MA 101
Mathematics-I
First Semester ( All Branch )
L
3
1
0
T
P
C
8
Differential Calculus :
Successive differentiation, Leibnitz’s theorem & its
application. Indeterminate forms,
L. Hospital’s Rules. Rolle’s Theorem, Lagrange’s Mean value theorem, Taylor’s &
Maclaurin’s theorems with Lagrange’s form of remainder for a function of one variable.
Curvature, radius & centre of curvature for Cartesian and polar curves.. Partial
differentiation, change of variables, Euler’s theorem & Jacobian.
Integral Calculus :
Reduction Formulae. Asymptotes for Cartesian and polar curves. Curve tracing. Area & length of
plane curves. Volume & surface area of solids of revolution (for Cartesian and polar curves).
Differential Equation :
Solution of ordinary differential equations of first order & of first degree: Homogeneous
equation, Exact differential equation, Integrating factors, Leibnitz’s linear equation,
Bernoulli’s equation.
Differential equation of first order but of higher degree, Clairaut’s equation. Differential
equations of second & higher order with constant coefficients. Homogeneous Linear
equations.
Reference Books:
1. Differential Calculus
Das & Mukherjee
U.N. Dhur & Sons Pvt. Ltd.
2. Integral Calculus
Das & Mukherjee
U.N. Dhur & Sons Pvt. Ltd.
3. Elementary Engineering Mathematics
4. Engineering Mathematics-II
B.S. Grewal
Santi Narayan
Khanna Publisher
S. Chand & Co.
MA 102
Mathematics-II
Second Semester ( All Branch )
L
T
P
C
3
1
0
8
Matrices :
Rank of a matrix , Elementary transformations, Consistency and solutions of a system of
linear equations by matrix methods .Eigen values & eigen vectors. Caley-Hamilton’s
theorem & its applications.
Solid geometry :
Straight lines. Shortest distance between skew lines . Sphere , cone, cylinder and conicoid .
Infinite & Fourier Series:
Convergence of infinite series & simple tests of convergence . Fourier series in any interval .Half
range sine & cosine series .
Complex Analysis:
Function of a complex variable, Analytic functions , Cauchy-Reimann equations, Complex line
integral , Cauchy’s theorem , Cauchy’s Integral formula. Singularities and residues, Cauchy’s
Residue theorem and its application to evaluate real integrals.
Differential calculus :
Taylor’s & Maclaurin’s theorems with Lagrange’s form of remainder for a function of
two
variables, Expansions of functions of two variables . Errors & approximations. Extreme values of
functions of two & more variables
.
.
Reference Books:
1. Matrices
2. Solid Geometry
3. Laplace Transforms
4. Higher Engineering Mathematics
Frank Ayres
Santi Narayan
M.R.Spiegel
B.S. Grewal
5. Engineering Mathematics
Bali & Iyengar
6..Advanced Mathematical Analysis
Malik & Arrora
Mc Graw Hills
S. Chand & Co.
Mc Graw Hills
Khanna Publisher
Laxmi Publications Ltd.
S. Chand & Co.
MA 201
Mathematics-III
Third Semester ( All Branch )
L
3
1
0
T
P
C
8
Integral & Vector Calculus :
Double & triple integrals, Beta & Gamma functions . Differentiation of vector functions of
scalar variables. Gradient of a scalar field , Divergence & Curl of a vector field and their
properties, directional derivatives. Line & surface integrals. Green’s theorem , Stokes’
theorem & Gauss’ theorem both in vector & Cartesian forms ( statement only) with
simple applications.
Integral transforms :
Laplace transform : Transform of elementary functions , Inverse Laplace transforms. Solution of
ordinary differential equation using Laplace transform.
Fourier transforms: Definition, Fourier sine and cosine transforms, properties, relation between
Fourier and Laplace transforms.
Z-transform: Definition, standard z-transforms, properties, initial and final value theorems,
convolution theorem. Inverse z-transform, application to difference equation.
Partial Differential Equation:
Formation of partial differential equations (PDE), Solution of PDE by direct integration.
Lagrange’s linear equation . Non-linear PDE of first order. Method of separation of
variables. Heat, Wave & Laplace’s equations (Two dimensional Polar & Cartesian Coordinates).
Reference Books:
1.Vector Analysis
Frank Ayres
2.Advanced Mathematical Analysis
Malik & Arrora
Mc Graw Hills
S. Chand & Co.
3. Advanced Differential Equations
M.D.Rai Singhaniya
4. Complex Analysis.
M.R.Spiegel.
5. Higher Engineering Mathematics
B.S. Grewal
6. Engineering Mathematics
MA 202
Bali & Iyengar
S. Chand & Co.
Schuam’s out line Series
Khanna Publisher
Laxmi Publications Ltd.
