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GOVERNMENT COLLEGE FOR WOMEN (AUTONOMOUS), KUMBAKONAM
Course Structure for B.Sc., Mathematics (CBCS)
(2008-2009 onwards)
Semester
I
II
Course Title
Part-I languages
Tamil
Part-II languages
English
Part-III
Core Course-I
Part-III
Core Course-II
Part-III Allied
Course-I
Part-III
Allied Course-II
Part-IV
Valued Based
Education
Part-IV
Skill Based Course
Total
Part-I languages
Tamil
Part-II languages
English
Part-III
Core Course-II
Part-III
Core Course-III
Part-III Allied
Course-II
Part-III
Allied Course-III
Part-IV
Skill Based Course
Environments
Studies
Total
Instr.
Hour
6
Credit Exam
Hour
3
3
Internal
Mark
25
External
Mark
75
Total
Mark
100
6
3
3
25
75
100
5
4
3
25
75
100
3
*
-
-
-
-
4
3
3
25
75
100
2
*
-
-
-
-
2
2
100
2
2
100
30
6
17
3
3
25
75
600
100
6
3
3
25
75
100
5
4
3
25
75
100
3
4
3
25
75
100
4
3
3
25
75
100
2
4
3
25
75
100
2
2
100
2
2
100
30
25
800
Semester
III
IV
Course Title
Part-I languages
Tamil
Part-II languages
English
Part-III
Core Course-IV
Part-III
Core Course-V
Part-III Allied
Course-IV
Part-III
Allied Course-V
Part-IV
Skill Based Course
Part-IV NonElective Course
Total
Part-I languages
Tamil
Part-II languages
English
Part-III
Core Course-II
Part-III
Core Course-III
Part-III Allied
Course-II
Part-III
Allied Course-III
Part-IV
Skill Based Course
Environments
Studies
Total
Instr.
Hour
6
Credit Exam
Hour
3
3
Internal
Mark
25
External
Mark
75
Total
Mark
100
6
3
3
25
75
100
5
4
3
25
75
100
3
*
-
-
-
-
4
4
3
25
75
100
2
*
-
-
-
-
2
2
100
2
2
100
30
6
18
3
3
25
75
600
100
6
3
3
25
75
100
5
4
3
25
75
100
3
4
3
25
75
100
4
3
3
25
75
100
2
3
3
25
75
100
2
2
100
2
2
100
30
24
-
-
-
800
Semester
V
VI
Course Title
Core Course-VII
Core Course-VIII
Core Course-IX
Core Course-X
Elective Course-I
Elective Course-II
Skill Based Course
Total
Core Course-XI
Core Course-XII
Core Course-XIII
Core Course-XIV
Elective Course-II
Elective Course-III
Skill Based Course
Total
Total No.of Paper
Total Hours
Credit
Extension Activites
Marks
Instr.
Hour
5
5
5
5
5
3
2
30
6
5
5
5
2
5
2
30
42
180
139
1
4200
Credit Exam
Hour
5
3
5
3
5
3
5
3
5
3
*
2
27
4
3
4
3
4
3
4
3
5
3
5
3
2
28
-
Internal
Mark
25
25
25
25
25
25
25
25
25
25
25
-
External
Mark
75
75
75
75
75
75
75
75
75
75
75
-
Total
Mark
100
100
100
100
100
100
600
100
100
100
100
100
100
100
700
CORE COURSE – I(CC)
DIFFERENTIAL AND INTEGRAL CALCULUS
UNIT – I
Methods of Successive Differentiation – Leibnitz’s Theorem and its applications –
Increasing & Decreasing functions.
UNIT-II
Curvature – Radius of Curvature in Cartesian and in Polar Coordinates – Centre of
Curvature – Evolutes & Involutes.
Chapter 10 Sections 2.1 to 2.6 of[1].
UNIT-III
Integration by parts – definite integrals & reduction formula.
Chapter 1 Sections 11,12,& 13 of[2].
UNIT-IV
Double integrals – Changing the order of Integration – Triple Integrals
Chapter 5 Sections 2.1 to 2.2 & section 4 of [2].
UNIT-V
Beta & Gamma functions and the relation between them – Integration using Beta &
Gamma functions
Chapter 7 Sections 2.1 to 2.4 of [2].
TEXT BOOK(S)
[1] T.K. Manicavachagam Pillai & others, Differential Calculus,
S.V.Publications, Chennai – Reprint July 2002.
[2] T.K.Manickavasagam Pillai & others, Inegral Calculus, S.V. Publications Reprint July 2002.
Reference(s)
[1] Duraipandian and Chaterjee, Analytical Geometry.
[2] Shanti Narayanan , Differential & Integral Calculus.
B.SC., PHYSICS/ CHEMISTRY STUDENTS
ALLIED MATHEMATICS
ALLIED COURSE-I(AC)
CALCULUS AND FOURIER SERIES
UNIT-I
Successive Differentiation – nth derivations of standard functions (problems only)Leibintz theorem (statement only) and its applications.
UNIT-II
Evaluation of integrals of types.
