FOR STUDENTS
ADMITTED
FROM 2010 -2011
MATHEMATICS I & II
(B.E. FIRST YEAR - COMMON FOR ALL BRANCHES)
(For students admitted from 2010-11)
UNIT I
(SOLID GEOMETRY)
Equation of a plane – Equation of a St. line – conditions for a line to lie in a plane –
Conditions for the two lines to intersect – S.D. between two lines – intersection of
three planes – sphere – equation of the tangent plane – cone - cylinder – right circular
cylinder - surfaces of revolution.
UNIT II
(MATRIX THEORY)
Rank of a matrix – Elementary transformation of a matrix - Gauss Jordon method of
finding inverse – Consistency of linear system of equations - Linear and orthogonal
transformations –– Eigenvalues and eigenvectors – Properties of eigenvalues – Cayley
Hamilton theorem (without proof) – Reduction to diagonal form – Reduction of
quadratic form to canonical form.
UNIT III
(LINEAR DIFFERENTIAL EQUATIONS)
Definitions – Complete solution – operator D – Complementary function – Inverse
operator – Particular Integral - Method of variation of parameters - Method of
undetermined coefficients – Equations reducible to linear equations with constant
coefficients: Cauchy's homogeneous linear equation - Legendre's linear equation Linear dependence of solutions - Simultaneous linear equations with constant
coefficients.
UNIT IV
(MULTIPLE INTEGRALS)
Double integrals - Change of order of integration - Double integrals in polar
coordinates - Areas enclosed by plane curves - Triple integrals - Volume of solids Volume as triple integral - Beta function - Gamma function - Relation between Beta
and Gamma functions.
UNIT V
(VECTOR CALCULUS)
Differentiation of vectors - Velocity and acceleration - Scalar and vector point
functions - ∇ applied to scalar point functions : Gradient - ∇ applied to vector
point functions : Divergence and curl - Physical interpretation of divergence and curl
- ∇ applied twice to point functions - ∇ applied to products of point functions Integration of vectors - Line integral - Surfaces - Green's theorem in the plane
(without proof) - Stoke's theorem (without proof) - Volume integral - Gauss
divergence theorem (without proof) .
Remark: Each Unit has to be covered in 12 hours (each of 50 minutes duration).
Questions may be set to test the problem solving ability of the students in the above
topics.
PRESCRIBED TEXT BOOK:
B.S.Grewal, Higher Engineering Mathematics, 40th Edition, Khanna Publishers,
New Delhi, 2007.
REFERENCES
1. Erwin Kreyszig, Advanced Engineering Mathematics, Eighth Edition, John
Wiley & Sons, 1999.
2. Veerarajan, T., Engineering Mathematics Vol. I, 5th Edition, Tata McGraw
Hill, New Delhi, 2008.
3. Kandasamy et al., Engineering Mathematics Vol. I, 5th Edition, S. Chand &
Co., New Delhi, 2002
4. Richard Bronson, Differential Equations, (Schaum's Outline Series),
McGraw Hill Company, 1975.
5. Murry R. Spiegel, Vector Analysis, (Schaums Outline Series) McGraw
Hill Company, 1974.
ENGINEERING MATHEMATICS - III
(B.E. THIRD SEMESTER - COMMON FOR ALL BRANCHES EXCEPT EEE)
(For students admitted from 2009-10)
UNIT I
(ANALYTIC FUNCTIONS)
Introduction - Limit and continuity of f ( z ) - Derivative of f ( z ) - Cauchy-Riemann
equations – Analytic functions – Harmonic functions - Orthogonal system –
Applications to flow problems – Conformal transformation – Standard
transformations: Translation, Magnification and rotation, Inversion and reflection
1
and Bilinear transformation - Special conformal transformations : e z , z 2 , z + , sin z.
z
UNIT II
(COMPLEX INTEGRATION)
Integration of complex functions – Cauchy’s theorem – Cauchy’s integral formula –
Series of complex terms – Taylor’s series – Laurent’s series – Zeros and
Singularities of an analytic function – Residues – Residue theorem – Calculation of
residues – Evaluation of real definite integrals.
