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**Syllabus for B.Sc. (CSM)-I for the Session 2012-13**

**1st Semester**

**Title of the Paper**

CSM 111 General English (Communication Skills)

CSM 112 Algebra

CSM 113 Trigonometry and Differential Calculus

CSM 114 Computer Oriented Statistical Methods-I

CSM 115 Probability Theory-I

CSM 116 Statistics Lab-I (Computer Oriented Practicals)

CSM 117 Introduction to Information Technology

CSM 118 Computer Programming Using C

CSM 119 Software Lab I (Programming in C and its Applications in Statistics)

**2nd Semester**

**Title of the Paper**

CSM 121 General English (Communication Skills)

CSM 122 Integral Calculus & Differential Equations

CSM 123 Geometry

CSM 124 Computer oriented Statistical Methods-II

CSM 125 Probability Theory-II

CSM 126 Statistics Lab-II (Computer Oriented Practicals)

CSM 127 Object Oriented Programming Using C++

CSM 128 Management Information System

CSM 129 Software Lab II ( Programming in C++)

**Syllabus for B.Sc. (CSM)-II for the Session 2012-13**

**3rd Semester**

**Title of the Paper**

CSM 231 Advanced Calculus

CSM 232 Differential Equations

CSM 233 Applied Statistics

CSM 234 Statistical Inference I

CSM 235 Statistics Lab-III (Computer Oriented Practicals)

CSM 236 Data Structure

CSM 237 Data Base Management System

CSM 238 Software Lab III (Practicals based on DBMS using MS Access and Data Structures)

Punjabi

**4th Semester**

**Title of the Paper**

CSM 241 Real Analysis

CSM 242 Topics in Analysis

CSM 243 Industrial Statistics

CSM 244 Statistical Inference II

CSM 245 Statistics Lab-IV (Computer Oriented Practicals)

CSM 246 Operating Systems

CSM 247 Web Technology

CSM 248 Software Lab IV

Environmental Studies

**Syllabus for B.Sc. (CSM)-III for the Session 2012-13**

**5th Semester**

**Title of the Paper**

CSM 351 Communication Skills

CSM 352 Abstract Algebra

CSM 353 Discrete Mathematics

CSM 354 Computer Oriented Numerical Methods

CSM 355 Sample Surveys

CSM 356 Statistics Lab-V (Computer Oriented Practicals)

CSM 357 Computer Networks and Data Communication

CSM 358 Visual Programming

CSM 359 Software Lab-V (Practicals based on Visual Programming)

**6th Semester**

**Title of the Paper**

CSM 361 Communication Skills

CSM 362 Mechanics

CSM 363 Linear Algebra

CSM 364 Linear Programming

CSM 365 Design and Analysis of Experiments

CSM 366 Statistics Lab-VI (Computer Oriented Practicals)

CSM 367 Oracle

CSM 368 Software Engineering

CSM 369 Software Lab-VI (Practicals based on Oracle)

**SYLLABUS**

** B.Sc. (Computer Science, Statistics, Mathematics) Part – I **

Outlines of Tests Syllabi and Courses of Reading.

Note:-Every theory paper will be of three hours duration.

**For Examination of Session 2012-13.**

** 1st Semester **

**________________________________________________________________________**

Code Title of paper/subject Hrs./ __Max Maks__ Week Conti. Univ. Total

Asmt. Exam.

CSM 111 General English 2 20 30 50

(Communication Skills)

CSM 112 Algebra 4 30 45 75

CSM 113 Trigonometry and 4 30 45 75

Differential Calculus

CSM 114 Computer Oriented 3 20 30 50

Statistical Methods-I

CSM 115 Probability Theory-I 3 20 30 50

CSM 116 Statistics Lab-I 4 20 30 50

(Computer Oriented Practicals)

CSM 117 Introduction to 3 20 30 50 Information Technology

CSM 118 Computer Programming 3 20 30 50

Using C

CSM 119 Software Lab I 4 20 30 50

(Programming in C and its

Applications in Statistics) ________________________________________________________________________

Total 200 300 500

_______________________________________________________________________

Note: The minimum pass marks in each paper is 33% in continuous assessment and University

examination separately subject to a minimum of 40% in aggregate.

