JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA1401
6
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
DIFFERENTIAL CALCULUS AND 3D
UNIT I
Successive Differentiation: nth derivatives of standard result - Trigonometrical
transformation. Formation of equations involving derivatives– Liebnitz’s theorem for nth
derivative of a product of functions – Applicable to some suitable problems
UNIT II
Homogeneous functions – Partial derivatives of a function of two functions – Maxima
and minima of function of two variables - Lagrange’s method of undetermined
Multipliers.
UNIT III
Curvature: Circle, Radius and Center of Curvature- Cartesian Formula for the Radius of
Curvature – Coordinates of the Centre of Curvature – Evolute and Involute - Radius of
Curvature when the curve is given in Polar coordinates.
UNIT IV
Equation of a sphere – Finding centre and radius – Length of the tangent from the point
to the sphere- Plane section of a sphere. Equation of a circle on a sphere – Intersection of
two spheres is a circle – Equation of the tangent plane to a sphere at a point - Related
examples.
UNIT V
Cone – Righr circular cone – Intersection of a straight line and a quadric cone –
Condition for the plane to touch the quadric cone – Cylinder – The equation of the
cylinder whose generators are parallel to the line and guiding curve – The equation of the
right circular cylinder with axix and radius of the guiding circle .
Text Books:
T.B.1. Calculus Vol.–I: T.K. Manickavasagam Pillai and Others R.Edition – 2004.
T.B 2. Analytical geometry of three dimensions, T.K. Manicavachagom Pillai and others.
UNIT I
Chapter III: Full T.B.1
UNIT II
Chapter VIII – Sec 1.6, 1.7 Sec 4, 5 T.B.1
UNIT III
Chapter X – Sec 2.1- 2.6 T.B.1
UNIT IV
Chapter - IV Sec 2 - 8 T.B 2
UNIT V
Chapter – V Sec. 2,3,5,8 T.B 2
Reference Books:
1. Differential and Integral Calculus by Philip Franklin.
2. Calculus by S. Arumugam and Issac.
3. Analytical Solid Geometry -Shanti Narayan, S.Chand & Company Ltd, New
Delhi.
4. Degree Level Analytical Geometry of Three Dimensions - Dasgupta Prasad,
Bharat Bhawar, publishers and distributors
1
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA1402
5
4
Max Marks:
Internal Marks:
External Marks:
100
25
75
INTEGRAL AND VECTOR CALCULUS
UNIT I
Multiple Integrals - Definition – Evaluation – Illustrative Examples – Double Integrals in
Cartesian coordinates and polar coordinates – change the order of Integration – Triple
Integral - Some more worked examples.
UNIT II
Gamma functions – Beta functions – Relation between Beta and Gamma functions –
Properties and examples – Integrals using Gamma and Beta functions – Applications of
Gamma functions to multiple Integrals.
UNIT III
Vector differentiation – vector and scalar field – divergence and curl – application of
Laplacian operator.
UNIT IV
Vector integration: Line integral – surface integral – volume integral – problems on these.
UNIT V
Gauss divergence theorem – Stoke’s theorem, Green’s theorem – simple verification of
theorems and problems.
Text Book:
T.B 1. Calculus Volume - II by T. K. Manicavachagom and others.S.Viswanathan
Publishers, Pvt. Ltd. (2004)
T.B 2. Vector Algebra and Analysis, Narayanan.S and Manicavachagom
Pillai. T.K. S.Viswanathan Pvt.Ltd. 1995
UNIT I:
Chapter 5 - Sec.2 – 4 T.B 1
UNIT II:
Chapter 7 - Sec.2 – 6 T.B 1
UNIT III:
Chapter 4: Sec.6 – 12 T.B 2
UNIT IV:
Chapter 6:Sec.2 – 5.1 T.B 2
UNIT V:
Chapter 6:Sec.6 – 10 T.B 2
Reference Books:
1. Calculus Volume – II, 2nd Edition, Tom.M. Apostol.
2. Vector Analysis, M.L.Khanna, Jai Prakash Nath & Co.
2
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA1701
2
2
Max Marks:
Internal Marks:
External Marks:
100
25
75
SBE1: THEORY OF EQUATIONS AND TRIGONOMETRY
UNIT I
Relation between the roots and coefficients of equations
UNIT II
Symmetric functions of the roots
UNIT III
Transformation of equation – Roots with sign changed, Roots Multiplied by a given
number –Diminishing, Increasing the roots of a given equation by a given quantity
UNIT IV
Summation of Trigonometrical Series - Methods of difference - Sum of sines of n angles
in A.P - Sum of cosines of n angles in A.P
UNIT V
Summation of series by using complex quantities - Gregory’s series – Euler’s series
Text Books:
T.B 1: Algebra (Volume-I), T.K.Manicavachagam Pillai, T.Natarajan, & K.S
Ganapathy, S. Viswanathan (Priters & Pubishers) Pvt. LTD., Chennai , 2004
T.B 2:. Trigonometry , S.Narayanan and T.K.Manicavachagom Pillai , S. Viswanathan
(Priters & Pubishers) Pvt. LTD., Chennai, 2006.
UNIT I :
UNIT II :
UNIT III :
UNIT IV :
UNIT V :
Chapter 6: Section 11
Chapter 6: Section 12
Chapter 6: Sections 15.1, 15.2, 17
Chapter 6: sections 1, 2
Chapter 6: section 3
T.B. 1
T.B. 1
T.B. 1
T.B. 2
T.B. 2
Reference Books:
1. Theory of Equations - M.L.Kanna, Jai Prakasnath & Co, Meerut.
2. Algebra ( Theory of Equations, Inequalities and Theory of numbers ),
Arumugam , Isaac, New Gamma Publishing House, Palayamkottai,2006.
3
JMC UG MATHEMATICS - 2008
SubCode:
Hours/Week:
Credit:
08UMA2403
6
4
Max Marks:
Internal Marks:
External Marks:
100
25
75
SEQUENCES AND SERIES
UNIT I
Sequences: Limit of a Sequence, upper and lower bounds of an aggregate - Bounded
Sequence, upper and lower limits of a sequence, Cauchy`s general principle of
convergence.
UNIT II
Monotone sequence: Infinite series – Definition of convergence, divergence and
oscillation – Limit of a monotone sequence - Necessary condition for convergence Geometric series – Some general theorems concerning infinite series – Series of positive
terms.
UNIT III
Tests of convergence: Comparison Tests - Tests of convergence of  1/ nk D’Alembert’s Ratio test – Simple problems.
UNIT IV
Tests of convergence: Cauchy’s root test - Raabe’s test – Alternate series – Absolutely
convergent series – Standard theorems – Series whose terms are alternately positive and
negative - Simple problems..
UNIT V
Kummer’s test, Logarithmic ratio test – Modified forms for Applications – Cauchy’s
condensation test – Gauss test – Cauchy Maclaurin Integral test.
Text Books:
T.B 1. Algebra volume I - Manicavasagom Pillai, Natarajan & Ganapathy.
T.B 2. Fundamental Real Analysis, S.L. Gupta and Nisha Rani, 2nd Edition, Vikas
Publishing House (P) Ltd.
