CENTURION UNIVERSITY OF TECHNOLOGY AND
MANAGEMENT, ODISHA
SCHOOL OF BASIC SCIENCES
3-YEAR B.Sc. PROGRAMME
IN
MATHEMATICS
1st YEAR SYLLABUS
Subject
Code
Subject
Contact
Hours
per
week
(L+T+P)
Sl
No
2+0+0
2
1
4+0+2
6
2
2
English Communications/
Environmental Science
C1 Calculus
3
C2 Linear Algebra
5+1+0
6
3
4
GE-1
5+1+0
6
20
4
1
TOTAL CREDITS
Subject
Code
Subject
English Communications/
Environmental Science
C3 Analysis - I
C4
Ordinary Differential
Equations (P)
GE-2
TOTAL CREDITS
Contact
Hours per
week
(L+T+P)
Credits
Sl
No
SEMESTER-II
Credits
SEMESTER-I
2+0+0
2
5+1+0
6
4+0+2
6
5+1+0
6
20
SEMESTER – I
CORE-1
Calculus (4-0-2)
(Total Marks: 100)
Part – I (Marks: 70)
(Theory: Internal-30 +External-40)
MODULE-I
Curvature, Asymptotes, Tracing of Curves: Cartenary, Cycloid, Folium of Descartes, Astroid, Limacon,
Cissoids, Cardioid, Lemniscate and Loops.
MODULE-II
Reduction Formulae, Rectification,Quadrature,Volume and Surface area of solids of revolutions.
MODULE-III
Vector Calculus: Vector valued functions of scalar variables, Differential operators, Integral
transformations: Line Integrals, Surface Integrals, Volume Integrals, Green’s Theorem, Gauss’s Theorem,
Stokes’ Theorem (without proof).
Part-II (Practical Marks: 30)
List of Practicals (Using any software)
Practical/ Lab work to be performed on a Computer.
1. Plotting the graphs of the functions eax+b, log (ax + b). 1/(ax + b), sin (ax + b), cos(ax + b),
|ax +b| and to illustrate the effect of a and b on the graph.
2. Plotting the graphs of the polynomial of degree 4 and 5, the derivative graph, the second derivative
graph and comparing them.
3. Sketching parametric curves (Eg. Trochoid, cycloid, epicycloids, hypocycloid).
4. Obtaining surface of revolution of curves.
5. Tracing of conics in Cartesian coordinates/polar coordinates.
6. Sketching ellipsoid, hyperboloid of one and two sheets, elliptic, cone, elliptic, paraboloid, hyperbolic
paraboloid using Cartesian coordinates.
Text Books:
Module I:1) A Text book of Calculus Part – II : Shantinarayan
Chapter : 8 (Art. 24, 25, 26),
2) A Text book of Calculus Part-III : Shantinarayan
Chapters : 1 (Art 1, 2,3), 3(Art 7,8,9)
Module II:3) A Text book of Calculus Part – II : Shantinarayan
Chapter : 10 (Art. 33,34,35,36,37,38)
4) A Text book of Calculus Part-III : Shantinarayan
Chapters : 4(Art 10,11,12) omitting Simpson’s rule), 5(Arts 13,14),6(Arts 15,16).
Module III:5) A Textbook of Vector Calculus by Shanti Narayan & P. K. Mittal, S. Chand & Co. , 2003
Chapters: 1, 6, 7 (7.1 to 7.6, 7.8 & 7.11)
Reference Books:
1. M.J. Strauss, G.L. Bradley and K. J. Smith, Calculus, 3rd Ed., Dorling Kindersley (India) P. Ltd.
(Pearson Education). Delhi, 2007, Chapters: 4(4.3,4.4,4.5&4.7), 9(9.4), 10(10.1-10.4).
2. H. Anton, I. Bivens and S. Davis, Calculus, 7th Ed., John Wiley and Sons (Asia) P. Ltd., Singapore,
2002. Chapters: 6. (6.2-6.5).7(7.8). 8(8.2-8.3, Pages:532-538), 11(11.1), 13(13.5)
3. G. B. Thomas and R. L. Finney. Calculus, 9th Ed., Pearson Education, Delhi, 2005
4. R. Courant and F. John Introduction to Calculus and Analysis (Volumes I & II). Springer-Verlag. New
York. Inc., 1989
CORE-2
Linear Algebra(4-0-2)
(Total Marks: 100)
Part – I (Marks: 70)
(Theory: Internal-30 +External-40)
MODULE-I
Vector spaces, definition and examples, subspaces, span of a set, linear dependence and independence,
dimension and basis.