** BREAK-UP OF CONTINUOUS ASSESSMENT OF 20 MARKS **

**THEORY PAPERS**

1. Two tests will be held and their average 50% Marks

will be considered for assessment.

2. Seminars/Assignments/Quizes/ 25% Marks

Class participation

3. Attendance 25% Marks

Marks will be given according to

below criteria:

75% attendance & above

but less than 80% 60% Marks of allotted marks to attendance

80% attendance & above

but less than 85% 80% Marks of allotted marks to attendance

85% attendance& above 100% Marks of allotted marks to attendance

** PRACTICAL PAPERS**

1. Two tests will be held and their average 50% Marks

will be considered for assessment.

2. Viva and Lab records 25% Marks

3. Attendance 25% Marks

Marks will be given according to

below criteria:

75% attendance & above

but less than 80% 60% Marks of allotted marks to attendance

80% attendance & above

but less than 85% 80% Marks of allotted marks to attendance

85% attendance& above 100% Marks of allotted marks to attendance

**CSM 111- : ****GENERAL ENGLISH (COMMUNICATION SKILLS)**

**No. of Lectures : 40 Max. Marks : **_{}** 50**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

Contents of the course :

I One literary Text 15 marks

II Translation 05 marks

II Grammar and Vocabulary 10 marks

1. Flights of Fancy : Edited by Bakhshish Singh, Punjabi University , Patiala .

Poems to be studied :

Sonnet 116 W. Shakespeare

On His Blindness John Milton

The Pebble and the Clod William Blake

The World is Too Much With Us William Wordsworth

Lucy Gray William Wordsworth

My Native Land Sir Walter Scott.

Love S.T. Coleridge

The Scholar Robert Southey

The River of Life Thomas Camp bell

The Journey Onward Thomas Moore

II Translation : From Pbi/Hindi into English : No book prescribed.

III Grammar and Vocabulary:

(a) Grammar : Living English Structures by W. Stannard Allen (units 1-20)

Vocabulary : Students ' Companion by Wilfred D. Best -one word substitutes

1.(a) words denoting numbers : (b) words denoting places ; (c) words denoting

professions or trades .

2. Antonyms

Testing : Guide lines for the paper setter :

Q.I (a) One essay type question with internal alternative on the main idea or

summary (150words) of a poem studied from the prescribed text book

is to be attempted .

6 marks

Three short-answer type questions of comprehension out of the given five (30 words each) from the poems studied from the prescribed text book are to be attempted . 3 marks

Q (II) Explanation with reference to the context of any two out of the given three

extracts from the poems prescribed for study are to be attempted .

6 marks

Q. III Translation from Punjabi/ Hindi into English of a short passage of five short

sentences.

OR

( For students who do not know Punjabi and Hindi )

A five line passage of poetry with three questions of comprehension.

5 marks

Q.IV Do as directed : Twelve sentences out of the given fifteen from the book Living

English Structures are to be attempted .

6 marks

Q.V(a) Four one- word substitutes from the given six phrases exclusively from Students'

Companion) are to be attempted .

2 marks

(b) Antonyms of four out of the given six words (exclusively from the Students'

Companion) are to be attempted. 2 marks

## CSM-112 ALGEBRA

**No. of Lectures : 55 Max. Marks : **_{}** 75**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from the respective sections of the syllabus and section C will consist of one compulsory question having eight parts of short-answer type covering the entire syllabus uniformly. All the questions will carry equal marks.

**Instructions for the candidates**

Candidates are required to attempt five questions in all, selecting two questions from each section A and B and the compulsory question of section C. All questions will carry equal marks.