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter II Sections 4 – 6
T.B 1
Chapter II Sections 7 - 9, 11, 12. T.B 1
Chapter II Sections 13-16
T.B 1
Chapter II Sections 17, 19, 21,22, 24 T.B 1
Chapter VI sections 6.4.2., 6.4.3., 6.4.4., 6.5, 6.5.2, 6.6. T.B 2
Reference Book:
Elements of Real Analysis, Shanthi Narayan, VI Edition.
4
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA3304:1
5
3
Max Marks:
Internal Marks:
External Marks:
100
25
75
MATHEMATICAL STATISTICS-I
UNIT I
Measures of central tendencies- Arithmetic Mean, Properties of Arithmetic Mean,
Weighted mean, Median, Mode, Geometric mean and Harmonic mean Graphical
Location of the Partition values. Merits and Demerits of Mean, Median and Mode.
UNIT II
Measures of Dispersion, Skewness and Kurtosis – Dispersion, , characteristics for ideal
measure of dispersion, Measures of Dispersion ,Range, Q.D, M.D and S.D, coefficient of
dispersion, coefficient of variation, Moments, Pearson’s  and  Co-efficients, Skewness
and Kurtosis - simple problems.
UNIT III
Theory of probability- Classical probability; empirical probability; Axiomatic approach
towards probability; Addition and Multiplication theorem; Conditional probability;
Baye’s theorem; simple problem.
UNIT IV
Random variable; Distribution function; Properties; Probability mass function;
Probability density function; Joint probability mass function; Joint probability density
function; Marginal and Conditional distribution – Simple problems.
UNIT V
Mathematical Expectation; Addition theorem of Expectation; Multiplication theorem of
Expectation; Moment Generating Function; Cumulant Generating Function and
cumulants, Additive Property of Cumulants – Simple problems.
Text Book:
Elements of mathematical statistics - S.C.GUPTA & V.K.KAPOOR, Sultan Chand
publication, Third edition, Reprint 2006
UNIT-I: Sec. 2.3 - 2.9.1 & 2.11.1
UNIT-II: Sec. 3.1 – 3.7, 3.7.3, 3.8, 3.8.1, 3.9, 3.10 - 3.12
UNIT-III: Sec. 4.1, 4.3.1, 4.3.2, 4.5, 4.6.2 – 4.9
UNIT-IV: Sec. 5.1 – 5.4.1, 5.5.1 – 5.5.5
UNIT-V: Sec. 6.1- 6.4, 6.10, 6.11 & 6.17
Reference Books:
1.Probability and Mathematical Statistics by Marek Fisz – John Wiley & Sons.
2.Modern Probability Theory by B.R. Bhat – Wily Eastern Ltd.
5
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA3404
5
4
Max Marks:
Internal Marks:
External Marks:
100
25
75
DIFFERENTIAL EQUATIONS AND FOURIER SERIES
UNIT I
Equations of the first order but of higher degree: Equations solvable for dy/dx - Equations
solvable for y - Equations solvable for x – Clairaut’s form – Equations that do not contain
x explicitly - Equations that do not contain y explicitly - Equations homogeneous in x and
y – Exact Differential Equations – Practical Rule – Rules for finding Integrating factors
UNIT II
Applications of first order equation: growth, decay and chemical reactions. Flow of water
from an orifice – Falling bodies and other rate problems – Free fall under gravity retarded fall.
UNIT III
Linear Equations with constant coefficients: Complementary function of a linear equation
with constant coefficients – General methods of finding Particular Integrals – Linear
Equations with variable coefficients – Equations reducible to the linear equations
UNIT IV
Partial differential equations (PDE): Definition - Formation of PDE by eliminating
constants – Formation of PDE by eliminating arbitrary functions – Types of solution of
PDEs – Solution of first order PDE – Standard forms I, II, III, and IV (Clairaut’s form) –
Lagrange’s Linear Equations – Solution of simultaneous Equations – Charpit’s method
UNIT V
Fourier series: Definition of Fourier series – Finding Fourier series expansion of a
periodic function with period 2л. Odd and Even functions – Development in cosine
series and sine series.
Text Books:
T.B 1. Differential Equation and its Application, S. Narayanan and T. K.
Manicavachagom Pillay, S. Viswanathan (Printers & Publishers) Private Limited, Ninth
edition (1996)
T.B 2. Dr. M. K. Venkataraman, Engineering Mathematics Volume III B- National
Publishing Company, 13th Edition, 1998.
T.B 3. Calculus, Volume -III - T.K.Manicavachagam pillai &Others
UNIT I
Chapter IV – Sec. 1 – 4 ; Chapter II – Sec. 6.1 – 6.4 . T.B 1.
UNIT II
Chapter III- Sec. 1 – 3. T.B 1.
UNIT III
Chapter V – Sec. 1 – 6. T.B 1.
UNIT IV
Chapter II – Sec. 1 – 4, 6 – 8, 12. T.B 2.
UNIT V
Chapter VI: 1, 2,3 and 5 T.B 3.
Reference Book:
1. A first course in Differential Equations with Applications – A.H.Siddiqi and P.
Manchanda.
2. Theory and Problems of Advanced Calculus by Murray. R. Spiegel. SI (Metric)
edition.
6
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA3405
4
4
Max Marks:
Internal Marks:
External Marks:
100
25
75
STATICS
UNIT I
Forces Acting at a point - parallelogram of forces – triangle of forces – Lamis Theorem –
Extended form of the parallelogram of law of forces – Resultant of any number of
coplanar forces acting at a point.
UNIT II
Resultant of two like and unlike parallel forces acting on a rigid body – Moments of a
force – Vargon’s Theorem of moments – couple – Equilibrium of two couples.
UNIT III
Equilibrium of three forces acting on a rigid body – Three coplanar forces – Two
trigonometrical theorems – coplanar forces – reduction of any number of coplanar forces
– conditions for a system of forces to reduce to a single force or to a couple – equation to
the line of action of the resultant.
UNIT IV
Friction – Laws of friction – Co-efficient of friction, angle and cone of friction –
Equilibrium of a particle on a rough inclined plane under any forces – problems on
friction.
UNIT V
Uniform string under the action of gravity - Equilibrium of strings and chain under
gravity – equation of common catenary – tension at any point – geometrical properties of
the common catenaries – problems.
Text Book:
A text book of Statics, Dr. M.K. Venkataraman , Agasthiar Publication, July 1971
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter 2: Sec. 3 to 5, 9,10 and 15
Chapter 3: Sec. 1 to 4, 7, 8, 12; Chapter 4: Sec 1 and 2
Chapter 5: Sec. 1, 2, 5; Chapter 6: Sec 1, 2, 3, 5 and 8
Chapter 8: Sec. 1 to 10 and 13
Chapter 11: sec 1 to 6
Reference Books:
1. Statics, A.V. Dharmapudam.
2. Statics, A.S. Ramsey.
7
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA3702
2
2
Max Marks:
Internal Marks:
External Marks:
100
25
75
SBE2: MATHEMATICS FOR COMPETITIVE EXAMINATIONS - I
UNIT I
Numbers: Problems on Addition, Subtraction, Multiplication and Division ( Shortcut
Methods) – Various tests for Divisibility – Prime and Composite numbers – Various
types of numbers.
UNIT II
HCF and LCM of numbers - Decimal fractions: Addition, Subtraction, Multiplication
and Division of Decimal fractions - H.C.F and L.C.M of Decimals – Rule for converting
Pure and Mixed Recurring Decimals into a Vulgar Fractions.