UNIT III
(LAPLACE TRANSFORMS)
Introduction - Definition - Existence conditions - Transforms of elementary
functions - Properties of Laplace transforms - - Transforms of derivatives Transforms of integrals - Multiplication by tn - Division by t - Evaluation of
integrals by Laplace transform - Inverse transforms – Other methods of finding
inverse - Convolution theorem (Without proof) - Application to differential
equations.
UNIT – IV
(FOURIER TRANSFORMS)
Introduction – definition – Fourier integrals - Fourier Sine and Cosine integral –
complex forms of Fourier integral - Fourier transform – Fourier sine and Cosine
transforms – properties of Fourier Transforms - Convolution theorem for Fourier
Transforms - Parseval’s identity for Fourier transforms. (without proof).
UNIT V
(Z - TRANSFORM)
Introduction - Definition – standard Z –transforms – Linearity property – Damping
rule –standard results – Shifting rules – Initial and final value theorems – inverse Z –
transforms – Convolution theorem – Evaluation of inverse transforms – Application
to difference equations.
Remark: Each Unit has to be covered in 12 hours (each of 50 minutes duration).
Questions may be set to test the problem solving ability of the students in the above
topics.
PRESCRIBED TEXT BOOK:
B.S.Grewal, Higher Engineering Mathematics, 40th Edition, Khanna Publishers,
New Delhi, 2007.
REFERENCES
1. Erwin Kreyszig, Advanced Engineering Mathematics, Eighth Edition, John
Wiley & Sons, 1999.
2. Veerarajan, T., Engineering Mathematics, Tata McGraw Hill, New Delhi,
2008.
3. Ronald N. Bracewell, The Fourier transform and its applications, McGraw
Hill Company, 1986.
4. John H. Mathews, Russel W. Howell, Complex Analysis for Mathematics
and Engineering, Third Edition, Narosa Publishing House, 1998.
5. Murry R. Spiegel, Complex Variables, (Schaum's Outline Series), McGraw
Hill 1981.
ENGINEERING MATHEMATICS - IV
(B.E. FOURTH SEMESTER - COMMON FOR ALL BRANCHES EXCEPT EEE, B.TECH. IT)
(For students admitted from 2009-10)
UNIT I
(FOURIER SERIES)
Introduction - Euler’s Formulae – Condition for Fourier expansion – Functions having points of
discontinuity – Change of interval – Odd and Even functions - Half-Range series – Parseval’s
formula.
UNIT II
(PARTIAL DIFFERENTIAL EQUATIONS)
Introduction - Formation of PDE – Solution of PDE – Equations solvable by direct integration –
Linear equations of first order - Homogeneous linear equations with constant coefficients –
Complementary Function –Particular Integral – solution of Homogeneous linear equation of any
order – Non-homogeneous linear equations.
UNIT III
(APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS - I )
Introduction - Method of separation of variables – Vibration of a stretched string – Wave
Equation – D’Alembert’s solution of the wave equation.
UNIT – IV
(APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS - II )
One dimensional heat flow equation – Two dimensional heat flow equation – Solution of
Laplace equation – Temperature distribution in long plates.
UNIT – V
(CALCULUS OF VARIATIONS)
Introduction – Functionals – solution of Euler’s equation – geodesic – isoperimetric problems –
several dependant variables – functionals involving higher order derivatives – Rayleigh-Ritz
method.
Remark: Each Unit has to be covered in 12 hours (each of 50 minutes duration). Questions
may be set to test the problem solving ability of the students in the above topics.
PRESCRIBED TEXT BOOKS
B.S.Grewal, Higher Engineering Mathematics, 40th Edition, Khanna Publishers, New Delhi,
2007.
REFERENCES
1. Erwin Kreyszig, Advanced Engineering Mathematics, Eighth Edition, John Wiley &
Sons, 1999.
2. C.Ray Wylie, Louis C. Barrett, Advanced Engineering Mathematics, Sixth Edition,
McGraw Hill Publishing Company,1995.
3. Ockendon, Howison, Lacey, Movchan, Applied Partial Differential Equations,
Oxford University Press, 1999.