[1] ∫
[2] ∫
[3] ∫
a+bsinx
[6] ∫
px+q
dx
2
ax +bx+c
px+q
dx
2
√ax +bx+c
dx
(x+p)
√ax2+bx+c
[4] ∫
dx
a+bcosx
[5] ∫
dx
(a cosx+b sinx+c dx
(p cosx+q sinx+r
UNIT-III
General properties of definite integrals – Evaluation of definite integrals of typesReduction formula(when n is a positive integer) for
[1] ∫eax xn dx
x
[4] ∫ eax xn dx
0
[2] ∫ sin n x dx [3] ∫ cos n x dx
П/2
[5] ∫ sinn x dx
0
п/2
[6] Without proof ∫ sin nx cos mx dx – and illustrations.
0
UNIT-IV
Evaluations of Double Integral – Triple integrals.
UNIT-V
Definition of Fourier Series – Finding Fourier Coefficients for a given periodic
function with period 2П – Odd and Even functions – Half range Fourier coefficients.
TEXT BOOKS:
[1] Allied Mathematics – I A. Singaravelu, June 2002.
[2] Allied Mathematics – II A. Singaravelu.
B.Sc., COMPUTER SCIENCE STUDENTS
ALLIED MATHEMATICS
ALLIED COURSE – I (AC)
NUMERICAL METHODS
UNIT I
Algebraic & Transcendental Equations – Finding a root of the given equation using
Bisection Method – Newton Raphson Method, Iteration Method.
UNIT II
Finite differences – Forward, Central and Backward differences – Newton’s forward &
backward interpolation formulae – Lagrange’s interpolation polynomial.
UNIT III
Numerical integration – Trapezoidal and Simpson’s 1/3 and 3/8 rules.
UNIT IV
Solutions to Linear Systems – Gaussian Elimination Method – Jacobi and Gauss Siedal
Iterative methods.
UNIT V
Numerical Solution of Ordinary Differential Equations: Solution by Taylor Series
Method –Euler’s Method – Euler’s modified Method – Runge – Kutta Second and fourth order
Methods.
[Need not necessary proof ,simple problems only for all units]
TEXT BOOK(S)
S.S. Sastry, Introductory Methods of Numerical Analysis, Prentice Hall of India, Private
limited, fourth Edition, 2005.
REFERENCE BOOK(S)
[1] Numerical Methods – A.Singaravelu – June 2002.
[2] Numerical Methods in Sciencce and Engineering – Dr. M.K.Venketaraman,
M.A.,M.Tech.,Ph.D.National Publishing Co., Chennai, June 2000.
CORE COURSE – II (CC)
PROBABILITYD AND STATISTICS
UNIT I
Theory of Probability – Different definitions of Probability Sample Space – Probability
of an event – Independence of events – Theorems of probability – Conditional Probability –
Baye’s Theorem.
UNIT II
Random variables –Distribution functions - discrete and Continuous random Variables –
Probability mass and density functions Joint P.d.f.
UNIT III
Expectation – variance – Covariance – Moment Generating Functions – Theorems on
Movements Generating functions – moments – Various Measures – Correlation & Regression –
Numerical Problems for finding the correlation and regression Coefficients (Omit all the
inequalities & related Problems).
UNIT IV
Theoretical Discrete distributions: Binomial and Poisson distributions – Moment
generating functions of these distributions – additive Properties of these distributions –
Recurrence relations for the moments about origin & mean for the Binomial and poisson
distribution.
UNIT V
Theoretical Continuous Distribution : Normal distribution – Moment generating function
& additive property of the distribution.
TEXT BOOK
Gupta. S.C. & Kapoor. V.K., Fundamentals of Mathematical Statistics, Sultan & Chand
Sons, New Delhi, Reprint 2002.
REFERENCE BOOK(S)
[1] probability & Statistics (Paper III) – A. Singaravelu – March 2002.
[2]Thambidurai. P. Practical Statistics, Rainbow Publishers – CBE(1991).
CORE COURSE – III (CC)
ANALYTICAL GEOMENTRY AND TRIGNOMETRY
UNIT I
Coplanar lines – Shortest distance between two skew lines – Equation of the Line of
Shortest distance.
Chapter 3 Sections 7 & 8 of [1]
UNIT II
Sphere – Standard Equation – Length of a tangent from any Point – Sphere Passing
through a given circle – intersection of two Spheres.
Chapter 4 Sections 1 to 8 of [1].
UNIT III
Expansions of sin(nx), cos(nx), tan(nx)- Expansions of sinnx, cosnx – Expansions of
Sin(x), Cos(x), tan(x) in Powers of x
Chapter 1 Selections 1.2 to 1.4 of [2]
UNIT IV
Hyperbolic functions – Relation between hyperbolic & Circular functions Inverse
hyperbolic functions
Chapter 2 Section 2.1 to 2.2 of [2].
UNIT V
Logarithm of a complex number – Summation of Trigonometric Series – Difference
method – Angles in arithmetic Progression method – Gregory’s Series.
Chapter 3 & Chapter 4 Sections 4.1, 4.2 & 4.4 of [2]
TEXT BOOK(S)
[1] T.K.Manicavachagam Pillai & others, Differential Calculus,
S.V. Publications, Chennai- Reprint July 2002.
[2] S.Arumugam & others, Trigonomentry , New Gamma Publications-1999.
REFERENCE(S)
[1] S.Arumugam and Isaac, Calculus, Volume I, New Gamma Publishing House, 1991
[2] S.Narayanan, T.K.manchavasagam Pillai, Trigonometry, s.Vishwanathan Pvt.Limited and
Vijay Nicole Imprints Pvt Ltd,2004.