UNIT III
Simplification - Square Root: Square Root by means of Factors – General Method –
Square Root of Decimal Fractions - Square Root of Vulgar Fractions - Cube Root.
UNIT IV
Percentage: Shortcut Method – Problems based on Population, Average, Ratio and
Proportion.
UNIT V
Partnership, Chain rule : Direct proportion – Indirect Proportion.
Reference books:
1. Arithmetic (Subjective And Objective) For Competitive Examinations,
R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.
2. Exhaustive Arithmetic, O.P. Agarwal, Avadh Prakashan, Agra
3. Objective Arithmetic, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.
4. Quantitative Aptitude, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.
Note:
75 Multiple choice questions only. 15 Questions from each unit.
8
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA3601
2
2
Max Marks:
Internal Marks:
External Marks:
100
25
75
NME1: BASIC STATISTICS
UNIT I
Classical definition of probability– Axiomatic Approach to probability -Addition theorem
– Conditional probability - Multiplication theorem.
UNIT II
Measures of Averages - Mean, Median, Mode, Geometric Mean and Harmonic Mean Merits and Demerits.
UNIT III
Measures of Dispersion - Range Quartile Deviation., Mean Deviation., and Standard
Deviation – Relative Measures - Merits and Demerits.
UNIT IV
Correlation – Rank Correlation – Properties of Correlation coefficient – Regression
Analysis – Properties of Regression coefficient ( Numerical problems only )
UNIT V
Curve Fitting – Principle of Least squares – Fitting a straight line – Fitting a second
degree polynomial – Fitting A curve of the form aebx , abx and axb
Text Book:
Mathematical Statistics, P.R. VITTAL, Margham Publications, Chennai, Reprint 2004.
UNIT I
UNIT II
UNIT III
UNIT IV
UNIT V
Part - I
Part - II
Part - II
Part - I
Part – I
Chapter 1 1.1 to 1.9
Chapter 5
Chapter 6
Chapter 8 & 9
Chapter 10
Reference Book:
Elements of mathematical statistics - S.C.GUPTA & V.K.KAPOOR, Sultan Chand
publication, Third edition, Reprint 2006
9
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA4305:1
5
3
Max Marks:
Internal Marks:
External Marks:
100
25
75
MATHEMATICAL STATISTICS – II
UNIT I
Theoretical discrete distribution – Binomial distribution: Moments, Recurrence relation
Moment generating Function Characteristic Function and Cumulants.
Poisson
distribution: Moments, Recurrence relation, Moment generating Function, Characteristic
Function and Cumulants - Simple Problems.
UNIT II
Theoretical continuous distribution - Rectangular (or) Uniform distribution, Normal
distribution, Moment generating Function, Cumulant generating Function, Moments;
Area Property, Fitting of Normal Distribution - Simple Problems.
UNIT III
Theoretical continuous distributions – Gamma Distribution, Moment generating
Function, Cumulant generating Function, Additive property, Beta Distribution of first
kind, Exponential Distribution - Simple Problems.
UNIT IV
Curve Fitting and Principles of Least squares – Curve Fitting, Fitting of straight line,
Fitting of second degree parabola, Fitting of polynomial of kth degree, Change of origin,
Most plausible solution of a system of linear equations - Simple Problems.
UNIT V
Bivariate distribution, Correlation, Scatter diagram, Pearson’s Coefficient of Correlation,
Properties, Rank correlation, Regression - Lines of Regression, Regression Coefficient
and its properties- Simple Problems.
Text Book:
Elements of mathematical statistics - S.C.Gupta and V. K. Kapoor, Sultan Chand
publication (Third edition, Reprint 2006)
Unit-I:
Unit-II:
Unit-III:
Unit-IV:
Unit-V:
Chapter 7: 7.1 to 7.5
Chapter 8: 8.1, 8.2 and 8.6
Chapter 13: 13.1 to 13.6; Chapter 14: 14.1 to 14.5.4
Chapter 12
Chapter 13, 13.7; Chapter14: 14.5.4 to14.5.10
Reference Books:
1. Probability and Mathematical Statistics by Marek Fisz – John Wiley & Sons.
2. Statistical Inference by H.C. Saxena and P.U. Surndran S.Chand & Co.
10
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA4306:1
5
4
Max Marks:
Internal Marks:
External Marks:
100
25
75
MATHEMATICAL STATISTICS – III
UNIT-1:
Introduction : parameter and statistic, sampling distribution; standard error; principle
steps in sample surveys; sampling versus census.
UNIT-2:
Simple random sampling; merits and limitation of simple random sampling with
specified precision.
UNIT-3:
Stratified random sampling; principal advantages of stratification; allocation of sample
size systematic sampling; variance of estimated mean; comparison between simple
random sampling and stratified random sampling.
UNIT-4:
Systematic sampling; Variance of estimated mean: Systematic sampling vs stratified
sampling: merits and demerits – Cluster sampling – multistage sampling – quota
sampling
UNIT-5:
Planning and execution of sample surveys; sampling design; sampling inspection;
Methods of data collection; Pilot survey; preparation of reports.
Text Books:
T.B. 1: Fundamentals of Applied Statistics, S.C.Gupta and V. K. Kapoor, Sultan Chand.
Publiation.
T.B. 2: Sampling Theory, Desraj, TMH Edition.
T.B. 3: Sampling Theory, M.N. Murthy.
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter 8: 8.1 to 8.8 T.B. 1
Chapter 8: 8.9 T.B. 1
Chapter 8: 8.10
T.B. 1
Chapter 8: 8.11 to 8.14
T.B. 1
Chapter 2: 2.5 T.B. 2 Chapter 14 T.B. 3
Reference Books:
1. Probability and Mathematical Statistics by Marek Fisz – John Wiley & Sons.
2. Statistical Inference by H.C. Saxena and P.U. Surndran S.Chand & Co.
11
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA4406
4
4
Max Marks:
Internal Marks:
External Marks:
100
25
75
DYNAMICS
UNIT I
Kinematics-Speed, Displacement - Velocity – Composition of velocities- Triangle of
velocities- Relative velocity – Angular velocity -Relative angular velocities –
Acceleration s– Motion in a straight line under uniform acceleration – Simple problems.
UNIT II
Projectiles – path of the projectile is a parabola – characteristics of the motion of a
projectile – Velocity of the projectile in magnitude and direction at the end of time “ t “–
Range on an inclined Plane– Simple problems.
UNIT III
Collision of elastic bodies – Newton’s experimental law – impact of a smooth sphere
on a fixed smooth plane – Direct impact of two smooth spheres – Loss of Kinetic Energy
-Oblique impact of two smooth spheres and loss of Kinetic Energy– Simple problems .
UNIT IV
Simple harmonic motion - Simple harmonic motion in a straight line – General solution
of a simple harmonic motion – Composition of two simple harmonic motions of the
same period and in the same straight line – Composition of simple harmonic motions of
the same period in two perpendicular directions – Simple problems.
UNIT V
Motion under the action of central forces – velocity and acceleration in polar coordinates
– differential equation of central orbits – pedal equation of the central orbit – Law of the
inverse square– Simple problems.