MODULE-II
Linear transformation, definition and examples, range and kernel, rank and nullity, the space L(U,V),
composition of Linear maps, matrix and linear map, linear operations, matrix multiplication, rand and
nullity of matrix, transpose of a matrix.
MODULE-III
Elementary row operations, Systems of linear equations, matrix inversion, determinants, minors and rank
of amatrix, product of determinants, application to linear equations, Eigen value and Eigen vector.
Part-II (Practical Marks: 30)
List of Practicals (Using any software)
Practical/ Lab work to be performed on a Computer.
1. Matrix addition and multiplication.
2. Matrix Inversion and Transpose.
3. Eigen Values and Eigen vectors of Matrix
4. Solution of AX=B using Gauss Elimination,Gauss Seidal, Gauss-Jacobi and Gauss methods
Text Book:
1) An Introduction to Linear Algebra by V. Krishnamurty,V.P.Mainra, J.L.Arora, Affiliated East-West
pressPvt.Ltd.
Chapters: 3,4 (4.1 to 4.7), 5,6 (6.5 to 6.8)
Reference Books:
1) Basic Structures in Algebra, Part-I : J.N. Patnaik
2) Matrix Theory and Linear Algebra : I.N. Herstein and D.J. Winter (Ma Chilan Publishing company)
3) First course in Linear algebra : Bhattacharya, Jain and Nagpaul (New Age International)
SEMESTER –II
The paper in English is of 100 (Hundred) percentage marks.
MODULE-I: Communication Skill
Communication: Definition, concept
Channels of Communication: Sender, receiver, channel, message, encoding, decoding, context, feedback
Verbal & Non-Verbal Communication: Spoken & written-advantages & disadvantages
Bias free English,
Formal & informal style.
MODULE-II: Communicative Grammar
Time, Tense & Aspect
Verbs of state & events
Modality
Active & Passive voice
Antonyms, Synonyms, Homonyms, one word substitutions & correction of errors
MODULE-III: Sounds of English
Length of vowels:
Long vowels as in the words feel, food, shoot, card etc.
Short vowels as in the words pen, sun, cut, shut, etc.
Consonants
Stress pattern
Intonation: Rising & Falling.
Text Books:
Effective technical communication by M.A.Rizvi
Reference Books:
Communicative English
Publication.
& Business Communication by R.K.Panda, J.Khuntia, M.Pati, Alok
Communicative Grammar of English Geoffery Leech
MSES 1201 ENVIRONMENTAL STUDIES (3-1-0)
SECOND SEMESTER
Module-I
Concepts of Ecology & Environment: Definition-Environment, Ecology & Ecosystem; Environmental
concepts – Atmosphere, Hydrosphere, Lithosphere & Biosphere, Environmental factors – Abiotic factors
(Climate & Edaphic) & Biotic factors, Environmental gradients & limiting factor.
Concept of Ecosystem & Processes: Type & Structure, Ecosystem Processes – Energy flow, food chain,
food web & ecological pyramids; Biogeochemical cycles – Hydrological cycle(water), gaseous
cycle(carbon & oxygen), sedimentary cycle(nitrogen & sulphur).
Module-II
Population ecology & Ecological succession:
Population ecology: Population density, natality, mortality, population age structure, population growth
curves & carrying capacity.
Ecological succession: Characteristics, types (Hydrosere&Xerosere) & Process.
Environmental Pollution: Water pollution, Noise pollution, Air pollution(source, effect, control measure),
Depletion of ozone layer – cause, effect & control measure, Green House Effects & Global warming, Acid
rain, Biological concentration and biomagnifications, Sewage & sewage treatment.
Module-III
Conservation of natural resources: Natural resources – renewable, non-renewable, abstract resources,
Biodiversity & its conservation, wild wife conservation, pollution control board, Environmental awareness
& mass education.
Text Books:
1. Text book of Environmental studies by A.K.Panigrahy&A.Sahu, SadagranthaMandir
Publishing, Berhampur.