ALLIED COURSE- II (AC)
ALGEBRAFD, ODE AND TRIGONOMETRY
UNIT I
Binomal, Exponential and Logarithmic series (formulae only) – Problems in summation
only.
UNIT II
Ordinary Differential Equation of first order but of higher degree – Equations Solvable
for x, solvable for dy Clairaut’s from (simple cases only)
─
dx
UNIT III
Linear equation with constant coefficients – Finding Particular integrals in the cases of
kk
e , sin(kx), cos(kx) (where k is a constant), Xk Where K is a positive integer and ekk f(x)
where f(x) is any function of x – (only problems in all the above – no proof neede for any
formula).
UNIT IV
Expansion of sin nθ , cos nθ, tan nθ (n being a positive integer) – Expansion of
n
Sin θ, cosn θ, sinn θ cosmθ in a series of sines & cosines of multiples of θ ( -given in radians)
- Expansion of sin θ, cos θ and tan θ in terms of (only problems).
UNIT V
Eular’s formula for eiө - Definition of Hyperbolic functions – formulae involving
Hyperbolic functions – Relation between Hyperbolic & circular functions – Expansions of sin
hx,cos hx and tan hx in power of x – expension of Inverse hyperbolic functions sin h-1 x,cosh-1 x
and tanh-1 x- Separation of real & imaginary parts of sin (x+iy), cos(x+iy), tanh(x+iy),
cosh(x+iy), tanh(x+iy).
TEXT BOOK(S)
[1] Arumugam, Isaac & Somasundaram, Trigonometry and Fourier series.
[2] Allied Mathematics (paper II) – A.Singaravelu – August 1998.
B.Sc., COMPUTER SCIENCE STUDENTS
ALLIED MATHEMATICS
ALLIED COURSE – I (AC)
OPERATIONS RESEARCH
Unit I:
O.R (Definition) –Linear Programming Problem – Mathematical formulation of LPP –
Graphical Solution methods – simplex with <=, >=, = Constraints.
Chapter 2: Sections 2.2,2.3,3.2,3.3,4.3.4.4
Unit II:
Transportation problems (definition) – Matrix from of T.P. – Initial Basic Feasible
Solution – The North West Corner Rule – The Row Minima Method – The Column Minima
Method – The Matrix Minima Method – Vogel’s Approximation Method Unbalanced T.P
Chapter 10: Sections 10.1,10.5, 10.8,10.9.
Unit III:
Assignment Problem – Hungarian Algorithm – Maximization Method –Minimization
Method – Some exceptional Cases- Unbalanced Assignment Problem.
Chapter 11: sections 11.1,11.2.
Unit IV:
Critical path Method: Basic Concepts – Activities – Nodes –Network – Critical path –
Constraints in Networks – Construction of Network – Time Calculation in Networks –Critical
path Calculations – Critical path method.
Chapter 25: Sections 25.1,25.2,25.3,25.4,25.6
Unit V:
PERT-PERT Calculations – Probability of meeting the schedule time
Chapter 25: Section 25.7.
[Simple problems only need not necessary book work for all units]
TEXT BOOK:
Operations Research – Kanti Swarup, P.K. Gupta and Manmohan, 13th Edition 2007,
Published by Sultan Chand & Sons.
ALLIED COURSE – III(AC)
LAPPLCAE TRANSFORM AND VECTOR CALCLUS
UNIT-I
Laplace Transform – Definition –L(eat),L(cos(at)), L(sin(at)), L(tn), where n is a positive
integer. Basci theorems In Laplace Transform (formula only)- L[e-stcos bt], L[e –st f(t)] –
L[f(t)],L[f(t)].
UNIT-II
Inverse Laplace Transforms related to the above standard forms – solving Second
Order ODE with constant coefficient using Laplace Transforms.
UNIT-III
Vector differentiation – velocity & acceleration vectors – Gradient of a vector –
directional derivation – unit normal vector – tanget plane – Divergence – Curl- solenoid &
irritation vectors- Double operators- Properties connecting grad., div.and curl of a vector.
UNIT-IV
Vector integration- Line integrals – Surface integrals – Volume integrals.
UNIT-V
Guass Divergence Theorem (statement only), Verification and application – Stoke’s
Theorem (statement only), Verification and application.
TEXT BOOK(S)
[1] Allied Mathematics –II., A.Singaravelu, June2002.
[2] Allied Mathematics –III., A.Singaravelu, August 1998.
B.SC., COMPUTER SCIENCE STUDENTS
ALLIED MATHEMATICS
ALLIED COURSE-III(AC)
PROBABILITY AND STATISTICS
UNIT 1
Theory of Probability-Different definitions of Probability Sample Space – Probability
of an event – Independence of events.
UNIT II
Random variables – Distribution functions – Discrete and Continuous random variables
– Probability mass and density functions.
UNIT III
Expectation – Variance – Covariance – Moment generating functions – Theorems on
Moments generating functions – moments – Various Measures – Correlation & Regression –
Numerical problems for finding the correlation and regression coefficients(Omit all the
inequlities & related problems)
UNIT IV
Theoretical Discrete distributions: Binomial and Poisson distributions – Moment
generating functions of these distributions – additive properties of these distributions –
Recurrence relations – additive properties of these distributions – Recurrence relations for the
moments about origin & mean for the Binomial and Poisson distributions.
UNIT V
Theoretical Continuous distribution: Normal distribution – Moment generating function
& additive property of the distribution.