Use of scientific non-programmable calculator is allowed

### SECTION-A

Relations between the roots and coefficients of general polynomial equation in one variable .Transformation of equations. Descarte's rule of signs. Solution of cubic equations (Cardon method). Biquadratic equations.

Mappings, Equivalence relations and partitions .Congruence modulo n.

Symmetric, Skew symmetric, Hermitian and Skew Hermitian matrices . Elementary operations on matrices. lnverse of a matrix .

### SECTION-B

Linear independence of row and column vectors. Row rank ,column rank and rank of a matrix . Equivalence of column and row ranks. Eigen values, eigen vectors and the characteristic equation of a matrix. Cayley Hamilton theorem and its use in finding inverse of a matrix. Applications of matrices to a system of linear ( both homogeneous and non-homogeneous ) equations. Theorems on consistency of a system of linear equations .

**TEXT BOOKS**

P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul, First Course in Linear Algebra,Wiley Eastern,New Delhi ,1983.

S.K. Jain, A. Gunawardena and P.B. Bhatacharya, Basic Linear Algebra with MATLAB, Key College Publishing (Sprinder-Verlag), 2001.

Chandrika Prased, Text Book on Algebra and Theory of Equations, Pothishala private Ltd., Allabhabad.

**RECOMMENDED READINGS**

K.B. Datta, Matrix and Linear Algebra, Prentice Hall of India Pvt.Ltd., New Delhi, 2000.

**CSM-113 : TRIGONOMETRY AND DIFFERENTIAL CALCULUS**

**No. of Lectures : 55 Max. Marks : **_{}** 75**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from the respective sections of the syllabus and section C will consist of one compulsory question having eight parts of short-answer type covering the entire syllabus uniformly. All the questions will carry equal marks.

**Instructions for the candidates**

Candidates are required to attempt five questions in all, selecting two questions from each section A and B and the compulsory question of section C. All questions will carry equal marks.

Use of scientific non-programmable calculator is allowed

### SECTION-A

**Trigonometry: **De Moivre's theorem and its applications . Direct and inverse circular and hyperbolic functions. Logarithm of a complex quantiy. Expansion of trigonometrical functions. Gregory's series. Summation of series.

**SECTION-B**

**Differential Calculus: ** definition of the limit of a function . Basic properties of limits . Continuous functions and classification of discontinuities .Differentiability . Successive differentiation . Leibnitz theorem . Asymptotes . Curvature. Tests for concavity and convexity. Points of inflexion . Multiple points. Tracing of curves ( Cartesian and parametric coordinates only ).

### TEXT BOOKS

S. L . Loney plane Trigonometry Part II, Macmillan and Company, London.

R.S. Verma and K.S. Shukla,Text Book on Trigonometry, Pothishala Pvt. Ltd., Allahabad.

P .K . Jain and S. K. Kaushik, An introduction to Real Analysis, S. Chand & Co. New Delhi, 2000.

Gorakh Prased Differential Calculus, Pothishala Private Ltd. Allahabad.

**RECOMMENDED READINGS**

1. Gabriel Klambauer, Mathematical Analysis , Marcel Dekkar,Inc. New York, 1975.

2. Murray R . Spiegel, Theory and problems of Advanced Calculus, Schaum's outline series, Schaum Publishing Co. New York

**CSM-114 : COMPUTER ORIENTED STATISTICAL METHODS **- I

**No. of Lectures : 40 Max. Marks : **_{}** 50**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from the respective sections of the syllabus and section C will consist of one compulsory question having eight parts of short-answer type covering the entire syllabus uniformly. All the questions will carry equal marks.

**Instructions for the candidates**

Candidates are required to attempt five questions in all, selecting two questions from each section A and B and the compulsory question of section C. All questions will carry equal marks.

Use of scientific non-programmable calculator is allowed

###### SECTION- A

Collection of data : Primary data – designing a questionnaire and a schedule. Secondary data - its major sources including some government publications. Concept of a Statistical population and samples from a population ;quantitative and qualitative data , discrete and continuous data ,nominal, ordinal , ratio & interval scales .