4. T. Veerarajan, Engineering Mathematics, (for semester III), 3rd Edition, Tata McGrawHill, New Delhi, 2005.
NUMERICAL METHODS AND STATISTICS
(BE FIFTH/SIXTH SEMESTER - COMMON FOR ALL BRANCHES EXCEPT EEE)
(For students admitted from 2010-11)
(Review Unit)
(COLLECTION AND ANALYSIS OF DATA)
Classification and tabulation of data - Frequency tables - Graphical representation Measures of central tendency : Averages, mean, median, mode, Geometric and harmonic
means - Measures of dispersion : Range, quartile deviation, Mean deviation, Standard
deviation - Relative distribution - Moments - Skewness - Kurtosis - Linear correlation Coefficient of correlation - Grouped data : calculation of correlation coefficient - Rank
correlation - Linear regression - Regression lines.
UNIT I
(SOLUTION OF ALGEBRAIC, TRANSCENDENTAL, AND SIMULTANEOUS
EQUATIONS)
Introduction – Bisection method - The method of False position - Newton-Raphson Iterative
method. Solution of linear simultaneous equations: Direct methods of solution – Gauss
elimination method - Gauss – Jordan method – Iterative methods of solution : Jacobi’s method ,
Gauss – Seidel method.
UNIT II
(INTERPOLATION, NUMERICAL DIFFERENTIATION AND INTEGRATION)
Finite differences – Newton’s interpolation formulae – Interpolation with unequal intervals –
Lagrange’s formula ; Newton’s divided difference formula – Inverse interpolation – Numerical
differentiation – Maxima and Minima of Tabulated functions - Numerical integration :
Trapezoidal rule - Simpson’s 1/3rd rule - Simpson’s 3/8th rule.
UNIT III
(NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS)
Numerical solution of ODE : Introduction –– Euler’s method – Modified Euler’s method –
Runge’s method – Runge-Kutta method – Predictor-corrector method : Milne’s method.
UNIT IV
(NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS)
Numerical solution of PDE: Introduction – Classification of second order equations – Finite
difference approximation to derivatives – Elliptic equations – Solution of Laplace’s equation –
Solution of Poisson’s equation – Parabolic equations – Solution of heat equation – Hyperbolic
equations – Solution of wave equation.
UNIT V
(SAMPLING THEORY)
Procedure of testing hypothesis - Standard error - Sampling distribution - Tests of significance
for attributes - Tests of significance for large and for small samples - Z-test of significance of
coefficient of correlation - Conditions for applying chi square test - Uses of chi square test - ChiSquare test for specified value of population variance - The variance ratio test - Assumptions in
F-test - Applications of F-test - Analysis of variance - Analysis of variance in two way
classification model.
PRESCRIBED TEXT BOOKS
1. B.S.Grewal, Higher Engineering Mathematics, 40th Edition, Khanna Publishers, New
Delhi, 2007.
2. S.P. Gupta, Statistical Methods, 28th Edition, Sultan Chand and Sons., New Delhi, 1997.
REFERENCES
1. Ward Chenny, David Kincaid, Numerical Mathematics and Computing, Fourth Edition,
Brookes and Cole Publishing Company, 1999.
2. George W. Snedecor, William G. Cocharan, Statistical Methods, Eighth Edition, Affiliated
East West Press, 1994.
DISCRETE MATHEMATICS
(B.E. FOURTH SEMESTER - COMPUTER SCIENCE ENGINEERING)
(For students admitted from 2009-10)
UNIT I
(LOGIC)
Logic – propositional equivalences predicates and quantifiers –sets – set operations – functions
– the growth of functions.
UNIT II
(MATHEMATICAL REASONING)
Methods of proof – Mathematical Induction – recursive definitions – recursive algorithms –
program correctness.
UNIT III
(RELATIONS)
Relations and their properties – n-ary relations and their applications – representing relations
- Closures of relations – equivalence relations – partial orderings.
UNIT IV
(BOOLEAN ALGEBRA)
Boolean functions – representing Boolean functions – Logic gates – minimization of circuits.
UNIT V
(GRAPHS)
Introduction to graphs – graph terminology – representing graphs and graph isomorphism –
connectivity – Euler and Hamilton path – shortest path problems – planar graphs – graph
coloring.
----Remark: Each Unit has to be covered in 12 hours (each of 50 minutes duration). Questions
may be set to test the problem solving ability of the students in the above topics.