TEXT BOOK
Gupta S.C. & Kapoor.V.K., Fundamentals of Mathematical Statistics, Sultan & Chand
Sons, New Delhi, Reprint 2002.
REFERENCE BOOK(S)
[1] Probability & Statistics (Paper III) – A.Singaravelu – March2002
[2] Thambidurai.P,Practical Statistics,Rainbow Publishers – CBE(1991)
CC IV-ALGEBRA AND THEORY OF NUMBERS
UNIT I
Relation between the roots and coefficients of Polynomial Equcations – Symmetric
functions – Sum of the rth powers of the roots – Two methods(Horner’s method and Newton’s
method)
UNIT II
Transformations of Equations – (Roots with sign changed – Roots multiplied by a given
number –Reciprocal roots)-Reciprocal equations – To increase or decrease the roots of given
equations quantity – Form the quotient and Remainder when a Polynomial is divided by a
binomial – Removal of terms – To form an equation whose roots are any power of the roots of a
given equation
UNIT III
Transformation in general – Descartes rule of signs(statement only-simple problems)
UNIT IV
Inequalities – elementary principles – Geometric & Arithmetic means – Weirstrass
inequalities – Cauchy inequality – Applications to Maxima & Minima.
UNIT V
Theory of Numbers – Prime and Composite numbers – Divisors of a given numbers N –
Euler’s function (N) and its value – The highest power of a prime P contained in n! –
Congruences – Fermat’s ,Wilson’s and Langrange’s Theorems.
TEXT BOOKS(S)
[1] T.K.Manicjavasagom Pillai & others Algebra Volume I, S.V.Publications – 1999
Reprint Edition
[2] T.K.Manicjavasagom Pillai & others Algebra Volume I, S.V.Publications – 2000
Reprint Edition
UNIT I
UNIT II
UNIT III
UNIT IV
UNIT V
: Chapter 6 Sections 11 to 14 of [1]
: Chapter 6 Sections 15,16,17,18,19,20 of [1]
: Chapter 6 Sections 21 and 24 of [1]
: Chapter 4 Sections 4.1 to 4.6,4.9 to 4.11,4.13 of [2]
: Chapter 5 of [2]
REFERENCE:
[1] H.S. Hall and S.R.Knight, Higher Algebra, Prentice Hall of India, New Delhi.
Non Major Elective Course-I-Mathematics for Competitive Examinations-I
(Offered by the Department of Mathematics)
UNIT I
Numbers – HCF and LCM – Decimal Fractions.
UNIT II
Square Roots and cube Roots – Percentage – Average – Ratio and Proportion –
Partnership – Profit and Loss.
UNIT III
Time and Work – Time and Distance.
UNIT IV
Problems on Trains – Problems on Numbers – Problems of Ages.
UNIT V
Area – Volume and Surface area.
TEXT BOOK:
R.S.Aggarwal, Objective Arithmetic, S.Chand and company Ltd., New Delhi,2008.
QUESTION PATTERN
SECTION-A
50 questions one Mark
Each Unit two questions for all topics.
One word
10 x1=10
Fill in the blanks
10 x1=10
Choose the correct answer
10 x1=10
True or False
10 x1=10
Match the following
10 x1=10
50x1=50
SECTION-B
Either or Type
5x5=25
TOTAL = 75
CC V – SEQUENCES AND SERIES
UNIT I
Sequence: Limit, Convergence of a sequence – Cauchy’s general principle of
convergence – Cauchy’s first theorem on limits – Bounded sequences- monotonic sequence
Always tends to a limit, finite or infinite
UNIT II
Infinite series – Definition of Convergence, Divergence & Oscillation – Necessary
condition for Convergence – Convergence of € 1/np and Geometric series.
UNIT-III
Comparison test, D’ Alembert’s Ratio test and Raabe’s test. Simple problems based on
above tests.
UNIT IV
Cauchy’s condensation test, cauchy’s Root test and their simple problems – Alternative
series with simple problems.
UNIT V
Binomial theorem for rational index – Exponential & Logarithmic series – Summation
of series & approximations using these theorems.
TEXT BOOK:
[1]
T.K.Manicavachagam Pillai, T.Natarajan, K.S.Ganapathy, Algebra, Volume
I,S.Viswanathan Pvt Limited, Chennai, 2004
UNIT I: Chapter 2(Sections 1 to 7)
UNIT II: Chapter 2(Sections 8,9,10,11,12,& 14)
UNIT III: Chapter 2(Sections 13,16,18 & 19)
UNIT IV: Chapter 2(Sections 15,17,21 to 24)
UNIT V: Chapter 3(Sections 5 to 11,14 & Chapter 4 Sections 2,3,5 to 9)
REFERENCE(S):
[1] M.K.Singal & Asha Rani Singal, A first course in Real Analysis, R.Chand &
Co., 1999
[2] Dr.S.Arumugam, Sequences & Series, New Gamma Publishers,1999
CC VI – DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS
UNIT I
Differential Equations – Linear differential equations with constant coefficients – the
operators D and D-1 - Particular Integral – Special Methods of finding Particular integral –
Linear equations with variable coefficients – To find the particular integral – Special methods of
evaluating the particular integral when x is of the form xm
UNIT II
Exact Differential Equations – Conditions of Integrability of Mdx+Ndy =0 – Particular
Rule for solving an Exact Differentia; Equation – Rules for finding integrating factors –
Equations of the first order but of higher degree – Solvable for x,y,dy/dx – Clairaut’s form –
Equations that do not contain x explicitly – Equations that do not contain y explicitly – Equations
Homogeneous in x and y.