Text Book:
A Text Book of Dynamics, Dr. M. K. Venkatraman, Agasthiar Publications, Aug- 1970
UNIT I:
Chapter III – 3.1 to 3.4, 3.7, 3.10, 3.11, 3.15, 3.17 and 3.22
UNIT II:
Chapter IV – 6.2, 6.4, 6.5, 6.9 and 6.12
UNIT III:
Chapter VIII – 8.3 to 8.8
UNIT IV:
Chapter X – 10.2, 10.3, 10.6 and 10.7
UNIT V:
Chapter XI –11.2, 11.4, 11.6, 11.8
Reference Books:
1. Dynamics , M.L.Khanna, Jaiprakash Nadhan and Company, Meerut, 10th Edition,
1975.
2. Dynamics , K. Visvanatha Naik and M.S. Kasi, Emerald Publishers, Chennai.
12
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA4602
2
2
Max Marks:
Internal Marks:
External Marks:
100
25
75
NME2: BASIC OPERATIONS RESEARCH
UNIT I
Operations Research – Origin and Development of OR – Nature and Features of OR
Applications of OR - General Linear Programming Problem – Mathematical Formulation
(Simple cases only)
UNIT II
Graphical method to solve an LPP - Solution, Feasible Solution, Optimum Solution,
Unbounded solution, Alternative optimum solution and Infeasible solution of an LPP.
UNIT III
Transportation Problem – Balanced and unbalanced TP - Determination of Initial Basic
Feasible Solution using 1. North West Corner Rule, 2. Least Cost Method and 3. Vogel’s
Approximation Method. (Optimum Solution not expected)
UNIT IV
Assignment Problem – Hungarian Algorithm – Unbalanced Assignment Problem –
Maximization A.P.
UNIT V
Introduction – Network and Basic Components, Logical sequencing, Rules of Network
Construction – Critical Path Analysis.
Text Book:
Operations Research – Kanti Swarup,P.K. Gupta and Man Mohan. Sultan Chand & Sons
(2005).
UNIT-I:
UNIT-II:
UNIT-III:
UNIT-IV:
UNIT-V:
Chapter – 1 :Sec 1.1,1.2 &1.7 Chapter - 2
Chapter – 3 :Sec 3.1,3.2 &3.4
Chapter – 10 :Sec 10.1-10.3, 10.9
Chapter – 11 :Sec 11.1 – 11.3, 11.4.1
Chapter – 21: Sec 21.1 – 21.5.
Reference Book:
Operations Research Theory And Applications, J.K. Sharma, Macmillan India Ltd., 2000.
13
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA5407
3
3
Max Marks:
nternal Marks:
External Marks:
60
15
45
C –PROGRAMMING
UNIT I
Constants, Variables and Data Types – Character set – C tokens – Keywords and identifiers –
Constants – Variables – Data types – Declaration of variables and storage class – Assigning
values to variables – Defining symbolic Constants – Operators and Expression – Arithmetic of
operators – Relational operators – Logical operators – Assignment operators – Increment and
decrement operators – Conditional operator – Bitwise operators – Special operators – Arithmetic
expressions – Evaluation of expressions – Precedence of arithmetic operators – Mathematical
Functions – Managing Input and Output Operators – Reading character – Writing a character
– Formatted input – Formatted output.
UNIT II
Decision Making and Branching – Decision making with IF statement – Simple IF statement –
The IF ELSE statement – Nesting IF…ELSE statements – The ELSE IF ladder – The switch
statement – The ?: operator – The GOTO statement - Decision Making and Looping – The
WHILE, DO, FOR statement – Jumps in loops.
UNIT III
Handling of Character String – Declaring and initializing string variables – Reading strings
from terminal – Wring strings to screen – Arithmetic operations on characters – Putting strings
together – Comparisons of two strings – String – Handling functions – Table of strings – Arrays
– One-dimensional, Two-dimensional arrays and Multi-dimensional arrays – Pointers –
Understanding pointers – Accessing the address of a variable – Declaring and initializing pointers
– Accessing a variable a variable through its pointer – Pointer expressions – Pointer increments
and scale factor – Pointers and arrays – Pointers and character strings.
UNIT IV
User-Defined Functions – Need for user-defined functions – A multi-function program – The
form of C functions – Return values and their types – Calling a function – Category of functions –
No arguments and no return values – Arguments with return values – Handling of non-integer
functions – Nesting of functions – Recursion.
UNIT V
File Management in C – Defining and opening a file – closing file – Input/Output operations on
files – Error handling during I/O operations – Random access to files.
Text Book:
Programming in ANSI C (Third Edition), E.Balgurusamy, Tata McGraw-Hill Publishing
Company Limited, New Delhi.
UNIT I - Chapter 2: 2.2 to 2.11; Chapter 3: 3.2 to 3.16; Chapter 4: 4.2 to 4.5
UNIT II - Chapter 5: 5.2 to 5.9; Chapter 6: 6.2 to 6.5
UNIT III - Chapter 8: 8.2 to 8.9; Chapter 7: 7.2 to 7.7; Chapter 11: 11.2 to 11.11
UNIT IV - Chapter 9: 9.2 to 9.16
UNIT V - Chapter 12: 12.2 to 12.6
Reference Book:
Let us C by Yashavant Kanetkar – 7th Edition BPB Publications.
14
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA5407P
3
2
Max Marks:
nternal Marks:
External Marks:
40
10
30
C PROGRAMMING LAB
1. Solving a Quadratic equation.
2. Sum of Series ( Sine, Cosine, ex)
3. Ascending and Descending Order of numbers.
4. Largest and Smallest of given numbers.
5. Sorting names in Alphabetical Order.
6. Finding Factorial, generating Fibonacci numbers using Recursive Functions.
7. Mean, Standard Deviation and Variance
8. Creation and Processing of sequential files for Payroll and Mark List Preparation.
15
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA5408
5
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
MODERN ALGEBRA
UNIT I
Groups: sub-groups-cyclic groups-co-sets and Lagrange’s theorem-Normal subgroups
and quotient groups-Homomorphism-Isomorphism theorems.
UNIT II
Rings: Definition of a ring and some examples-some properties of rings-some special
classes of rings-sub rings and subfields-ideals and quotient rings-homomorphism.
UNIT III
Euclidean Rings: Definition and some properties of Euclidean Rings- Unique
factorization theorem – Gaussian Integers.
UNIT IV
Vector spaces: Definition and some properties of a vector space-Subspaces and quotient
spaces-sums and direct sums-linear independence- basics and dimensions.
Vector spaces: Homomorphisms - Dual spaces-inner product spaces.
UNIT V
Linear Transformations and Matrices: Algebra of Linear Transformations – Eigen Values
and Eigen Vectors – Algebra of Matrices.
Text Book:
Modern Algebra by Dr. M.L. Santiago. Arul Publications,Madras (1988).
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter 2: Sec 2.4 – 2.9
Chapter 3: Sec 3.1 – 3.6
Chapter 4: Sec 4.1 – 4.3
Chapter 6: Sec 6.1 – 6.5,6.8
Chapter 7: Sec 7.1 – 7.3
Reference book:
Modern Algebra by Frank Ayres .JR. McGraw – Hill Book Company.
16
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA5409
5
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
OPERATIONS RESEARCH
UNIT I
Definitions of O.R - Application of O.R - Linear Programming Problem-Mathematical
formulation - Graphical Solution Method, Alternative optimal solution, Unbounded
solution, Infeasible solution, General LPP- Standard LPP-Basic Solution-Basic Feasible
and Infeasible solution-Degenerate solution.