PRESCRIBED TEXT BOOK
Kenneth H. Rosen, Discrete Mathematics and its Applications, 6th Edition, Tata McGraw Hill,
New Delhi. (2007).
REFERENCES
1. B. Kolman, R.C. Busby and S. Ross, Discrete Mathematical Structures for Computer
Science, Fifth Edition, Prentice Hall of India, New Delhi, 2006.
2. Susanna S. Epp, Discrete Mathematics with applications, Second Edition, Brookes/Cole
Publishing Company, 1995.
3. J.P.Trembley, R.Monahor, Discrete Mathematical Structures with Applications to Computer
Science, Tata McGraw Hill, New Delhi, 1997.
4. S. Lipschutz, M. Lipson, Discrete Mathematics, Second Edition, Schaum's Outline Series,
Tata Mc Graw Hill, 1999.
5. Stephen A. Wiitala, Discrete mathematics - A Unified Approach, McGraw Hill Company,
1987.
GRAPH THEORY
(BE - COMPUTER SCIENCE ENGINEERING)
(For students admitted from 2009-10)
UNIT I
(PATHS, TREES, AND CIRCUITS)
Graphs - Subgraphs - Walks, Paths, Circuits - Connected graphs, Disconnected graphs,
Components - Euler graphs - Operations on graphs - Hamiltonian paths and circuits - Trees
- Properties of trees - Pendant vertices, Distance and centers in a Tree - Rooted and binary trees Spanning trees - Fundamental circuits - Spanning trees in a weighted graph : Kruskal's algorithm.
UNIT II
(CUT SETS, PLANAR AND DUAL GRAPHS)
Cut sets - Properties of cut sets - Fundamental circuits and cutsets - Connectivity and
separability - Planar graphs - Kuratowski's two graphs - Representations and detection of
plalar graphs - Geometric and combinatorial duals.
UNIT III
(MATRIX REPRESENTATION AND COLORING)
Incidence matrix - Circuit matrix - Application to a switching network - Cutset matrix - Path
matrix - Adjacency matrix - Chromatic number - Chromatic Partitioning - Chromatic
polynomial - Matchings - Coverings - Five color theorem.
UNIT IV
(DIRECTED GRAPHS)
Types of digraphs - Digraphs and relations - Directed paths and connectedness - Euler
digraphs - Trees with directed edges - Fundamental circuits in a digraphs - Adjancency
matrix of a digraph - Paired comparisons and tournaments.
UNIT V
(GRAPH THEORETIC ALGORITHMS)
Computer representation of a graph - Basic algorithms : connectedness and components,
spanning tree, fundamental circuits, cut vertices and separability, directed circuits- Shortest
path algorithms - Depth first search on a graph - Planarity testing - Isomorphism.
------Remark: Each Unit has to be covered in 12 hours (each of 50 minutes duration). Questions
may be set to test the problem solving ability of the students in the above topics.
PRESCRIBED TEXT BOOK
Narsingh Deo, Graph Theory (With Applications to Engineering and Computer Science),
Prentice Hall of India, New Delhi, 2002.
REFERENCES
1. Harary, Graph Theory, Narosa Publishing House, New Delhi, 1998.
2. Douglas B. West, Introduction to Graph Theory, Prentice Hall of India, 1999.
3. Robin J. Wilson, Introduction to Graph Theory, Longman Ltd., 2000.
4. K.R.Parthasarathy, Basic Graph Theory, Tata McGraw Hill Publishing Company, 1994.
PROBABILITY THEORY AND STOCHASTIC PROCESSES
(B.E. FIFTH SEMESTER – ECE AND E&I )
(For students admitted from 2010-11)
UNIT I Probability Theory
Discrete distributions:- Binomial, Poisson, Geometric, Negative Binomial
Continuous distributions: - Normal,, Gamma and Exponential distributions
UNIT II: Stochastic Processes
Introduction- Stationary processes-Martingales-Markov chains- Classification of
states and chains- Determination of higher transition probabilities- Stability of a Markov system.
UNIT III Poisson processes
Introduction- Generalisation – Birth and death process- Continuous time Markov
chains – Randomization – Erlang processes.