UNIT III
Partial Differential Equations – Derivation of Partial Differential Equations by elimination
of constants,arbitrary functions – Different integrals of P.D.E. – Solutions of P.D.E. in some
simple cases –
Standard types of firt order equations – Standard I,II,III,IV – Equations reducuble to the standard
forms – Lagrange’s equation.
UNIT IV
Then Laplace Transforms – Sufficient conditions for the existence of the Laplace
Transforms – Laplace Transforms of Periodic functions – General Theorems – Eveluation of
certain integrals using Laplace Transforms.
UNIT V
The Inverse transforms – Inverse transforms of functions – Method of Partial fractions –
Applications of Laplace Transforms to solve ordinary differential equations with constants coefficients.
TEXT BOOK:
S.Narayanan and T.K .Manickalculus Volume III, S. Viswanathan Pvt.,Ltd., 1999
UNIT I:
UNIT II:
UNIT III:
UNIT IV:
UNIT V:
Chapter 2 Sections 1,1.2,2,3,4,8,8.1,8.2,8.3
Chapter 1 Sections 3.1-3.3,4.5,5.1-5.5,6.1,7.1-7.3)
Chapter 4Sections 1.2,2.1,2.2,3.4,5,5.1-5.5,6
Chapter 5 Sections 1,1.1,1.2,2.3,3.4,5)
Chapter 5 Sections 6,7,8
REFERENCE(S)
1. M.K. Venkararaman, Engineering Mathematics, S.V. Publications, 1985,
Revised Edition
2. Arumugam and Isaac, Differential equations and applications, New Gamma
Publishing House,2003
Non Major Elective Course-I-Mathematics for Competitive Examinations-II
(Offered by the Department of Mathematics)
UNIT I
Simple Interest – Compound Interest
UNIT II
Permutation and Combination – Probability
UNIT III
Heights and Distances – Odd Man Out and Series.
UNIT IV
Tabulation – Bar Graphs.
UNIT V
Pie Charts – Line Graphs
TEXT BOOK:
R.S. Aggarwal, Objectve Arithmetic, S.Chand and company Ltd., New Delhi,2008
QUESTION PATTERN
SECTION –A
50 questions one Mark
Each Unit two questions for all topics.
One word
10 x1=10
Fill in the blanks
10 x1=10
Choose the correct answer
10 x1=10
True or False
10 x1=10
Match the following
10 x1=10
50x1=50
SECTION-B
Either or Type
5x5=25
TOTAL =75
CC VII – ABSTRACT ALGEBRA
UNIT I : Groups
Subgroups – Cyclic groups – Order of an element – Cosets and Lagrange’s theorem.
UNIT II :
Normal subgroups and Ouotient groups – Isomorphism – Homomorphisms
UNIT III : Rings
Definition and Examples – Elementary properties of rings – Types of rings –
Characteristics of a rings – Subrings – Ideals – Quotient rings – Maximal & Prime ideals –
Homomorphism of rings – Isomorphism of rings.
UNIT IV : Vector Spaces
Definition and Examples – Subspaces – Linear Transformation – Span of a set – Linear
independence.
UNIT V :
Basis and Dimension – Rank and Nullity – Matrix of a Linear Transformation.
TEXT BOOK:
[1] Modern Algebra by S.Arumugam and A.Thangapandi Isaac Scitech Publications
(India) PVT, Ltd-December 2004 1st print.
UNIT I : Chapter 3 (Sections 3.5 to 3.8)
UNIT II : Chapter 3 (Sections 3.9 to 3.11)
UNIT III: Chapter 4 (Sections 4.1 to 4.10)
UNIT IV: Chapter 5 (Sections 5.1 to 5.5)
UNIT V: Chapter 5 (Sections 5.6 to 5.8)
REFERENCE(S):
[1] A Text book of Modern Abstract Algebra by Shanti Narayan.
[2] Modern Algebra by K.Sivasubramanian
[3] A Text book of Modern Abstract Algebra by R.Balakrishnan and N. Ramabadran
CC VIII – VECTOR CALCULUS, FOURIER SERIES AND MATRICES
UNIT I
Vector differentiations – Velocity & acceleration Vectors – Vector & Scalar fields –
Gradient of a vector – Unit normal – Directional derivative - Divergence & Curl of a vector
Solenoidal & Irrotational vectors – Laplacian double operators – Simple problems.
UNIT II
Vector integration – Tangential line integral – Conservative force field – scalar potential
– work done by a force – Normal surface integral – Volume integral – Simple problems.
UNIT III
Gauss Divergence theorem – Stoke’s theorem – Green’s theorem – Simple problems &
Verification of the theorems for simple problems. (Statement only – Proof not included)
UNIT IV
Fourier series – definition – Fourier series expansion of periodic functions with period
2∏ and period 2a – Use of odd & even functions in Fourier series.
UNIT V
Rank of a matrix – Consistency – Eigen Values, Eigen vectors – Cayley Hamilton’s
theorem (Statement only) – Symmetric, Skew Symmetric, Orthogonal, Hermitian, Skew
Hermitian & Unitary Matrices-simple problems only
TEXT BOOK(S):
[1] K. Viswanatham & S.Selvaraj, Vector Analysis, Emerald Publishers Reprint 1999.
