms on trees -Application of trees.

UNIT II: PLANARITY OF GRAPHS AND COLORING (20 Hrs)

Planar graphs-Euler's formula-Graphs on other surfaces-Dual graphs-Infinite graphs-

Coloring graphs- Coloring vertices-Brook's theorem-coloring maps-coloring edges-chromatic

polynomials-Algorithm on planarity testing.

UNIT III : DIGRAPHS, MATCHING AND MENGER’S THEOREM (20 Hrs)

Digraphs- Eulerian digraphs and tournaments-Markov chains- Matching-Hall's 'marriage'

theorem-Transversal theory-Application of Hall's theorem-Menger's theorem-Network flows.


26

TEXT BOOK:

1. R.J.Wilson, Introduction to Graph Theory, Fourth Edition, 2003, Pearson, New Delhi.


1. G.Chartrand and P.Zhang, Introduction to Graph Theory, 2006, Tata McGraw-Hill, New Delhi.

2. G.Chartrand and L.Lesniak, Graphs and Digraps, Fourth Edition, 2004, CRC Press, Boca

Raton.

3. F.Harary, Graph Theory, 1988, Narosa.

4. S.Arumugam and S. Ramachandran, Invitation to Graph Theory, 2006, Scitech, Chennai.

5. N.Deo, Graph Theory with Applications to Engineering and Computer Scinece, 2009, PHI, New

Delhi.


1. http://www.ecp6.jussieu.fr/pageperso/bondy/books/gtwa/gtwa.html

2. http://www.personal.kent.edu/~rmuhamma/GraphTheory/graphTheory.htm

3. http://www.utm.edu/departments/math/graph/

4. http://diestel-graph-theory.com/

5. http://www.ti.inf.ethz.ch/ew/courses/GT05/

6. http://users.utu.fi/harju/graphtheory/graphtheory.pdf

7. http://www.mathcove.net/petersen/

8. http://www.maths.nottingham.ac.uk/personal/pmznd/g13gra/sylgra.html

9. http://www3.interscience.wiley.com/journal/35334/home

10. http://people.math.gatech.edu/~thomas/FC/fourcolor.html


MAT 535: GRAPH THEORY

Part Unit and No. of subdivisions to be set

in the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 3

9 2 18 Unit II 4

Unit III 3

C Unit I and II 6

8 6 48 Unit III 4


Total 100

27

4.10 MAT 536: NUMBER THEORY



MAT 536: NUMBER THEORY

UNIT – I : DIVISIBILITY THEORY IN INTEGERS (20 Hrs)

The division algorithm – The greatest common divisor – The Euclid algorithm – Basic properties of

congruence – special divisibility tests – Linear congruencies - The Diophantine Equations ax + by =

c.

UNIT – II : FERMATS THEOREM (20 Hrs)

The Little Fermat’s theorem and pseudoprimes – Wilson Theroem – The Fermat-Kraitchik

Factorization Method - The function and - The Mobius inversion formula – The greatest integer

function .

UNIT – III : EULER’S THEOREM AND SUM OF SQUARES (20 Hrs)

Euler’s Phi-function – Euler’s theorem – Some properties of the Phi-function – Euler’s criterion –

The Legendre’s symbol and its properties – Quadratic reciprocity – The Diophantine Equations

x2 + y

2 = z

2, x

4 + y

4 = z

4.


28

Text Book:

1. David M. Burton, Elementary Number Theory, 6th Edition, Sixth Reprint 2008, New Delhi, Tata

McGraw-Hill.

Reference Books:

1. J. Niven and H.Zuckerman, An Introduction to the Theory of Numbers, 1991, 5th Edition, New

York, .John Wiley & Sons Inc.

2. Elementary Number Theory & its applications – Kenneth Rosen, 1987, 2nd

Edition, Reading Mass

Addision – Wesley.