Presentation of data: Diagrammatical representation of data , frequency distribution , graphical representation , Histogram , Frequency polygon , Frequency curves and ogives .

**SECTION-B**

Analysis of quantitative data : univariate data concepts of central tendency , dispersion , skewness and kurtosis and their measures including those based on quartiles and moments .Sheppard's correction for moments (without derivation).

#### TEXT BOOKS

1. Goon, A.M., Gupta Fundamental of Statistics. Vol. 1. 1991, world

M.K., Dasgupta, B. Press. Calcutta.

###### RECOMMENDED READINGS

1. Bhat B.R, Srivenkatramana T and Rao Madhava K.S. (1997): Statistics : A

Beginner's Text, Vol, I , New Age International (P) Ltd.

2. Croxton F.E, Cowden D. J and Kelin S (1973) : Applied General statistics, Prentice Hall of India .

3. Spiegel, M.R. (1967): Theory & Problems of Statistics, Schaum's Publishing Series.

4. W.W. Daniel : Bio Statistics : A foundation for Analysis in the Health Sciences 7th Ed. (1999)

5. Wiley Series in Probability and Statistics. Applied Probability and statistics section.

** CSM-115 : PROBABILITY THEORY – I**

**No. of Lectures : 40 Max. Marks : **_{}** 50**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

**Instructions for the candidates**

Use of scientific non-programmable calculator is allowed

### SECTION- A

Important concepts in probability :Random experiment, trial, sample point and sample space, definition of an event, mutually exclusive, exhaustive, independent and equally likely events. Definition of the probability-classical and relative frequency approach to probability, their demerits and axiomatic approach to probability. Properties of probability based on axiomatic approach, conditional probability, Bayes theorem and its applications.

** Section- B**

Random Variable** : **Definition of discrete random variables, probability mass function ,continuous random variable, probability density function illustrations of random variables and its properties, expectation of a random variable and its properties-moments, measures of location and dispersion, moment generating function and probability generating function. Two dimensional random variables –joint, marginal and conditional distributions (concepts & simple applications)** .**

## TEXT BOOKS

P.L. Meyer ( 1970 ) : Introductory Probability and Statistical ApplicationsAddison-Wesley.

Goon, A.M., Gupta, M.K., Dasgupta, B.(1999) : Fundamental of Statistics

*,*Vol. I, World Press ,Calcutta .Mood A.M., Graybill F.A and Boes D.C. (1974) : Introduction to the Theory of Statistics, McGrawh Hill .

**REFERENCE READINGS**

Bhat B.R, Srivenkatramana T and Rao Madhava K.S. (1997) : Statistics : A Beginner's Text, Vol. II, New Age International (P) Ltd.

David S (1996) : Elementary Probability, Oxford Press. John E. Freund's Mathematical Statistics 6th Ed. Pub. Pearson Education

**CSM-116: STATISTICS LAB-I (COMPUTER ORIENTED PRACTICALS)**

**Total Practical Sessions: 25 Max. Marks : **_{}** 50**

**(each of two hours)**

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

**Instruction for the Paper Setter and the Candidates**

The setting and evaluation will be done by a board of examiners consisting of Head, External examiner and the teacher(s) involved with the teaching of this paper.

The practical paper will consist of four exercises and the candidates will be required to attempt any three exercises.

The break-up of marks for the University Examination will be as under:

Lab. Record : 6

Viva-voice : 6

Exercises : 18

**Lab Course:**

The exercises will be based on the syllabus of the papers CSM-114(Computer Oriented Statistical Methods-I) and CSM-115(Probability Theory-I).