[2] S. Narayanan, T.K. Manicavachagam Pillai, Calculus Volume III, S.Viswanathan Pvt
Limited and Vijay Nicole Imprints Pvt Ltd,2004.
[3] S. Arumugam & A. Thangapandi Isaac, Modern Algebra, New Gamma publishing
House,2000
UNIT I : Chapter 1 Section 1 & Chapter 2 (Sections 2.1 to 2.2.5,2.3 to 2.5.1) of [1]
UNIT II : Chapter 3 (Sections 3.1 to 3.7) of [1]
UNIT III : Chapter 4 (Sections 4.1 to 4.5.1) of [1]
UNIT IV : Chapter 6 (Sections 1 to 3) of [2]
UNIT V : Chapter 7 (Sections 7.2,7.5,7.6,7.7 ) of [3]
REFERENCE:
[1] M.L. Khanna, Vector Calculus, Jai Prakash Nath and Co.,
CC IX – REAL ANALYSIS
UNIT I
Real number system – Field axioms – Order in R – Absolute value of a real number & its
properties – Supremum & Infimum of a set – Order Completeness property – Countable &
Uncountable sets.
UNIT II
Limit of a Function – Algebra of Limits – Continuity of a function – Types of
discontinuities – Elementary properties of continuous functions – Intermediate value theoremInverse Function theorem – Uniform continuity of function.
UNIT III
Differentiability of a function – Derivability & Continuity – Algebra of Derivatives –
Inverse Function Theorem – Darboux’s theorem on derivatives.
UNIT IV
Rolle’s theorem – Mean Value theorem on derivatives – Taylor’s theorem with remainder
Power series expansion.
UNIT V
Riemann integration – Definition – Darboux’s theorem – Conditions for integrability –
Integrability of continuous & Monotonic functions – Integral functions – Properties of Integrable
functions – continuity & Derivability of integral functions – The First Mean Value theorem and
the Fundamental theorem of calculus.
TEXT BOOK(S):
[1] M.K. Singal & Asha Rani Singal, A first course in Real Analysis, R.Chand &
Co.,Publishers, New Delhi, 2003.
[2] Shanthi Narayanan, A Course of Mathematical Analysis, S.Chand & Co.,1995.
UNIT I : Chapter 1 of [1]
UNIT I1 : Chapter 5 of [1]
UNIT III : Chapter 6 of [1] (Sections 1 to 5)
UNIT IV : Chapter 8 of [1] (Sections 1 to 6)
UNIT V : Chapter 6 of [2] (Sections 6.1 to 6.9)
REFERENCE:
[1] Gold Berge, Richar R, Methods of Real Analysis , Oxford & IBHP Publishing co.,
New Delhi, 1970
CC X – STATICS
UNIT I
Force – Resultant of two forces – Three forces related to a triangle – resultant of several
forces – Equilibrium of a particle under three or more forces.
UNIT II
Forces on a rigid body – Moment of a force – Equivalent system of forces – parallel
forces – Varignon’s Theorem – Forces along a Triangle – Couples – Equilibrium of a rigid body
under three coplanar forces – reduction of coplanar forces into a force and a couple.
UNIT III
Types of forces – Friction – Laws of Friction – Coefficient of Friction, Angle and Cone
of Friction – Limiting equilibrium of a particle on a rough inclined plane – Tilting of a body –
Simple Problems.
UNIT IV
Virtual Work – Principle of Virtual Work – applied to a body or a system of bodies in
equilibrium – Equation of Virtual Work – Simple Problems.
UNIT V
String – Equilibrium of Strings under gravity – Common Catenary – Suspension bridge.
TEXT BOOK:
[1] P. Duraipandiyan, Mechanics (Vector Treatment),S. Chand and Co., June 1997.
UNIT I : Chapter 2 & Chapter 3:Section 3.1
UNIT II : Chapter 4 & Section 4.1,4.3 to 4.9 & Chapter 5: Section 5.1
UNIT III : Chapter 2 & Section 2.1.2 to & Chapter 3: Section 3.2 & Chapter 5:
Section 5.2
UNIT IV : Chapter 8
UNIT IV : Chapter 9
REFERENCES(S):
[1] M.K. Venkataraman, Statics, Agasthiyar Publications, 2002
[2] A.V. Dharmapadham, Statics,S.Viswanathan Publishers Pvt., Ltd.,
[3] S.L. Lony, Elements of Statics and Dyanmics,Part – I,A.I.T.Publishers,1991.
EC I – OPERATIONS RESEARCH
UNIT I
Introduction to operation Research - Mathematical Formulation of the Problem –
Graphical Solution Method – Simplex method – Big(M) Method
Chapter 2 : Sections 2.1,2.2
Chapter 3 : Sections 3.1,3.2
Chapter 4 : Sections 4.1,2.4
UNIT II
Transportation Problem – North West Corner rule – Least cost method – Vogel’s
approximation method – MODI Method – Assignment problems.
Chapter 10 : Sections 10.1,10.2,10.7,10.8,10.11
Chapter 11 : Sections 11.1,11.2,11.3,11.4
UNIT III
Sequencing Problems – Introduction – Problem of Sequencing – Basic Term Used in
Sequencing –Processing n Jobs through 2 Machines – Processing n Jobs through k Machines –
Processing 2Jobs through k Machines.