UNIT II
Simplex Algorithm-Artificial variable Techniques – Big M method and Two-phase
method – Alternate optimal solution – Degeneracy – Unbounded and Infeasibility.
UNIT III
Introduction – General Primal Dual pair – Formation of a Dual problem - Duality and
Simplex method, Dual simplex method.
UNIT IV
Introduction – General Transportation Problem -Finding an Initial Basic Feasible
Solution using North-West Corner Rule, Least Cost Entry Method and VAM - MODI
method –Assignment problem – Hungarian method.
UNIT V
Network scheduling by CPM and PERT – Network Basic components logical
sequencing, Rules of network constructions – Critical Path Analysis – Probability
consideration in PERT, Distinction between CPM & PERT.
Note: Theoretical proof not expected.
Text Book:
Operation Research: Kanti Swarup, P.K.Gupta and Man Mohan, Sultan Chand and sons,
New Delhi, XIIth Edition 2004
UNIT I:
Chap: 1.1, 1.2, 1.7, 2.1, 2.2, 3.1 to 3.5.
UNIT II:
Chap: 4.3 and 4.4.
UNIT III:
Chap: 5.1, 5.2, 5.3, 5.7, 5.9
UNIT IV:
Chap: 10.1, 10.2,10.9.10.12,10.14,11.2 to11.4.
UNIT V:
Chap: 21.1-21.7.
Reference Books:
1. Problems in O.R (methods & solutions) P.K.Gupta and Man mohan Sultan chand and
sons.
2. Operation Research Theory and Application.
J.K.Sharma, Macmillian India Ltd 2000.
17
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA5410
5
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
REAL ANALYSIS
UNIT I
Countable and uncountable sets - Limit of a function - Theorems based on limits – Order
relation and limits - Infinite limits and limits at infinity
UNIT II
Continuous functions - Algebra of continuous functions - Properties of continuous
functions - Uniform continuity - Discontinuities of a function.
UNIT III
Derivative of a function – Algebra of derivatives – Derivative of the composition of two
functions - Derivative of the inverse of a function – Darboux’s Theorem - Derivatives of
higher order.
UNIT IV
Rolle’s theorem-Lagrange’s Mean Value theorem - Cauchy’s Mean Value theorem –
Taylor’s theorem with Lagrange’s form of remainder – Taylor’s theorem with Cauchy
form of remainder.
UNIT V
Riemann Theory of Integration - Upper and Lower Integrals- Riemann Integral - some
classes of Integrable Functions - Algebra of Integrable Functions – Inequality relationsMean value theorems of Integral Calculus - Fundamental theorem of Integral Calculus.
Text Book:
Real Analysis by P.K.Gupta and Sharda Gupta, 1st edition, 1993, Sultan Chand & Sons,
New Delhi-2.
UNIT I: Chapter-1 Sec 1.7, Chapter-4: Sec 4.1 to 4.4
UNIT II: Chapter-4 Sec 4.5 to 4.9
UNIT III: Chapter-5 Sec 5.1 to 5.4, 5.6, 5.7
UNIT IV: Chapter-6 Sec 6.1,6.2, 6.4 Chapter-8 Sec 8.1,8.2
UNIT V: Chapter-9 Sec 9.2 to 9.8, 9.10
Reference Books:
1. Real Analysis, M.K.Singhal & Asha Rani Singhal, 14th Edition, 1991, R.Chand &Co,
New Delhi.
2. Elements of Real analysis for Under Graduates, Dr. K.C. Sharma and Dr.G.N. Purohit, 3 rd
Revised Edition, 1983, Ramesh Book Depot. Jaipur
18
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA5501
5
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
MBE1: NUMERICAL METHODS
UNIT I
Solution of Algebraic and Transcendental equation – Bisection Method, Iteration
Method, Method of False position, Newton Raphson Method, Generalised Newton`s
Method.
UNIT II
Finite differences – Forward differences, Backward differences, Central differences,
Symbolic relations, Newton`s formula for interpolation. Interpolation with unevenly
spaced points – Lagranges interpolation formula, divided differences and their properties,
Newton`s general interpolation formula.
UNIT III
Numerical differentiation and integration - Numerical differentiation (Excluding cubic
spline method, maximum and minimum values of a tabulated function), Numerical
integration – Trapezoidal Rule and Simpson`s Rule.
UNIT IV
Solution of linear Systems - Direct Methods – Gaussian Elimination method, Method of
Factorization, Iterative method – Jacobi and Gauss Seidal methods.
UNIT V
Numerical Solution of ordinary differential equations – Solution by Taylor Series,
Picard’s method of Successive approximations, Euler method, Modified Euler method,
Runge-Kutta methods
Text Book:
Introductory Methods of Numerical Analysis, S.S. SASTRY, Third Edition, Prentice Hall
of India Pvt. Ltd. New Delhi. 2000
UNIT I: Chapter 2: Section 2.1 to 2.5.1
UNIT II: Chapter 3: Section 3.3,3.6, 3.9.1, 3.10, 3.10.1
UNIT III: Chapter 5: Section 5.1, 5.2 (Excluding 5.2.1 and 5.2.2), 5.4, 5.4.1, 5.4.2
UNIT IV: Chapter 6: Section 6.3, 6.3.2, 6.3.2, 6.3.4, 6.4.
UNIT V: Chapter 7: Section 7.2 to 7.4, 7.4.2, 7.5
Reference Book:
Introduction to Numerical Analysis by F.B. Hildebrand TMH Edition (II).
19
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA5703
2
2
Max Marks:
Internal Marks:
External Marks:
100
25
75
SBE3: SPSS - PRACTICALS
1. Calculation of Means, Standard deviations, Variances, correlation and regression.
2. Application of t-test for one sample problem.
3. Application of t-test for two sample problems.
4. Application of t-test for testing the significance of Correlation Coefficient.
5. One-tailed and Two-tailed tests.
20
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA5704
2
2
Max Marks:
Internal Marks:
External Marks:
100
25
75
SBE4: MATHEMATICS FOR COMPETITIVE EXAMINATIONS - II
UNIT I
Time and work, Pipes and Cisterns.
UNIT II
Time and Distance, Trains, Boats and Streams
UNIT III
Profit and Loss, Mixture.
UNIT IV
Simple interest and Compound interest, Calendar.
UNIT V
Volume and Area of Solid figures
Reference books:
1. Arithmetic (Subjective And Objective) For Competitive Examinations,
R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.
2. Exhaustive Arithmetic, O.P. Agarwal, Avadh Prakashan, Agra
3. Objective Arithmetic, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.
4. Quantitative Aptitude, R.S. Aggarwal, S.Chand & Company Ltd, New Delhi, 2004.
Note:
75 Multiple choice questions only. 15 Questions from each unit.
21
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA6411
5
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
GRAPH THEORY AND ITS APPLICATIONS
UNIT I
Introduction: Graph – Finite and Infinite graphs – Incidence and Degree – Isolated vertex,
pendant vertex and Null graphs. Paths and Circuits: Isomorphism – sub-graphs – walks,
paths and circuits – Connected and disconnected graphs – Euler graphs –Hamiltonian
paths and circuits.