3. Gareth A Jones, Elementary Number Theory, 2005, J.Mary Jones, Springer


1. http://www.numbertheory.org/

2. http://www.mathpages.com/home/inumber.htm

3. http://mathworld.wolfram.com/NumberTheory.html

4. http://www.math.niu.edu/~rusin/known-math/index/11AXX.html


MAT 536: NUMBER THEORY


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks

for the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 3

9 2 18 Unit II 4

Unit III 3

C Unit I and II 6

8 6 48 Unit III 4


Total 100

29

4.11 MAT 631: REAL AND COMPLEX ANALYSIS


B.Sc Mathematics (Honours) – VI Semester

MAT 631: REAL AND COMPLEX ANALYSIS

UNIT I : OPEN SETS, CLOSED SETS, COUNTABLE SETS AND SEQUENCES (10 Hrs)

Limit of a set, Open sets, Closed sets, closure of a set, countable and uncountable sets -

Sequences: Definition of Sequences – limit of a sequence – algebra of limits of a sequence –

convergent, divergent and oscillatory sequences - problems thereon. Bounded sequences – every

convergent sequence is bounded – converse is not true – Monotonic sequences and their properties –

problems using the properties – Cauchy sequence – Results related to Cauchy’s sequences.

UNIT II: INFINITE SERIES (25 Hrs)

Infinite Series: Definition of convergence, divergence and oscillation of series – properties of

convergent series – a series of positive terms either convergences or diverges – Cauchy’s criterion –

Statement only – Geometric series. – Tests of convergence of series - p series – comparison tests –

D’Alembert’s test, Raabe’s test, Cauchy’s root test – Absolute and conditional convergence, Leibnitz

test for alternating series. – Summation of Binomial, Exponential and Logarithmic series.

UNIT III : COMPLEX ANALYSIS (25 Hrs)

Continuity and Differentiability of complex functions – Analytic Functions – Cauchy-

Riemann equations – Harmonic functions – Definite integrals – Contours – Line integrals – The

Cauchy’s Integral theorem and its direct consequences – Cauchy’s Integral formula for the functions

and derivatives – Morera’s theorem – Applications to the Evaluation of Simple line integrals –

Cauchy’s inequality – Liouville’s Theorem – Fundamental theorem of Algebra – power series –

Taylors series – Laurent’s series – circle and radius of convergence – sum functions - Transformations –

Definition of Conformal Mapping – Bilinear Transformation – Cross ratio – Properties – Inverse points –

Bilinear Transformation transforms Circles into circles or lines – Problems there on – Discussion of

various Transformations.


30

TEXT BOOKS:

1. S C Malik and S Arora , Mathematical Analysis , 2nd

Edition , 1992, New Age international (P) Ltd. (Chapter2,

Chapter 3 : Sections 1, 2, 3, 4, 5, 6, 7, 9 ; Chapter 4 : Sections 1.1, 1.2, 1.3, 1.4, 2, 2.1, 2.2, 2.3, 3, 3.1,

3.2, 4, 5, 6, 10, 10.1, 10.2)

2. R V Churchil & J W Brown, Complex Variables and Applications, 5th

Edition, 1989, Mc. Graw Hill Companies.

(Sections:14,15,16,17,18,19,20,21,22,23,24,25,36,37,38,39,40,41,47,48,49,51, 52, 53,,54, 55, 56, 57,58, 83, 84,

85, 86, 87, 88, 89, 90, 94)


1. Richard R Goldberg, Methods of Real Analysis, Indian Edition, 1970, Oxford and IBH Publishing Co.

2. L V Ahlfors, Complex Analysis, 3rd

Edition, 1979, Mc Graw Hill.