Chapter 12:12.1,12.2,12.3,12.4,12.5,12.6.
UNIT IV
Replacement Problems – Introduction – Replacement of Equipment / asset that
Deteriorates Gradually – Replacement of Equipment that Fails Suddenly.
UNIT V
Network Scheduling by PERT/CPM – Introduction – Network and Basic Components –
Rules of Network Construction – Critical path Analysis – Probability Consideration – Rules of
Network Construction – Critical path Analysis – Probability Consideration in PERT –
Distinction between PERT and CPM.
Chapter 21:21.1,21.2,21.4,21.5,21.6,21.7.
TEXT BOOK:
Operations Research – Kanti Swarub, P.K.Gupta, Man Mohan,Sultan Chand & Sons
Educational Publishers New Delhi, Ninth thoroughly Revised Edition.
REFERENCE(S):
[1] Hamdy A.Taha,Operations Research (7th E.dn.,),Prentics Hall of India,2002.
[2] Richard Bronson, Theory and Problems of Operations Research, Tata McGraw Hill
Publishing Company Ltd, New Delhi,1982.
EC II – DISCRETE MATHEMATICS
UNIT I:
Connectives.
UNIT II:
Normal forms – The theory of inference for the Statement calculus.
UNIT III:
The Predicate calculus; Inference Theory of Predicate calculus.
UNIT IV:
Lattices.
UNIT V:
Boolean Algebra: Boolean Functions.
TEXT BOOK:
[1] J.P.Trembly and R.Manohar: Discrete Mathematical Structures with Applications to
Computer Science, TMH Edition 1997.
UNIT I Chapter 1: Sec 1.2(omit 1.2.5 & 1.2.15)
UNIT II Chapter 1: Sec 1.3(omit 1.3.5 & 1.3.6),Sec 1.4(Omit 1.4.4)
UNIT III Chapter 1: Sec 1.5 & Sec 1.6
UNIT IV Chapter 4: Sec 4.1
UNIT V Chapter 4: Sec 4.2,4.3
REFERENCE:
G.Ramesh and Dr.C.Ganesamoorthy, Discrete Mathematics, First Edition, Hi-Tech
Publications, Mayiladuthurai, 2003
CC XI – COMPLEX ANALYSIS
UNIT I
Functions of a complex variable – Limits – Theorems on Limits – Continuous functions –
Differentiability - Cauchy-Riemann equations – Analytic functions – Harmonic functions.
UNIT II
Elementary transformations – Bilinear transformations – cross ratio – fixed points of
Bilinear transformation – some special bilinear transformations.
UNIT III
Complex integration – definite integral – Cauchy’s theorem – Cauchy’s integral formula
– Higher derivatives.
UNIT IV
Series expansion – Taylor’s series – Laurent’s series – Zeros of analytical functions –
Singularities.
UNIT V
Residues – Cauchy’s Residue theorem – Evaluation of definite integrals.
TEXT BOOK:
[1] S.Arumugam, A.Thangapandi Isaac & A.Somasundaram, Complex Analysis, New
Scitech Publications (India) Pvt.Ltd. November 2003.
UNIT I: Chapter 2 Sections 2.1 to 2.8
UNIT II: Chapter 3 Sections 3.1 to 3.5
UNIT III: Chapter 6 Sections 6.1 to 6.4
UNIT IV: Chapter 7 Sections 7.1 to 7.4
UNIT V: Chapter 8 Sections 8.1 to 8.3
REFERENCE(S):
[1] P.P.Gupta – Kedarnath & Ramnath, Complex Variables, Meerut – Delhi.
[2] J.N. Sharma, Functions of a Complex Variable, Krishna Prakasan Media (p) Ltd. 13th Edition
1996-97
[3] T.K.Manickavachagam Pillai, Complex Analysis,S.Viswanathan Publishers Pvt. Ltd 1994
CC XII – NUMERICAL ANALYSIS
UNIT I
Algebraic and Transcendental equation – Finding a root of the given equation using
Bisection Method, Method of False Position, Newton Raphson Method, Iteration method.
UNIT II
Finite differences – Forward, Backward and Central differences – Newton’s forward and
backward difference interpolation formulae – Interpolation with unevenly spaced intervals –
Lagrange’s interpolating Polynomial.
UNIT III
Numerical – Integration using Trapezoidal rule and Simpson’s 1/3 and 3/8 rules.
UNIT IV
Solution to Linear Systems – Gauss Elimination Method – Jacobi and Gauss Siedal
iterative methods.
UNIT V
Numerical solution of ODE – Solution by Taylor’s Series Method, Picard’s Method,
Euler’s Method,Runge Kutta second and fourth order methods.
TEXT BOOK:
[1] S.S. Sastry, Introductory Methods of Numerical Analysis, Prentices Hall of India
Pvt.,Limited, 2001 Third Edition.
UNIT I : Chapter 2 : Sections 2.2,2.3,2.4,2.5
UNIT II : Chapter 3 : Sections 3.3.1,3.3.2,3.3.3,3.3.4,3.6,3.9,3.9.1
UNIT I : Chapter 2 : Sections 5.4,5.4.1,5.4.2,5.4.3
UNIT I : Chapter 2 : Sections 6.3,6.3.2
UNIT I : Chapter 2 : Sections 8.3.1,8.3.2
UNIT I : Chapter 2 : Sections 7.1,7.2,7.3,7.4,7.4.2,7.5
REFERENCE(S):
[1] S.Narayanan and Others, Numerical Analysis, S. Viswanathan Publishers, 1994
[2] A. Singaravelu, Numerical Methods, Meenachi Agency, June 2000.