**CSM - 117 : INTRODUCTION TO INFORMATION TECHNOLOGY**

**No. of Lectures : 40 Max. Marks : **_{}** 50**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

**Instructions for the candidates**

Use of scientific non-programmable calculator is allowed

SECTION-A

Information Technology : Introduction, hardware and software, the information processing cycle. Information systems, software and data, IT Applications; Types of computers, Anatomy of a computer, Binary numbers, Binary arithmetic, digital revolution, computer as a digital device, Moore’s Law, Bits and bytes, CPU, Memory : RAM and ROM, Registers, System buses, i/o Buses, communication with peripherals. Input and Output devices : Keyboards-virtual and ergonomic, OCR, handwriting recognition, bar code and speech recognition, scanners resolution, printers-Laser, dot matrix and inkjet.

Secondary Storage : Storage devices and media, sequential and random storage, tracks and sectors, speed, storage capacity, Removable media. Storage Media : floppy and hard disks. RAID, Optical discs, Increasing storage capacity, backup and smart cards.

###### SECTION B

Computer languages: Machine language, assembly language, higher level language, 4GL. Introduction to Compiler, Interpreter, Assembler, System Software Application Software. Number System: Non-positional and positional number systems, base-conversion, fractional numbers, various operations on numbers. Computer code: BCD, EBCDIC, ASCII.

WWW and Internet: Introduction, home page, connecting to web, browsing, information search, multimedia. Computer Network and communication: Network types, network topologies, network communication devices, physical communication media. Introduction of E-Commerce: Meaning, its advantages and Limitations, Type of E- Commerce Applications.

**TEXT BOOK :**

1. Curtin D.P., Foley K., Sen K., Morin C “Information Technology” : The breaking wave, TMH.

2. V. Rajaraman ";Fundamentals of computer";, PHI, N. Delhi,1996.

3. Chetan Srivastva,” Fundamentals of information Technology, Kalayani Publishers, 2003.

**REFERENCE READINGS:**

1. Williams B. K., Sawyer S.C., Hutchinson S. E., Using Information Technology, 3rd Edition,

TMH.

###### CSM - 118 : COMPUTER PROGRAMMING USING “C”

**No. of Lectures : 40 Max. Marks : **_{}** 50**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

**Instructions for the candidates**

Use of scientific non-programmable calculator is allowed

** Section-A**

Problem Solving with Computer : Algorithms, Pseudocodes and Flowcharts. Data types, constants, variables, arithmetic and logical expressions, data input and output, assignment statements, conditional statements, iteration.

Arrays, string processing, User-defined data types.

** SECTION-B**

Functions recursion, Parameter Passing by reference & by value. Structures, Multiple structures, Arrays of structures, Unions, Files: Reading , Writing text and binary files, Pointers, character pointers, pointers to arrays, Array of pointers, pointers to structures.

Debugging, testing and documentation ; structured programming concepts, top down & Bottom-Up design approaches.

(The programming language C is to be taught along with the course in detail)

** TEXT bookS**

1. E. Balagurusamy, ";Programming in C";, Tata McGraw Hill.

2. Kanetkar, ";Let Us C";, BPB Publications.

** reference READINGS**

1. Richie and Kerningham, "; C Programming";.

2. Rajaraman, V: Fundamentals of Computers (PHI, 1992)

3. D. Dromey: How to solve it by Computer (Prentice-Hall 1985)

** CSM-119 : SOFTWARE LAB-I **

**( PROGRAMMING IN ";C"; AND ITS APPLICATIONS IN STATISTICS)**

**Total Practical Sessions: 25 Max. Marks : **_{}** 50**

**(each of two hours)**

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

**Instruction for the Paper Setter and the Candidates**

The setting and evaluation will be done by a board of examiners consisting of Head, External examiner and the teacher(s) involved with the teaching of this paper.

The practical paper will consist of four exercises and the candidates will be required to attempt any three exercises.

The break-up of marks for the University Examination will be as under:

Lab. Record : 6

Viva-voice : 6

Development of programmes : 18

& their execution

**Lab Course:**

The exercises will be based on the syllabus of the papers CSM-114(Computer Oriented Statistical Methods-I) and CSM-118(Computer Programming using ";C";).