UNIT IV : Brownian motion and Renewal processes
Introduction- Wiener process – Kolmogorov equations – Time distribution –
Ornstein-Uhlenbeck process, Renewal process in continuous time -Renewal Equation
UNIT V : Stationary processes and Time series
Introduction – Models of time series – power spectrum – statistical analysis of
time series. M/M/1 queuing system in steady state
Text Book:
1. Gupta S.C and Kapoor.V.K , “Fundamental of Mathematical Statistics”, S.Chand
and Company, New Delhi (1999). (For UNIT I )
2. J.Medhi, “Stochastic processes”, Wiley Eastern Limited, New Delhi, 1994. (UNITS
II – V)
References :
1.
Peebles P.Z.Jr, “Probability, Random Variables and Random Signal Principles
(Fourth ed)”, Tata Mc.Graw Hill publications, New Delhi .(2002)
2.
T. Veerarajan, “Probability, Statistics and Random Processes (Second ed)” – TataMcGraw Hill Publication, New Delhi. (2006)
APPLIED STATISTICS AND PROBABILITY
(B.TECH. FOURTH SEMESTER)
(For students admitted from 2009 - 10)
UNIT – I
(PROBABILITY)
Sample Spaces and Events: Random experiments – samples spaces – events. Interpretation :
Introduction – axioms of probability – addition rules – conditional probability – multiplication
and total probability rules: Multiplication rule – total probability rule – independence – Baye’s
theorem – random variables.
UNIT – II
(DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS)
Discrete random variables – probability mass functions – cumulative distribution functions –
mean and variance of discrete random variable – discrete uniform distributions – binomial
distribution – geometric and negative binomial distribution: geometric distribution –
Hypergeometric Distribution – Poisson distribution.
UNIT – III
(CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS)
Continuous random variables – probability density function – cumulative distribution – mean
and variance of a cont random variables – continuous uniform distribution – normal distributions
– exponential distribution – Weibull distribution.
UNIT – IV
(JOINT PROBABILITY DISTRIBUTIONS)
Two discrete random variables - Joint probability distribution – marginal probability distribution
– conditional probability distribution – independence. Two continuous random variables: Joint
probability distribution – marginal probability distribution – conditional probability distribution
– independence. Covariance and Correlation.
UNIT – V
(DESIGN AND ANALYSIS OF SINGLE FACTOR EXPERIMENTS)
Introduction : Statistical hypothesis – general procedure for hypothesis test. Designing Engg
experiments – The completely randomized single factor experiment – The analysis of variance –
multiple comparisons following ANOVA. Randomized block design – design and statistical
analysis – multiple comparisons.
Remark: Each Unit has to be covered in 12 hours (each of 50 minutes duration). Questions
may be set to test the problem solving ability of the students in the above topics.
TEXT BOOK:
Douglas C. Montgomery and George C. Runger, Applied Statistics and Probability for
Engineers, Third Edition, John Wiley & Sons, Inc, 2003, India.
REFERENCES:
1. Kishore S. Trivedi, Probability and Statistics with Reliability, Queueing and Computer
Science Applications, Prentice Hall of India, 1996.
2. Richard Isaac, The Pleasures of Probability, Springer Verlag, 1995.
3. Murry R.Spiegel, Larry J. Stephens, Statistics, Third Edition (Schaum's Outline Series),
McGraw Hill Company, 1999.
INTRODUCTION TO AUTOMATA THEORY
(B.E. SIXTH SEMESTER - COMPUTER SCIENCE ENGINEERING)
(For students admitted from 2009-10)
UNIT I
(FINITE AUTOMATA)
Deterministic finite acceptors: Deterministic finite acceptors and transition graphs –
languages and DFA’s – Regular languages - Non deterministic finite accepters - Definition of
NFA - Equivalence of deterministic and non deterministic finite acceptors – reduction of the
number of states in finite automata.
UNIT II
(REGULAR LANGUAGES AND REGULAR GRAMMAR)
Regular expressions: Formal definition of RE – languages associated with RE - Connection
between regular expressions and regular languages – closure properties of regular languages Identifying some non regular languages using pumping lemma.