1. http://www.math.unl.edu/~webnotes/contents/chapters.htm

2. http://www-groups.mcs.st-andrews.ac.uk/~john/analysis/index.html

3. http://web01.shu.edu/projects/reals/index.html

4. http://www.mathcs.org/analysis/reals/index.html


MAT 631: REAL AND COMPLEX ANALYSIS


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 2

10 1 10 Unit II 4

Unit III 4

B

Unit I 2

9 2 18 Unit II 4

Unit III 4

C Unit I and II 6

8 6 48 Unit III 4


Total 100

31

4.12 MAT 632: NUMERICAL METHODS



MAT 632: NUMERICAL METHODS

UNIT I. NUMERICAL SOLUTION OF ALGEBRAIC AND SYSTEM OF EQUATIONS (20 Hrs)

Errors and their analysis – Floating point representation of numbers – Solution of Algebraic and

Transcendental Equations : Bisection method, Iteration method, the method of False Position, Newton

Raphson method.

Solution of linear systems – Matrix inversion method – Gaussian Elimination method – Modification

of the Gauss method to compute the inverse – Method of factorization – Iterative methods.

UNIT II. FINITE DIFFERENCES AND INTERPOLATION (20 Hrs)

Finite differences: Forward difference, Backward difference and Shift Operators – Separation of

symbols – Newton’s Formulae for interpolation – Lagranges interpolation formulae - Hermite, Cubic-Spline

interpolation formulas, Bivariate interpolation and least square approximation.

UNIT III. NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS (20 Hrs)

Numerical differentiation – Numerical integration: Trapezoidal rule, Simpson’s one-third rule and

Simpson’s three-eighth rule.

Numerical solution of ordinary differential equations – Taylor’s series – Picard’s method – Euler’s

method – Modified Euler’s method – Runge Kutta methods - second order (with proof) and fourth order

(without proof).


32

TEXT BOOKS:

1. S S Sastry , Introductory methods of Numerical Analysis, 3rd

Edition, 1999, Prentice Hall of India,

(Sections : 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 5.3.1, 5.3.2, 5.3.3, 5.4, 3.3.1, 3.3.2, 3.3.3, 3.9.1, 3.9.3 ,

3.10, 4.2, 4.4.1).

2. Francis Schcid, Schaums Outline of Numerical Analysis, Revised edition, , 2006, Mc.Graw Hill.


1. M K Jain, S R K Iyengar and R K Jain, Numerical Methods for Scientific and Engineering Computation, 4th

Edition, 2003, New Delhi: New Age International.



1. http://www.amtp.cam.ac.uk/lab/people/sd/lectures/nummeth98/index.htm

2. http://math.fullerton.edu/mathews/numerical.html

3. http://www.onesmartclick.com/engineering/numerical-methods.html


MAT 632: NUMERICAL METHODS


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 3

9 2 18 Unit II 4

Unit III 3

C Unit I and II 6

8 6 48 Unit III 4


Total 100

33

4.13 MAT 633: ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELING



MAT 633: ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL

MODELLING

Unit 1: ORDINARY DIFFERENTIAL EQUATIONS (15 Hours)

Power Series solutions: Series solutions of first order equations, Second order equations – Ordinary

points, Regular singular points and Method of Frobenius.

Unit 2: SPECIAL FUNCTIONS (15 Hours)

Special functions: Legender Differential equations – Legender polynomials, Legender Series and

Orthogonolity property. Bessel Differential equations Gamma function, General solution of Bessel

equation, Identities and Orthogonality property.

Unit3: MATHEMATICAL MODELING (30 Hours)

Mathematical Modeling; Need, Techniques, Classifications and Simple Illustrations through

Geometry, Algebra and Calculus. Limitations of Mathematical Modelling. Modeling through

Ordinary Differential equations: First order – Linear and non linear Growth and Decay Models,

Compartment Models, Mathematical Modelling in Dynamics, Mathematical modeling of Geometrical

problems. Population dynamics, Epidemics, Mathematical modeling in Economics, Models in

medicines, Arm race,. Battles. Second order – Planetary motion, Circular motion, Satellites motion.

Mathematical modeling through second order linear differential equations.


34

Text Books:

1. Differential Equations with Applications and Historical Notes , George F. Simmions , Tata

Macghaw Hill. (Unit 1 and 2)

2. Mathematical Modelling, J. N. Kapur New age international Publishers, (Unit 3 and 4)

Reference Books:

1. A First Course in Mathematical Modeling (third edition) by Giordano, Weir, and Fox. Published

by Thomson Brooks/Cole in 2003.