**Syllabus**

**2nd Semester **

**For Examination of Session 2012-13.**

**________________________________________________________________________**

Code Title of paper/subject Hrs./ __Max Marks__ Week Cont. Univ. Total

Asmt. Exam.

CSM 121 General English 2 20 30 50

(Communication Skills)

CSM 122 Integral Calculus &

Differential Equations 4 30 45 75

CSM 123 Geometry 4 30 45 75

CSM 124 Computer oriented 3 20 30 50

Statistical Methods-II

CSM 125 Probability Theory-II 3 20 30 50

CSM 126 Statistics Lab-II 4 20 30 50

(Computer Oriented

Practicals)

CSM 127 Object Oriented 3 20 30 50

Programming Using C++

CSM 128 Management Information 3 20 30 50

System

CSM 129 Software Lab II 4 20 30 50

( Programming in C++)

________________________________________________________________________

Total 200 300 500

________________________________________________________________________

Note: The minimum pass marks in each paper is 33% in continuous assessment and University examination separately subject to a minimum of 40% in aggregate.

**BREAK-UP OF CONTINUOUS ASSESSMENT OF 20 MARKS **

**THEORY PAPERS**

1. Two tests will be held and their average 50% Marks

will be considered for assessment.

2. Seminars/Assignments/Quizes/ 25% Marks

Class participation

3. Attendance 25% Marks

Marks will be given according to

below criteria:

75% attendance & above

but less than 80% 60% Marks of allotted marks to attendance

80% attendance & above

but less than 85% 80% Marks of allotted marks to attendance

85% attendance& above 100% Marks of allotted marks to attendance

** PRACTICAL PAPERS**

1. Two tests will be held and their average 50% Marks

will be considered for assessment.

2. Viva and Lab records 25% Marks

3. Attendance 25% Marks

Marks will be given according to

below criteria:

75% attendance & above

but less than 80% 60% Marks of allotted marks to attendance

80% attendance & above

but less than 85% 80% Marks of allotted marks to attendance

85% attendance& above 100% Marks of allotted marks to attendance

**CSM 121- : GENERAL ENGLISH (COMMUNICATION SKILLS)**

**No. of Lectures : 40 Max. Marks : **_{}** 50**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

Contents of the course :

I One literary Text 15 marks

II Composition : 05marks

II Grammar and Vocabulary 10 marks

Poems to be studied :

1 . Love's Philosophy Percy Bysshe Shelley

2. Bright Star John Keats

3. Dream Peddler Thomas Lovell Beddoes

3. How Do I Love Thee Elizabeth Barret Browning

4. To One In Paradise Edgar Allan Poe

5. Home Thought from Abroad Robert Browning

6. Invictus W.E. Henley

7. Leave This Chanting Rabindra Nath Tagore

8. Stopping By Woods Robert Frost

10.The Highway Man Alfred Noyes

II Composition : Para graph (Descriptive) No book prescribed.

III Grammar and Vocabulary:

(a) Grammar : Living English Structures by W. Stannard Allen (units 21-30)

Vocabulary : Students ' Companion by Wilfred D. Best : one word

substitutes :

(i) Names by which persons with certain characteristics are known .

(ii) Words pertaining to government. (iii) marriage (iv) medical profession.

(v) death (vi) opposites (vii) scientific instruments .

Synonyms

Testing : Guide lines for the paper setter :

Q.I (a) One essay type question with internal alternative on the main idea or

summary (150words) of a poem studied from the prescribed text book

is to be attempted . 6 marks

(b) Three short answer type questions of comprehension out of the given five

(30 words each) from the poems studied from the prescribed text are to be

attempted 3 marks

Q.II Explanation with reference to the context of any two of the given three extracts from the poems prescribed for study are to be attempted. 6 marks

Q. III A paragraph (Descriptive) one out of the given three topics is to be

attempted (150words)

5 marks

Q.IV Do as directed : Twelve sentences out of given fifteen from Living

English Structures are to be attempted .