UNIT II
Trees and fundamental circuits: Trees – Properties of Trees – Pendant vertices in a Tree –
Distance and centers in a Tree – Spanning Trees – Fundamental circuits – Spanning trees
in a weighted graph.
UNIT III
Cut sets and cut vertices: Cut sets – Properties of a cut set – all cut sets in a graph –
Fundamental circuits and cut sets – Connectivity and Separability.
UNIT IV
Planar and dual graphs: Planar graphs – Kuratowski’s two graphs – Representation of a
planar graph – Detection of planarity – Geometric dual.
UNIT V
Matrix Representation of graphs: Incidence Matrix – Circuit matrix – Fundamental
circuit matrix and Rank of circuit matrix – Cut set matrix – Relationship among Af, Bf
and Cf – Path matrix.
Text Book:
Graph theory with application to Engineering and Computer Science, Narsingh Deo –
Prentice Hall of India Pvt Ltd, 2005
UNIT I: Chapter 1: sections 1.1, 1.3 – 1.5. Chapter 2: sections 2.1, 2.2, 2.4 – 2.6 and 2.9.
UNIT II: Chapter 3: sections 3.1 – 3.4, 3.7,3.8, 3.10
UNIT III: Chapter 4: sections 4.1 – 4.5.
UNITIV: Chapter 5: sections 5.2 – 5.6.
UNIT V: Chapter 7: sections 7.1 – 7.4 & 7.6 – 7.8.
Reference Books:
1. Invitation to Graph Theory, Arumugam.S and Dr.Ramachandran.S, New
Gamma Publishing House, Palayamkottai, 2006.
2. Graph Theory, Choudum.S.A –Macmillan India Limited, New Delhi.
3. Graph Theory, Harary.F –Narosa Publishing House, New Delhi.
22
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA6412
5
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
NUMBER THEORY
UNIT I
Divisibility theory in the Integers: The division algorithm-the greatest common divisorthe Euclidean algorithm-the Diophantine equation ax + by = c
UNIT II
Primes and their distribution: The fundamental theorem of arithmetic- The Sieve of
Eratosthenes- The Goldbach Conjecture.
UNIT III
The theory of congruences: Karl Friedrich Gauss- Basic properties of congruenceSpecial divisibility tests- linear congruences.
UNIT IV
Fermat’s theorem: Pierre de Fermat – Fermat’s factorization method – The Little
theorem- Wilson’s theorem
UNIT V
Number – theoretic functions: The functions τ and σ – The MÖbius inversion formulaThe greatest integer function.
Text Book:
Elementary Number Theory (Second Edition), David M. Burton, Universal Book Stall,
New Delhi, 1991
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter II
Chapter III
Chapter IV
Chapter V
Chapter VI
Reference Book:
An introduction to the Theory of Numbers, Third Edition Ivan Niven and Herbert S.
Zuckerman, Wiley Eastern Ltd, 1972
23
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA6413
6
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
COMPLEX VARIABLES AND APPLICATIONS
UNIT I
Analytic Functions-Functions of a Complex Variable, Limits, Theorem on Limits,
Continuity, Derivatives, Differentiation Formulas, Cauchy-Riemann Equations,
Sufficient Condition for Differentiability, Polar Coordinates, Analytical functions,
Harmonic Functions.
UNIT II
Integrals - Derivatives of function w(t), Definite integrals of function w(t), Contours,
Contour integrals, Cauchy-Goursat Theorem, Proof of the Theorem, Simply and Multiply
Connected Domains, Cauchy Integrals Formula, Derivative of analytic function,
Liouville’s theorem and Fundamental theorem of Algebra.
UNIT III
Series-Taylor’s Series, Laurent series – Linear Fractional Transformations, An implicit
form
UNIT IV
Residues and Poles - Residues, Cauchy’s Residue Theorem, Using a Single Residue, The
three types of Isolated Singular Points, Residue at Poles, Zeros of Analytic Functions,
Zeros and Poles.
UNIT V
Applications of Residues - Evaluation of Improper Integrals – Improper integrals from
Fourier Analysis, Jordan’s Lemma, Indented Paths, Definite Integrals involving Sines
and Cosines, Argument Principle, Rouche’s Theorem.
Text Book:
Complex Variables and Applications – Seventh Edition, James Ward Brown, Ruel V.
Churchill (2003)
UNIT I UNIT II UNIT III UNIT IV UNIT V -
Chapter 2
Chapter 4
Chapter 5
Chapter 6
Chapter 7
- Sections 11, 14, 15, 17 - 25.
- Sections 36 - 40, 44 - 49
- Sections 53 – 56 and Chapter 8: Sec 86, 87
- Sections 62 - 69
- Sections 71 – 75, 78 - 80
Reference Book:
Complex Analysis, Arumugam and Isaac, New Gamma Publishing House,
Palayamkottai, 2006.
24
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA6502
5
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
MBE2: DISCRETE MATHEMATICS
UNIT I
Recurrence relation - Permutation functions - Growth of functions
UNIT II
Partially ordered sets - External elements of partially ordered sets - Lattices
UNIT III
Finite Boolean algebra – Functions of Boolean algebra- Expressing Boolean functions as
Boolean polynomials
UNIT IV
Coding of Binary information and Error Detection
UNIT V
Decoding and Error Correction
Text Book:
Discrete Mathematical Structure ( 3th Edition – Twelfth printing ) – Kolman Busby Ross,
Prentice-Hall of India, New Delhi, 2001.
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter 3 - 3.5, Chapter 5 - 5.3, 5.4
Chapter 7 - 7.1 to 7.3
Chapter 7 - 7.4 to 7.6
Chapter 11 – 11.1
Chapter 11- 11.2
Reference Books:
1.Discrete Mathematical structures with Applications to Computer Science –
J.P.Tremblay and R.Manohar.
2.Introduction to Automata Theory, Languages and Computation – John E.Hopcroft,
Jeffery D.Ullman.
25
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA6503
5
5
Max Marks:
Internal Marks:
External Marks:
100
25
75
MBE3: LAPLACE AND FOURIER TRANSFORMS
UNIT I
Laplace Transforms – Sufficient conditions for the existence of the Laplace transforms –
Properties of Laplace transforms – Laplace transforms of Periodic functions – Some general
theorems – Evaluation of integrals. The inverse Laplace transforms.
UNIT II
Application of Laplace transforms – Solution of ODE with constant coefficients – Solution of
ODE with variable coefficients – Solution of simultaneous ODE – Solution of PDE.
UNIT III
Dirichlet’s Conditions – Fourier Transforms – Inversion Theorem for complex Fourier
Transforms – Sine and Cosine transforms – Linearity Property of Fourier Transforms – Change of
scale property – Shifting property – Modulation Theorem.
UNIT IV
Finite Fourier sine and cosine transforms – Inversion formula for sine and cosine transforms –
Multiple finite Fourier Transforms – Operational properties of finite Fourier sine and cosine
transforms – Combined properties of finite Fourier sine and cosine Transforms – Convolution.
UNIT V
Application of infinite Fourier Transforms – Choice of infinite sine or cosine transforms –
Application of finite Fourier Transforms – Finite Fourier Transforms of Partial derivatives –
Choice of finite sine and cosine transforms – Examples.
Text Books:
T.B.1. Differential Equations and its applications – S. Narayanan & T.K.
Manickavachagom Pillay.