1. http://ocw.mit.edu/OcwWeb/Mathematics/18-306Fall-2009/MATLABResources/index.htm

2. http://www.sosmath.com/diffeq/modeling/modeling.html

3. http://www.encyclopedia.com/doc/1G1-200987672.html

4. http://serc.carleton.edu/sencer/ode_real_world/index.html

5. http://www.worldscibooks.com/mathematics/7573.html

FORMAT OF QUESTION PAPER MAT 633: ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELLING


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks

for the part

A

Unit I 3

10 1 10 Unit II 3

Unit III 4

B

Unit I 3

9 2 18 Unit II 3

Unit III 4

C Unit I and II 6

8 6 48 Unit III 4


Total 100

35

4.14 MAT 634: INTRODUCTION TO MATHEMATICAL PACKAGES



MAT 634: INTRODUCTION TO MATHEMATICAL PACKAGES

Unit I: INTRODUCTION (20 Hrs)

Starting with MATLAB, Creating Arrays – Mathematical Operations with Arrays: Addition and

Subtraction – Array Multiplication – Array division – Element by element operations – Using Arrays

in Matlab built in math functions – Built in functions for analyzing arrays – Script Files : Creating

and Saving script files – global variables – input / output commands - functions and functions files.

Unit II: PROGRAMMING AND GRAPHICS (20 Hrs)

Relational and Logical Operators – Conditional Statements – The Switch-Case Statement – Loops –

Nested Loops and Nested Conditional Statements – The break and continue commands – Two

dimensional Plots : The plot command – the fplot command – Plotting multiple graphs in the same

plot – Formatting plot – Plot with Logarithmic axes – Plots with special graphics – polar plots –

plotting multiple plots on the same page – Three dimensional plots: Line plots – Mesh and Surface

plots – Plots with special graphics – The view command.

Unit III: APPLICATIONS IN MATHEMATICS (20 Hrs)

Bracketing Methods for Locating a Root : Bisections Method of Bolzano, Regula Falsi Method –

Solution of Linear Systems AX=B: PA=LU Factorization with pivoting, Jacobi Iteration Method,

Gauss seidel Iteration method - Trigonometric polynomials – Numerical Differentiation:

Differentiation Using Limits, Differentiation Using Extrapolation – Numerical Integration: Composite

Trapezoidal Rule , Composite Simpsons Rule – Numerical Optimization: Golden Search for

minimum, Fibonacci Search for a Minimum.


36

Text Books:

1. Amos Gilat, MATLAB-An introduction with Applications, 2009, New Delhi, Wiley India.

(Chapter 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 3.1, 3.2, 3.3,

3.4, 3.5, 3.6, 3.7, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 6.1, 6.2, 6.3,

6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 9.1, 9.2, 9.3, 9.4)

2. John H Mathews, Kurtis D Fink, Numerical Methods Using MATLAB, Fourth Edition, 2008,

Pearson Prentice Hall. (Chapter 2.2, 3.5, 3.6, 5.4, 6.1, 7.2, 8.1, 8.2)

Reference Books:

1. Desmond J Higham, Nicholas J Higham, MATLAB Guide, Second Edition, 2005, SIAM.

2. Brain R Hunt, Ronald L Lipsman, Jonathan M Rosenberg, A Guide to MATLAB for Beginners

and Experienced Users, Cambridge University Press, First South Asian Edition 2002, Reprint

2006, Replika Press Private limited, India.