6 marks

Q.V(a) Four one words substitutes from the given six phrases (exclusively from

Students' Companion) are to be attempted

2 marks

(b) Synonyms of four out of the given six words (exclusively from Students'

Companion). are to be attempted .

2 marks

**CSM 122: INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS**

**No. of Lectures : 55 Max. Marks : **_{}** 75**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

**Instructions for the candidates**

Use of scientific non-programmable calculator is allowed

### SECTION-A

Integration of irrational algebraic and transcendental functions . Reduction formulae. Definite integrals . Quadrature and rectification . Volumes and surfaces of solids of revolution .

Degree and order of a differential equation . Equation of first order and first degree. Equations in which the variables are separable . Homogeneous equations . Linear equations and equations reducible to the linear from . Exact differential equations .

### SECTION-B

First order higher degree equations solvable for x, y, p. Clairaut's form and singular solutions . Geometrical meaning of a differential equation .Orthogonal trajectories .Linear differential equation with constant coefficients .Homogeneous linear ordinary differential equations.

Linear differential equations of second order .Transformation of the equation by changing the dependent variable / the independent variable. Method of variation of parameters .

### TEXT BOOKS

Gorakh Prasad, Integral Calculus, Pothishala Private Ltd., Allahabad.

D.A. Murray, Introductory Course in Differential Equations, Orient Longman (India),1967.

**RECOMMENDED READINGS**

1. H.T.H. Piaggio, Elementary Treatise on Differential Equations and their Applications. C.B.S. Publisher & Distributors, Delhi , 1985.

2. Erwin Kreyszing, Advanced Engineering Mathematics, John Wiley and Sons, 1999.

## CSM 123- GEOMETRY

**No. of Lectures : 55 Max. Marks : **_{}** 75**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

**Instructions for the candidates**

Use of scientific non-programmable calculator is allowed

### SECTION-A

Transformation of axes , shifting of origin, Rotation of axes, Reduction of the second degree equation into standard forms by transformation of co-ordinates. The invariants t , and . Identification of curves represented by second degree equation.

Pole and polar, pair of tangents from a point, chord of contact ,equation of the chord in terms of midpoint and diameter of conic .

Conjugate diameters, Conjugate hyperbola .Asymptotes of a hyperbola, rectangular hyperbola . Special properties of parabola, ellipse and hyperbola.

Polar equations of conics and equations of chords, tangents and normals only .

### SECTION-B

Sphere . Cone . Cylinder . Central conicoids. Paraboloids. Plane Sections of Concoids. Generating lines. Confocal Conicoids . Reduction of Second degree equation to standard forms.

### TEXT BOOKS

S.L. Loney, The Elements of Coordinate Geometry, Macmillan and Company, London.

Gorakh Prasad and H.C. Gupta, Text Book on Coordinate Geometry , Pothishala Pvt. Ltd., Allahabad.

P.K. Jain and Khalil Ahmad, A Text Book of Analytical Geometry of two Dimensions, Wiley Eastern Ltd.,1994.

N. Saran and R.S. Gupta, Analytical Geometry of Three Dimensions, Pothishala Pvt. Ltd., Allahabad.

**RECOMMENDED READINGS**

R.J.T. Bell, Elementary Treatise on Coordinate Geometry of Three Dimensions, Macmillan India Ltd., 1994.

**CSM-124**** : ****COMPUTER ORIENTED STATISTICAL METHODS -II **

**No. of Lectures : 40 Max. Marks : **_{}** 50**

**to be delivered **

**Time Allowed : 3 Hours Min. Pass : **_{}** 40% Aggregate Marks**

### INSTRUCTIONS FOR THE PAPER SETTER

**Instructions for the candidates**

Use of scientific non-programmable calculator is allowed

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