Reference Books:
1.
2.
3.
4.
5.
6.
Fundamentals of Ecology by E.P.Odum
Environmental Engineering by G.Kiely
Fundamentals of Environmental studies by N.K.Tripathy
Environmental Biology by P.D.Sharma
Ecology & Environment by P.D.Sharma
Principles of Environmental Engineering & Science by Davis &Masten
CORE-3
Analysis-I (5-1-0)
(Total Marks: 100)
(Theory: Internal-40 +External-60)
MODULE-I
Ordered field of Real numbers, l.u.b. and g.l.b. completeness of R(Not through Dedkind cuts), complex
numbers, Inequalities, Metric properties of R, limit points, closed sets, open sets, Bolzano-Weirstrass
theorem.
MODULE-II
Convergence of real sequence and series, monotonic sequences, Cauchy Criteria of convergence, limit
superior, limit inferior, Tests of convergence of spaces of positive terms, comparison tests, Ratio test,
Root test, Absolute convergence, Alternating series test.
MODULE-III
Limit and continuity of functions, properties of continuous functions, discontinuities, uniform continuity,
Differentiability of real functions, Higher derivations, Leibnitz theorem, Mean value theorems, Taylor’s
theorem with reminder, Taylor’s series.
MODULE-IV
Functions of several variables, Neighbourhood of points in R2 and R3 , Limit of a function, repeated limits,
continuity, Partial derivatives, differentiability, Partial derivative of higher orders, Derivatives of
composite functions, change of variables, Taylor’s Theorem, Extreme value, Implicit functions
(Statement of implicit function theorem only),Jacobians, derivatives of implicit functions, Lagrange’s
method of multipliers (application without proof).
Text Book:
1) Mathematical Analysis (Wiley Eastern) : S.C. Malik and S.Arora
Chapters: 1 (excluding 4.3 and 4.4), 2,3,4 (upto Art.5 and 10.1, 10.2), 5,6, 15 (upto Art. 10)
Reference Books:
1) Fundamentals of Real Analysis :S.L.Gupta&Nisha Rani
2) Mathematical Analysis-II : Sharma &Vasistha
3) Fundamental of Mathematical Analysis :G.das&S.Pattanayak
CORE-4
Ordinary Differential Equation (4-0-2)
(Total Marks: 100)
Part – I (Marks: 70)
(Theory: Internal-30 +External-40)
MODULE-I
Differential equations and mathematical models.First order and first degree ODE (variables separable
homogeneous, exact, and linear).Equations of first order but of higher degree. Applications of first order
differential equations (Growth, Decay and Chemical Reactions, Heat flow, Oxygen debt, Economics).
MODULE-II
Second order linear equations (homogeneous and non-homogeneous) with constant coefficients, second
order equations with variable coefficients, variation of parameters, method of undetermined coefficients,
equations reducible to linear equations with constant coefficients, Euler’s equation. Applications of
second order differential equations.
MODULE-III
Power series solutions of second order differential equations.Legendre’s Equation and its simple
properties, Bessel’s Equation and Bessel’s Function.
Part-II (Practical Marks: 30)
List of Practicals (Using any software)
Practical/ Lab work to be performed on a Computer.
1. Plotting of second order solution of family of differential equations.
2. Plotting of third order solution of family of differential equations.
3. Growth model (exponential case only).
4. Decay model (exponential case only).
5. Oxygen debt model.
6. Economic model.
7. Vibration problems.
Text Book:
1. J. Sinha Roy and S. Padhy, A Course of Ordinary and Partial Differential Equations, Kalyani
Publishers, New Delhi.
Chapters: 1, 2(2.1 to 2.7), 3, 4(4.1 to 4.7), 5, 7(7.1-7.4)
Reference Books:
1. Martin Braun, Differential Equations and their Applications, Springer International.
2. M. D. Raisinghania-Advanced Differential Equations, S. Chand & Company Ltd., New Delhi.
3. G. Dennis Zill-A First Course in differential Equations with Modeling Applications, Cengage
Learning India Pvt. Ltd.
4. Text Book of Differential Equations : N.M. Kapoor
5. Introductory course in Differential Equations : D.A. Murray
6. S. L. Ross, Differential Equations, John Wiley & Sons, India, 2004.
Other semesters syllabus is under preparation