Suggested Web Link:

1. http://www.mathworks.com/access/helpdesk/help/techdoc/

2. http://www.nd.edu/~dtl/cheg258/notes/doc/ReferenceTOC.html

3. http://www.artefact.tk/software/matlab/m2html/doc/

FORMAT OF THE QUESTION PAPER

MAT 634: INTRODUCTION TO MATHEMATICAL PACKAGES


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks

for the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 3

9 2 18 Unit II 4

Unit III 3

C Unit I and II 6

8 6 48 Unit III 4


Total 100

37

4.15 MAT 635: OPERATIONS RESEARCH



MAT 635: OPERATIONS RESEARCH

Unit I: Introduction to linear and non-linear programming (20 Hrs) (16 hours)

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the

Dual Problem – Primal Dual relationships – Dual simplex methods – Unconstrained

problems , Necessary and sufficient conditions – Constrained Problems, equality constraints

and inequality constraints (Karush-Kuhn-Tucker conditions).

Unit II Queuing Theory and game theory (30 Hrs)

Elements of a queuing Model – Pure Birth Model – Pure Death Model – Specialized Poisson

Queues – Steady state Models: (M/M/1):(GD/ / ) – (M/M/1):(FCFS/ / ) -

(M/M/1):(GD/N/ ) – (M/M/c):(GD/ / ) – (M/M/ ):(GD/ / ).

Game Theory: Optimal solution of two person zero – sum games – Solution of Mixed

strategy Games (both graphical and Linear programming solution) – Goal Programming: -

Formulation – Tax Planning Problem – Goal programming algorithms – The weights method

– preemptive method.

Unit III Network Models (10 Hrs)

Linear programming formulation of the shortest-route Problem. Maximal Flow model:-

Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of

Maximal Flow Model. CPM and PERT:- Network Representation – Critical path

computations – Construction of the Time Schedule – Linear Programming formulation of

CPM – PERT calculations.


38

Text Book:

A.H. Taha, Operations research, 8th

Edition, 2007, Pearson Education.

Reference Books:

1. R. Ravindran, D.T. Philips and J.J. Solberg, Operations Research: Principles and

Practice, 2nd

Edition, 1976, John Wiley & Sons,

2. R. Bronson, Operations research, Shaum’s Outline Series, 2nd

Edition, 1997, McGraw

Hill.

3. F.S. Hillier and G.J. Lieberman, Introduction to operations research, 9th

Edition, 2009,

McGraw-Hill.

4. Chandrasekhara Rao & Shanthi Lata Mishra, Operations research, 2005, Alpha Science

International.

Web Links:

1. http://www.universalteacherpublications.com/univ/cs51contents.htm

2. http://people.brunel.ac.uk/~mastjjb/jeb/or/netex.html


MAT 635: OPERATIONS RESEARCH


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks

for the part

A

Unit I 3

10 1 10 Unit II 5

Unit III 2

B

Unit I 3

9 2 18 Unit II 5

Unit III 2

C Unit I 3



Total 100

39

4.16 MAT 636: MECHANICS



MAT 636: MECHANICS

UNIT I: STATICS (20 Hours)

Forces acting at a point-Resultant and components, Parallelogram law of forces, Magnitude and

direction of the resultant forces acting at an angle α ,Components of a force in two given directions,

Resolved part of a force in a given direction, Triangle law of forces, Converse, λ-µ theorem , Lami’s

theorem, Converse. Moments- Geometrical interpretation, Varignon’s theorem of moments, Centre

of parallel forces, Moment of force about a line. Equilibrium of rigid bodies acted on by three

forces-Three forces acting on a rigid body kept in equilibrium must be coplanar, must either be

concurrent or parallel, Three parallel forces in equilibrium, Three concurrent forces in equilibrium.

General conditions of equilibrium of Co-planar forces acting on a rigid body-Theorems .

UNIT II: STATICS(Cont…) (20 Hours)

Friction – Types, Laws, co-efficient, Angle of friction, Centre of gravity (C.G) - C.G of a number

of particles arranged in a straight line, C.G of a number of weights placed at points in a plane, C.G of

a uniform thin lamina in the shape of a parallelogram, C.G of a uniform triangular lamina, C.G of

three uniform rods forming a triangle or a uniform wire bent into the shape of a triangle, C.G of a

compound body, Determination of C.G by integration(uniform rod, uniform tetrahedron, solid right

circular cone, curved surface of a hollow right circular cone, solid hemisphere, segment of a solid

sphere, hollow hemisphere, segment of a hollow sphere)Stable and unstable equilibrium-

Definitions, Test for the determination of the nature of stability.