T.B.2. Integral transforms – A.R. Vasistha & R.K. Gupta.
UNIT-I:
UNIT-II:
UNIT-III:
UNIT-IV:
UNIT-V:
Chapter IX – Sec 1 to 7
Chapter III – Sec 3.1 to 3.4
Chapter VI – Section 6.1 to 6.13
Chapter VII – Section 7.1 to 7.9
Chapter VIII – Section 8.1 to 8.5
T.B.1.
T.B.2.
T.B.2.
T.B.2.
T.B.2.
Reference Book:
A First course in Differential equations with applications by A.H. Siddiqi & P.H
Manchanda.
26
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA6705
2
2
Max Marks:
Internal Marks:
External Marks:
100
25
75
SBE4: MAT LAB
MATLAB Basics – Input and output – Arithmetic – Algebra – Symbolic Expressions,
variable precession, and Exact Arithmetic – Managing variables – Errors in Input-Online
Help – Variables and Assignments – Solving Equations – Vectors and Matrices – Vectors
– Matrices – Suppressing Output -Functions – Built in function – User – defined
functions – Graphics - The MATLAB Interface – M – Files – Loops
TEXT BOOK
Brian R . Humt, Ronald L . Lipsman, Jonathan M. Rosenberg , “ A guide to MATLAB
beginners and Experienced Users”, Cambridge University Press Edition, 2002.
Chapters 2 & 3
MATLAB - PRACTICALS
1. Write a MATLAB program involving matrix manipulation such as multiplication,
inverse, determinant
2. Write a MATLAB program to solve a system of linear equations.
3. Write a MATLAB program to solve quadratic equation.
4. Write a MATLAB program to solve algebraic equation using bisection method,
Newton Raphson method and Gauss elimination method.
27
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA6706
2
2
Max Marks:
Internal Marks:
External Marks:
100
25
75
SBE 6 : WEB DESIGNING
UNIT I
Introduction to the Internet: Computers in Business – Networking – Internet – E Mail –
Resource Sharing – Gopher – WWW – USENET – TELNET.
UNIT II
Internet Technologies: MODEM – Internet Addressing – Physical Connections –
Telephone lines.
UNIT III
Internet Browsers: Internet Explorer – Window – Menus: File, Edit, View, Favorites,
Tools – Tool Bar.
UNIT IV
Introduction to HTML – HEAD Section – title – BODY section – Heading Printing –
Aligning the heading – Horizontal Rule – Paragraph - IMG tag.
UNIT V
Advanced Concepts: Anchor – Ordered and Unordered Lists – Nested Lists – Tables –
Handling Frames.
Text Book:
World Wide Web design with HTML, C.Xavier, TMH 2000.
Reference Books:
The Complete Reference HTML , Second Edition, Thomas A. Powell, TMH 2000
The Complete Reference Web Design, Thomas A. Powell, TMH 2000
28
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA3304:2
5
3
Max Marks:
Internal Marks:
External Marks:
100
25
75
A4: ALLIED MATHEMATICS- I
(For Physics and Chemistry Major)
UNIT I
ALGEBRA: Binomial Series, Exponential series, Logarithmic series.
UNIT II
THEORY OF EQUATIONS: Relation between the coefficients and the roots of an
algebraic equation, Transformation of equations, Reciprocal equations.
UNIT III
MATRICES: Various types of Matrices – Rank of a matrix, Simultaneous linear
equations, Eigen values and Eigen vectors - Verification of Cayley-Hamilton theorem.
UNIT IV
FINITE DIFFERENCES: Interpolation – Newton’s (Forward and Backward)
Interpolation formula, Lagrange’s Interpolation formula.
UNIT V
TRIGONOMETRY: Hyperbolic functions - Inverse hyperbolic functions - separation
into real and imaginary parts, Logarithm of complex numbers.
Text Book:
Ancillary Mathematics, Vol.1, S. Narayanan, R. Hanumantha Rao and T.K.
Manicavachagom Pillay, S.Viswanathan (Printers and Publishers) Pvt Ltd, Revised
Edition 2007.
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
Chapter 1 : Sec. 1.2 to 1.4
Chapter 2: Sec 2.2 to 2. 4
Chapter 3: Sec 3.1 to 3.4
Chapter 4: Sec 4.1 and 4.3
UNIT V:
Chapter 5: Sec 5.4 and 5.5
Reference Book:
Allied Mathematics by A. Abdul Rashid, Vijay Nicole Publishing Company.
29
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA4305:2
4
3
Max Marks:
Internal Marks:
External Marks:
100
25
75
A5: ALLIED MATHEMATICS – II
(For Physics and Chemistry Major)
UNIT I
Higher Derivatives – The nth derivatives of standard functions – Trigonometrical
transformation, Formation of equations involving derivatives - Leibnitz theorem
(Statement only)
UNIT II
Jacobian, Curvature, Cartesian formula for radius, circle and centre of curvature, Evolute
and involute.
UNIT III
Integration of rational algebraic functions, Integration of irrational functions.
UNIT IV
Properties of definite Integrals – Integration by parts - Reduction Formulae for xne ax dx,
sin n x dx, Cos n x dx, sin m x cos n xdx.
Unit V
Fourier series – Even and Odd function and Half range series
Text Books :
T.B.1. Ancillary Mathematics, Vol. I, S. Narayanan, R. Hanumantha Rao and T.K.
Manicavachagom Pillay, S.Viswanathan (Printers and Publishers) Pvt Ltd, Revised
Edition 2007.
T.B.2. Ancillary Mathematics, Vol. II, S. Narayanan, R. Hanumantha Rao and T.K.
Manicavachagom Pillay, S.Viswanathan (Printers and Publishers) Pvt Ltd, Revised
Edition 2007.
UNIT I
UNIT II
UNIT III
UNIT IV
UNIT V
– Chapter 6: Sec 6.1
– Chapter 6: Sec 6.2 and 6.4
– Chapter 1: Sec:7 to 10
– Chapter 1: Sec 11, 12, 13.1,13.3, 13.4, 13.5
- Chapter 2: Sec 1 to 5
T.B.1.
T.B.1.
T.B.2.
T.B.2.
T.B.2.
Reference Book:
Allied Mathematics by A.Abdul Rashid, Vijay Nicole Publishing Company.
30
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA4306:2
4
3
Max Marks:
Internal Marks:
External Marks:
100
25
75
A6: ALLIED MATHEMATICS –III
(For Physics and Chemistry Major)
UNIT I
Differential equations of the first order with higher degree - Equations solvable for p
Equations Solvable for y – Equations Solvable for x - Clairaut’s form.
UNIT II
Partial Differential Equations of the first order – Formation of PDE by eliminating
arbitrary constants, Standard type of first order equations I, II, III and IV (Clairaut’s
form), Lagrange’s equations.
UNIT III
Laplace transforms of the function e at, e-at, f’(t), f”(t), cos at, sin at, cosh at, sinh at, tn ,
e-at f(t), where n is a positive integer – Inverse transforms relating to the above standard
functions, Application to ODE of order two with constant coefficients .
UNIT IV
Vector differential operator - Gradient – Direction and magnitude of gradientDivergence and Curl – Laplacian Operator.
UNIT V
Line Integral –Volume integral – Surface integral – Application of Gauss and Stoke’s
Theorems (Statement Only), Simple Problems.