CC XIII – DYNAMICS
UNIT I
Kinematics: Velocity – Relative Velocity – Acceleration – Coplanar Motion –
Components of Velocity and Acceleration – Newton’s Laws of Motion.
UNIT II
Simple Harmonic motion – Simple Pendulum – Load suspended by an elastic string –
Projectile – Maximum height reached,ranges,time of flight – Projectile up/down an inclined
plane.
UNIT III
Impulsive force – Conservation of linear momentum – Impact of a sphere and a plane –
Direct and Oblique Impact of two smooth Spheres – Kinetic energy and impulse
UNIT IV
Central Orbit – Central force – Conservation of linear momentum – Impact of a sphere
and a Plane – Direct and Oblique Impact of two smooth spheres – Kinetic energy and impulse.
UNIT V
Moment of Inertia of simple bodies – Theorems of Parallel and Perpendicular axes –
Motion in Two dimension – equation of motion for two dimensional motion.
TEXT BOOK:
[1] P.Duraipandiyan, Vector Treatment as in Mechanics, S.Chand and Co., June 1997
Edition.
UNIT I : Chapter 1 & Chapter 2 (Section – 2.1.1.)
UNIT II : Chapter 12 (Sections – 12.1 to 12.3), Chapter 15 (Section:15.6) & Chapter 13
UNIT III : Chapter 14
UNIT IV : Chapter 16
UNIT V : Chapter 17 & Chapter 18
REFERNCES(S)
[1] M.K. Venkataraman, Dyanamics, Agasthiar Book Depot, 1990.
[2] A.V.Dharmapadam, Dynamics,S.Viswanathan Publishers,1981
CC XIV – GRAPH THEORY
UNIT I
Definition of a graph, application of a graph – finite and infinite graphs – incidence and
degree – isolated, pendant vertices and Null graph – Isomorphism – subgroups – walks, paths
and circuits – Connected and disconnected graphs – components – Euler graphs – Operations on
Graphs – More on Euler graphs – Hamiltonian paths and circuits.
UNIT II
Trees – properties of trees – pendant vertices in a Tree – distance and centers in a Tree –
Rooted and Binary Trees – Spanning Trees – Fundamental circuits.
UNIT III
Cut-Sets – Properties of a Cut-set – all Cut-sets in a graph – Fundamental circuits and Cut
sets – Connectivity and separability.
UNIT IV
Vector Spaces of a Graph – Sets with one,two operations – modular arithmetic – Galois
Fields – Vectors and Vectors Spaces – Vector Space Associated with a Graph – Basis vectors of
a graph – circuit and cut-set subspaces – Orthogonal vectors and spaces.
UNIT V
Matrix representation of graphs – Incidence matrix - Circuit Matrix – Fundamental
Circuit Matrix and Rank of B – Cut-set matrix.
Chromatic Number – Chromatic partitioning – Chromatic polynomial.
TEXT BOOK:
[1] Marsingh Deo, GraphTheory with application to Engineering and Computer Science,
Prentice Hall of India Pvt.Ltd., New Delhi,Reprint 2004
UNIT I : Chapter 1(Sections 1.1 to 1.5) & Chapter 2 (Sections 2.1,2.2,2.4 to 2.9)
UNIT II : Chapter 3(Sections 3.1 to 3.5,3.7,3.8)
UNIT III : Chapter 4(Sections 4 .1 to 4 .5)
UNIT IV : Chapter 6(Sections 6.1 to 6.8)
UNIT V : Chapter 7(Sections 7.1 to7. 3,7.4,7.6) & Chapter 8 (Sections 8.1 to 8.3)
REFERENCE(S)
[1] Dr.S.Arumugam and Dr.S.Ramachandran, Invitation to Graph Theory, Scitech Publications
India Pvt Limited, Chennai 2001.
[2] K.R.Parthasarathy, Basic Graph Theory, Tata Mcgraw Hill Publishing Company, New
Delhi,1994.
[3] G.T.John Clark,Derek Allan Holten, A First Look at Graph Theory, World Scientific
Publishing company, 1995.
EC III – ASTRONOMY
UNIT I
Relevant properties of a sphere and relevant formulae for spherical trigonometry (All
without proof) – Diurnal motion.
Chapter 1
Chapter 2
UNIT II
Earth- Dip of Horizon- Twilight – Refraction- Tangent and Cassini’s Formula.
Chapter 3: Sections 1,2,5,6
Chapter 4: Sections 117 to 122,129,130.
UNIT III
Kepler’s Laws of Planetary motion (statement only) – Newton’s deduction from them –
Three anomalies of the Earth and relation between them.
Chapter 6
UNIT IV
Equation of time, Calendar – Geocentric Parallax – Aberration of light.
UNIT V
Moon (except Moon’s liberations) – Motions of planet (assuming that orbits are circular)
– Eclipses.
Chapter 12
TEXT BOOK:
[1] S. Kumaravelu and Prof.Susheela Kumaravelu,Astronomy,SKV Publications,2004.
REFERENCE:
[1] V.Thiruvenkatacharya,A Text Book of Astronomy, S.Chand and Co.,Pvt Ltd.,1972