UNIT III: DYNAMICS (20 Hours)

Constrained Motion in Vertical Circles - Motion on the outside and inside of a smooth vertical

circle, vertical circular tube, Motion of a particle attached to the end of a string. Constrained Motion

in Horizontal Circles - Motion in a horizontal circle with uniform speed, Relative rest inside a

rotating sphere. Constrained Motion in a Plane-Motion of a heavy particle on a smooth curve in a

vertical plane, Cycloid and related results, Motion on a smooth cycloid in a vertical plane ,Motion

under constraint in various curves. Motion in Three Dimensions- Cylindrical (polar) co-ordinates,

components of velocity and acceleration of a moving point in terms of cylindrical co-ordinates,

Spherical polar co-ordinates, Problems.


40

TEXT BOOKS:

1. N.P.Bali, Golden Mathematics Series STATICS, Sixth Edition, 2007, Laxmi Publications (P) Ltd.

2. M.D.Raisinghania, Dynamics, 2006, S.Chand and co.


1. S.L.Loney, The elements of Statics and Dynamics, 2008, London, Kessinger Publishing .

2. S.L.Loney, An Elementary Treatise on the Dynamics of a particle and of rigid bodies, Paperback November

2007, Kessinger Publishing.

3. M.Ray, G.C.Sharma, ATextbook on Dynamics, 13th

Edition, 2005, India, S.Chand & Company Ltd.

4. Russell C. Hibbeler, Engineering Mechanics: Statics, 12th Edition, 2010, Prentice Hall.


1. http://scitation.aip.org/AMR/

2. http://plato.stanford.edu/entries/qm/

3. http://oli.web.cmu.edu/openlearning/forstudents/.../engineering-statics

4. http://www.aerostudents.com/files/statics/staticsFullVersion.pdf

5. http://www.physicsforums.com/forumdisplay.php?f=101


MAT 636: MECHANICS


the unit

No. of

subdivisions to

be answered

Marks for each

subdivision

Max. marks for

the part

A

Unit I 4

10 1 10 Unit II 3

Unit III 3

B

Unit I 3

9 2 18 Unit II 4

Unit III 3

C Unit I and II 6

8 6 48 Unit III 4


Total 100

41

5 SYLLABI FOR CERTIFICATE COURSES

5.1 MAT 101: FOUNDATIONS OF MATHEMATICS

UNIT I : SET THEORY (10 Hrs)

Set Theory – Definition – Types of Sets – Operation on sets ( Union, Intersection Complement, Difference )

– Venn Diagram – Application problems.

UNIT II : EQUATIONS (10 Hrs)

Linear Equations – solution of linear equation – Quadratic equations – solutions of Quadratic equations –

The equation x2 + 1 = 0 and introduction to complex numbers - Square roots, cube roots and fourth roots of unity.

UNIT III: MATRICES AND DETERMINANTS (10 Hrs)

Matrices – Types of Matrices – Operations on Matrices – Expansion of 2nd

and 3rd

order Determinants –

Minors – Co-factors – Adjoint – Singular and Non-singular matrices – Inverse of a matrix – Solution of system of

linear equation by matrix and determinant methods.

UNIT IV: DIFFERENTIAL AND INTEGRAL CALCULUS (15 Hrs)

Limits – Differentiation – Methods of differentiation – Second order derivative – Maxima and Minima

– Applications to Revenue Function, Cost function, profit function, Elasticity of demand, Break even point.

Indefinite integral – Standard results – substitution method – application to cost and revenue functions.