Text books
Ancillary Mathematics, Vol. II, S. Narayanan, R. Hanumantha Rao and T.K.
Manicavachagom Pillay, S.Viswanathan (Printers and Publishers) Pvt Ltd, Revised
Edition 2007.
UNIT I:
UNIT II :
UNIT III:
UNIT IV:
UNIT V:
Chapter 4: Sec. 1 to 4 (PP. 228 to 236)
Chapter 6: Sec. 2.1, 5 and 6
Chapter 7: Sec. 1 to 6
Chapter 8: Sec. 16 to 20 and 22
Chapter 8: Sec. 2 to 6 and 9.
Reference Book:
Allied Mathematics by A.Abdul Rashid, Vijay Nicole Publishing Company.
31
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA1301:3
5
3
Max Marks:
Internal Marks:
External Marks:
100
25
75
A1: ALLIED MATHEMATICS –I
Fourier Series , Differential Equations and Vector Calculus
(For Computer Science Major)
UNIT I
Fourier series: Definition - Even and Odd function - Half range Fourier series –
Development in cosine series and sine series.
UNIT II
Linear Equations with constant coefficients– Complementary function – General methods
of finding particular integrals – Linear Equation with variable coefficients.
UNIT III
Partial Differential Equations of the first order – Different integrals of PDE – Standard
type – Solutions of PDE in some simple cases – Standard types of first order equationStandard forms I,II,III and IV(Clairaut’s form ) – Lagranges methods of Solving Linear
equations Pp +qQ = R.
UNIT IV
Laplace transforms of the function e at, e-at, f’(t), f”(t), cos at, sin at, cosh at, sinh at, tn ,
e-at f(t), where n is a positive integer – Inverse transforms relating to the above standard
functions - Solution of ODE of order two with constant coefficients using Laplace
transforms.
UNIT V
Vector differential operator –Vector and Scalar field - Gradient – Direction and
magnitude of gradient- Divergence and Curl – Laplacian Operator.Line Integral –Volume
integral – Surface integral – Gauss and Stoke’s Theorems (Statement Only),
Verifications. - Simple Problems.
Text Books:
1. Ancillary Mathematics (Volume II) Narayanan S., R. Hanumantha Rao and
Manicavachagom Pillai T.K: S.Viswanathan Pvt. Ltd., Chennai, Revised
Edition, 2007.
2. Differential Equations and its Applications, Narayanan S. and Manicavachagam
Pillai T.K S. Viswanathan Pvt Ltd, 2006
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter 2: Sec 1 to 5
Chapter V: Sec. 1 to 5
Chapter 6: Sec. 1 to 5.4
Chapter 7: Sec. 1 to 6
Chapter 8: Sec. 1.15 to 1.20 and1. 22,2 to 6 and 9.
T.B 1
T.B 2
T.B 1
T.B 1
T.B 1
Reference Books:
1. Vector Analysis, Khanna M.L., Jai Prakash Nath & Co.
2. Trigonometry and Fourier Series, Arumugam, Isaac & Somasundaram,
Gamma Publishing Houses
32
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA2302:3
5
3
Max Marks:
Internal Marks:
External Marks:
100
25
75
A2: ALLIED MATHEMATICS – II
Probability and Statistics
(For Computer Science Major)
UNIT I
Theory of probability: Classical probability- Axiomatic approach to probability –
Probability function – Law of addition of probability - Law of Multiplication –
Independent events - Baye’s theorem- Simple problems.
UNIT II
Random variable-Distribution function – Properties of distribution function - discrete
random variable - Probability mass function - Discrete distribution function. - Continuous
random variable- Probability density function
UNIT III
Joint probability law - joint probability mass function - joint probability density function
- Marginal and Conditional distribution - Mathematical Expectation - Definition Moment generating function.
UNIT IV
Correlation and Regression – Bivariate distribution, correlation – scatter diagram – KarlPearson’s coefficient of correlation – Calculation of correlation coefficient for a bivariate
frequency distribution – Rank correlation – Regression - Properties of correlation and
regression coefficients. (Numerical Problems only)
UNIT V
Theoretical discrete distribution: Binomial, Poisson distributions, Moment generating
function of these distributions and moments - recurrence relation for the moments of
these distributions
Text Book:
Elements of Mathematical Statistics, S.C.GUPTA & V.K.KAPOOR, Sultan Chand &
Sons, New Delhi, 3rd Edition (Reprint), 2006.
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter 4: Sec 4.3, 4.5, 4.6, 4.7, 4.8 and Chapter 5: Sec 5.1 to 5.3.2.
Chapter 5: Sec 5.1 to 5.3.2, 5.4.1;
Chapter 5: Sec 5.5.1 to 5.5.5 and Chapter 6: 6.1 to 6.4, 6.9
Chapter 10: 10.1 to 10.4, 10.6 to 10.7.4
Chapter 7: Sec 7.2.1, 7.2.2, 7.2.6, 7.3.1, 7.3.2, 7.3.4, 7.3.5 and
Reference Books:
1. Probability and Mathematical Statistics by MAREK FISZ – John Wiley & Sons.
2. Modern Probability Theory, B.R. Bhatt, Wiley Eastern publishers.
33
JMC UG MATHEMATICS - 2008
Sub Code:
Hours/Week:
Credit:
08UMA2303:3
5
4
Max Marks:
Internal Marks:
External Marks:
100
25
75
A3: ALLIED MATHEMATICS – III
Numerical methods and Operations Research
(For Computer Science Major)
UNIT I
Algebraic Equations – Solving by Newton – Raphson Method, Gauss Elimination method
of solving system of Equations – Gauss Sedial Method of Iteration.
UNIT II
Solving an ordinary Differential Equation by Euler’s Method, Improved Euler’s method
and Modified Euler’s method- Runge – Kutta’s second order and fourth order method of
solving ordinary Differential equations.
UNIT III
Operations Research: Formulation of Linear Programming Problem - Solving a LPP by
Graphical method. Solving LPP with (≤) constraints using Simplex Method.
UNIT IV
Transportation Problem - Finding Initial Basic Feasible Solution by North West Corner
Rule, Least Cost Entry Method and Vogel’s Approximation method for a given
Transportation Problem (Balanced and unbalanced ) - Assignment Problem (Balanced
and unbalanced) – Hungarian Method.
UNIT V
Network Scheduling – finding Critical Path – Computation of Total Float – Free Float
and Independent Float.
Text Books:
T.B.1. Numerical Methods in Science and Engineering – Dr.M.K. Venkatraman,
National Publishing (1999), Madras.
T.B.2. Operations Research – P.R. Vittal and V. Malini, Margham Publications,
Chennai, 2004.
UNIT I: Chapter III – Sec 1, 5; Chapter IV: Sec 1, 2, 6. 2
T.B.1.
UNIT II: Chapter XI: Sec 10,11,12,14,15
T.B.1.
UNIT III: Chapter II, III, IV
T.B.2.
UNIT IV: Chapter X, XI
T.B.2.
UNIT V: Chapter XIV
T.B.2.
Reference Books:
1. Introductory Methods of Numerical Analysis - S.S. Sastry, Prentice Hall of India
Ltd., (1994) New Delhi.
2. Operations Research – S.D. Sharma, Kedarnath and Ramnath Publishers and Co.,
34