UNIT III
(CONTEXT FREE LANGUAGES, SIMPLIFICATIONS AND NORMAL FORMS)
Context free grammars - Parsing and ambiguity - Context free grammars and programming
languages - Simplifications - Two normal forms.
UNIT IV
(PUSHDOWN AUTOMATA AND PROPERTIES OF CFL)
Non deterministic pushdown automata - PA and CFL - Deterministic PA and deterministic
CFL - Properties of CFL - Decision algorithms - A pumping lemma for CFL - A pumping
lemma for linear languages.
UNIT V
(TURING MACHINES)
The standard turing machine - Minor variations on the turing machine theme - Non
deterministic turing machines - A universal turing machine - linear bounded automata –
Hierarchy of formal languages and automata.
Remark: Each Unit has to be covered in 12 hours (each of 50 minutes duration). Questions
may be set to test the problem solving ability of the students in the above topics.
PRESCRIBED TEXT BOOK
Peter Linz, An introduction to formal languages and automata, Fourth Edition, Narosa
Publishing House, New Delhi. (2006).
REFERENCES
1. John E.Hopcroff, Jeffery D.Ullman, Introduction to Automata theory, Languages
and Computation, Narosa Publishing House.
2. J.C.Martin, Introduction to languages and the Theory of Computation, Tata McGraw
Hill Publishing Company Ltd.)
RESOURCE MANAGEMENT TECHNIQUES
(B.E. COMPUTER SCIENCE SEVENTH SEMESTER)
(For students admitted from 2009-10)
UNIT I
(LINEAR PROGRAMMING AND SIMPLEX METHOD)
Mathematical formulation of the problem - Graphical solution method - Exceptional cases General linear programming problem - Canonical and standard forms of linear programming
problem - The simplex method - Computational procedure : The simplex algorithm Artificial variable techniques : Big M method - problem of degeneracy.
UNIT II
(TRANSPORTATION, ASSIGNMENT AND ROUTING PROBLEMS)
Mathematical formulation of the transportation problem - Triangular basis - Loops in a
transportation table - Finding initial basic feasible solution (NWC, LCM and VAM methods) Moving towards optimality - Degeneracy in transportation problems- Transportation algorithm
(MODI method) - Unbalanced transportation problems - Assignment algorithm : Hungarian
assignment method - Routing problems : Travelling salesman problem.
UNIT III
(GAME THEORY)
Two person zero sum games - Maxim in Minimax principle - Games without saddle points
(Mixed strategies) - Solution of 2 X 2 rectangular games - Graphical method - Dominance
property - Algebraic method for m x n games - Matrix oddments method for m x n games.
UNIT IV
(REPLACEMENT AND SEQUENCING PROBLEMS)
Replacement of equipment or asset that deteriorates gradually - Replacement of equipment
that fails suddenly - Recruitment and promotion problem - Problem of sequencing - Problems
with n jobs and 2 machines - Problems with n jobs and k machines - Problems 2 jobs and k
machines.
UNIT V
(NETWORK MODELS)
Network and basic components - Rules of network construction - Time calculations in networks
- Critical path method (CPM) - PERT - PERT calculations - Negative float and negative Slack Advantages of network (PERT/CPM) - Project Cost - Time Cost Optimization Algorithm Linear Programming formulation - Precedence planning - Updating - Resource allocation
Scheduling.
Remark: Each Unit has to be covered in 12 hours (each of 50 minutes duration). Questions
may be set to test the problem solving ability of the students in the above topics.
PRESCRIBED BOOK
Kanti Swarup, P.K.Gupta and Man Mohan, Operations Research, Eighth Edition, Sultan Chand
& Sons, New Delhi, 1999.
REFERENCES
1. H.A.Taha, Operations Research, Sixth Edition, Mac Millen Ltd.,
2. Richard Bronson, Operations Research, (Schaum's Outline Series, McGraw Hill Company,
1982.
3. S.Hillier and J.Liebermann, Operations Research, Sixth Edition, Mc Graw Hill Company,
1995.
4. J.K.Sharma, Operation Research (Theory and Applications), Mac Millen Ltd., 1997.
5. Barry Render, Ralph M. Stair, Allynan Bacon, Quantitative Analysis for Management,
Fifth Edition, Boston, 1994.