(2 credits ) Total Hours : 45

TEXT BOOKS :

1. D.C. Sancheti and V K Kapoor, Business Mathematics, 1995, Sultan Chand and sons.

2. Sathtyaprasad, Anantharam, Nirmala and Saha, Business Mathematics, 2004, Himalaya publishing House.


1. Shanthi Narayanan, Text book of Matrices, 10th Edition, 2004, Chand and Co.

2. Navaneetham , Business Mathematics, reprint, 1997, Gemini Publishing House, Tanjore.

Suggested Web Links: 1. http://planetmath.org/encyclopedia/SetTheory.html

2. http://plato.stanford.edu/entries/set-theory/

3. http://mathworld.wolfram.com/Logarithm.html 4. http://www.sosmath.com/algebra/logs/log1/log1.html

5. http://www.mathagonyaunt.co.uk/STATISTICS/ESP/Perms_combs.html

6. http://www.mathsisfun.com/combinatorics/combinations-permutations.html

7. http://home.scarlet.be/math/matr.htm

8. http://www.maths.surrey.ac.uk/explore/emmaspages/option1.html

42

5.2 MAT 201: QUANTITATIVE TECHNIQUES FOR MANAGERS

1 : LINEAR PROGRAMMING (20 Hrs)

Definitions of O.R.- Definition of Linear Programming Problem (L.P.P) - Formulation of L.P.P. –

Linear Programming in Matrix Notation – Graphical Solution of L.P.P – Simplex Method – Big M Technique

– Two Phase Method - Concept of Duality – Formulation of Primal Dual Pairs – Dual Simplex Method.

2 : TRANSPORTATION AND ASSIGNMENT PROBLEMS (10 Hrs)

Introduction to Transportation Problem – Initial Basic Feasible solution – Moving towards Optimality

– Degeneracy in Transportation Problems – Unbalanced Transportation Problem – Assignment Problems.

3 : GAME THEORY (15 Hrs)

Games and Strategies – Introduction – Two person zero sum games – Maximin and Minimax

Principles – Games without saddle point – mixed strategies – Solution of 2 x 2 rectangular games – Graphical

method – Dominance Property – Algebraic Method for m x n games

Total Hours : 45

(2 credits)

TEXTBOOK:

1. Kanti Swarup, P K Gupta, ManMohan, Operations Research, reprint 1994, Sultan Chand & Sons.


1. G Hadley, Linear Programming, reprint 2002, Narosa Publishing House.

2. K V Mittal, C Mohan, Optimization Methods in Operation Research and System Analysis, reprint, 1996,

New Age International Pvt. Ltd.

4. Hamdy A Taha, Operations Research- an introduction, 6th edition, 1996, Prentice Hall of India,

New Delhi.


1. http://www.zweigmedia.com/RealWorld/Summary4.html

2. http://people.brunel.ac.uk/~mastjjb/jeb/or/lpmore.html

3. http://www2.isye.gatech.edu/~jswann/casestudy/assign.html

4. http://mathworld.wolfram.com/GameTheory.html

43

5.3 MAT 301: INTRODUCTION TO MATHEMATICA

UNIT I : ALGEGRAIC COMPUTATION: (10 Hrs)

Simplification of algebraic expression, simplification of expressions involving special functions, built-

in functions for transformations on trigonometric expressions, definite and indefinite symbolic integration,

symbolic sums and products, symbolic solution of ordinary and partial differential equations, symbolic linear

algebra, equations solving, calculus, polynomial functions, matrix operations.

UNIT II : MATHEMATICAL FUNCTIONS: ( 07 Hrs)

Special functions, inverse error function, gamma and beta function, hyper-geometric function,

elliptic function, Mathieu function.

UNIT III: NUMERICAL COMPUTATION: (10 Hrs)

Numerical solution of differential equations, numerical solution of initial and boundary value

problems, numerical integration, numerical differentiation, matrix manipulations and optimization techniques.

UNIT IV : GRAPHICS: (08 Hrs)

Two and Three dimensional plots, parametric plots, contours, typesetting capabilities for labels and

text in plots, direct control of final graphics size, resolution etc.

UNIT V : PACKAGES: (10 Hrs)

Algebra, linear algebra, calculus, discrete math, geometry, graphics, number theory, vector analysis,

Laplace and Fourier transforms, statistics.

Total Hours : 45

(2 credits)

TEXT BOOKS:

1. Stephen Wolfram, The Mathematica book , 2003, Wolfram Research Inc.

2. Michael Trott, The Mathematica guide book for programming, 2004, Springer.

3. P. Wellin, R. Gaylord and S Kamin, An introduction to programming with Mathematica, 3rd

Edition,

2005, Cambridge.


1. http://www.math.montana.edu/frankw/ccp/modeling/topic.htm

2. http://library.wolfram.com/

44

5.4 MAT 401: QUANTITATIVE APTITUDE FOR COMPETITIVE EXAMINATIONS

1. PERCENTAGES, AVERAGES AND PROGRESSIONS: (10 Hrs)

Number System,

HCF and LCM: – Factors – Multiples – HCF – LCM – Product of two numbers – Difference between HCF and LCM,

Fraction: Fractional part of a number – To find the fraction related to Balance amount,

Square roots - Cube roots,

Percentage: Fraction to Rate Percent – Rate Percent to Fraction – Rate Percent of a Number – Expressing a given

quantity as a Percentage of Another given quantity – Converting a percentage into decimal – converting a decimal into a

percentage – Effect of percentage change on any quantity – Rate change and change in quantity available for fixed

expenditure ,

Average: Average of different groups – Addition or removal of items and change in average – replacement of some of the

items,

Arithmetic progression and Geometric Progression.

2 : RATIOS AND PROPORTIONS (25 Hrs)

Ratio and Proportions: Properties of Ratio – Dividing a given number in the given ratio – comparison of ratios – useful

results on proportion – continued proportion – relation among the quantities more than two – direct proportion and

indirect proportion,

Profit and Loss: Gain percentage and Loss Percentage – Relation among cost price, sale price, Gain/Loss and Gain% or

Loss% - Discount and Marked Price,

Time and work: Basic concepts – examples,

Pipes and Cistern: Basic concepts – examples,

Time and Distance: Definition – Average speed – distance covered is same, different – stoppage time per hour for a train

– time taken with two difference modes of transport,

Boats and Streams: Introduction, Speed of Man (Boat) and stream – Important formulae,

Mixture: Allegation rule – Mean Value of the Mixture – Six golden rules to solve problems on mixture – Removal and

replacement by equal amount.

3 : COMMERCIAL ARITHMETICS (10 Hrs)

Simple interest: Definition – Effect of change of P, R and T on simple interest – amount – amount becomes N times the

principal – Repayment of debt in equal installments – Rate and Time are numerically equal,

Compound Interest: Basic Formula - conversion period – to find the principal/time/rate – difference between compound

interest and simple interest – equal annual installments to pay the debt amount – growth – depreciation

Shares and Debentures : Basic facts – Approach to problems on stock – Approach to problems on Shares – regular

problems - Debentures.

Total Hours : 45

(2 credits)

45

Text Book :

1. Abhijit Guha, Quantitative Aptitude for competitive examinations, 3rd

Edition, Fourth reprint, 2005, Tata

McGraw-Hill.


1. Dinesh Khattar, Quantitative Aptitude, 3rd

Indian print, 2005, Pearson Education.

2. Muhamed Muneer, How to prepare for CAT, 2003, Tata Mc Graw, Hill.


1. http://www.ascenteducation.com

2. http://www.winentrance.com/MCA-Entrance-Exam-Question-Bank-CD.html

External Experts:

1) Dr. Y B Maralabhavi,

Professor and Chairman,

Department of Mathematics,

Bangalore University, Bangalore

2) Prof. Jayanthi Purandar,

Professor and Head,

Department of Mathematics,

Jyothi Nivas College, Bangalore.

3) Dr. Reena K Abraham,

Infosys Technologies Ltd,

Electronics City.

Hosur Road,

Bangalore – 561229.

b.sc., mathematics (honours) syllabus - christ university mathematics honours... · differential...

Documents