Probability Theory & Stochastic Processes
Third Semester ( ET & CS Branch )
3
1
L
T
0
8
P
C
Probability :
Introduction, joint probability, conditional probability , total probability, Baye’s theorem , multiple events,
independent events.
Random Variable:
Introduction, discrete and continuous random variables, distribution function , mass / density function ,
Binomial, Poisson , Uniform, Exponential, Gaussian and Gamma random variables, conditional
distribution and density function, function of a random variable .
Bivariate distributions, joint distribution and density, marginal distribution and density functions,
conditional distribution and density, statistical independence, distribution and density of a sum of random
variables.
Operation on one Random variable:
Expected value of a random variable , conditional expected value , moments about the origin , central
moments , moment generating function, variance , skewness and Kurtosis,covariance, correlation and
regression, monotonic and non-monotonic transformation of a random variable (both discrete and
continuous).
Stochastic Processes:
Definition of a stochastic process , classification of states, Random walk, Markov chains, poisson
process, Wiener process ,stationary and independence, distribution and density functions, statistical
independence, Kolmogorov equations, first order stationary processes, second order and wide sense
stationary, time averages and ergodicity , correlation functions, covariance function.
Spectral characteristics of random processes:
Power density spectrum and its properties, bandwidth of the power density spectrum, relationship
between power spectrum and autocorrelation function, cross power spectral density and its properties.
Noise:
White Noise , shot noise, thermal noise, noise equivalent bandwidth.
Reference Books:
1. An Introduction to Probability Theory and its Applications (Vol. 1 & II)-W Feller (John Wiley & Sons).
2. Probability , Random
Variables & Stochastic processes
3. Probability & Stochastic processes
Papoulis
McGraw Hill
C.W.Helstrom
McMillan, New York
A.Leon-Garcia
Addison Wisley
for engineers
4. Probability & Random processes
for electrical engineers
5. The Theory of Stochastic Processes – D R Cox and H D Miller ( Chapman & Hall Ltd.)
6. An Introduction to Probability Theory and its Applications (Vol. 1 & II)-W Feller (John Wiley & Sons).
MA 203
Discrete Mathematics
Fourth Semester ( CS Branch )
L T
3
1
P C
0
8
Boolean algebra:- Binary relation , equivalence relation , Partial order relations, PO-set, Totally
ordered set, Maximal and Minimal elements. Well ordered set. Lattice, bounded lattices,
sublattice, distributive lattice, modular lattice, irreducible elements, complemented lattice.
Boolean Algebra, Boolean functions & expression ,
minimization of
Boolean functions &
expressions.(Algebraic method and Karnaugh map method)
Logic gates :- Introduction, Design of digital circuits
and application of Boolean algebra in
switching circuits.
Graph theory:-. Introduction, Basic definition, incidence and degree, adjacency, paths and
cycles, matrix representation of graphs( directed and non-directed). Digraphs. Trees.
Mathematical Logic:
Statement Calculus- sentential connectives, Truth tables, Logical equivalence, Deduction
theorem.
Predicate Calculus- Symbolizing everyday language., validity and consequence.
Modern Algebra:
Algebraic structures, Semi group, Monoid, Group, Cyclic group, Subgroup, Normal subgroup,
Quotient group, Homomorphism of groups.
Ring, Integral domain, Field. Vector space , Linear dependence & independence . Basis &
Dimension.
Recurrence relations & Generating functions.
Reference Books:
1. Set Theory and Logic
R.R Stoll.
2. Discrete Mathematical Structures
G. S. Rao
3.Discrete Mathematics and Structures
S. Balgupta
4. Modern Algebra
5. Graph theory
S. Chand.& Co.
New age International
Laxmi Publications
Herstein
New age International
Harary
Narosa Publishing House
MA 204
Mathematics-IV
Fourth Semester ( CE & ME Branch )
L
2
1
T
0
P
C
6
Statistics :
Measures of central tendency, dispersion, moments, skewness & kurtosis.
Probability density function, distribution function, Binomial, Poisson & Normal distributions.
Curve fitting- Method of Least squares, fitting of straight line & parabola.
Correlation & Regression- determination of correlation & regression coefficients &
determination of lines of regression.
Numerical Analysis:
Finite differences, Interpolation & extrapolation. Newton’s forward & backward formulae,
Lagrange’s formula & Newton’s divided difference formula for unequal intervals.(statements &
applications of the formulae only)
Numerical differentiation & integration, Trapezoidal rule, Simpson’s 1/3rd & 3/8th rules.
Numerical solution of transcendental & algebraic equations- Method of Iteration &
Newton-Raphson method.
Solution of system of linear equations :
Gaussian elimination method, Gauss Seidal method, LU decomposition & Cholesky
decomposition.& their application in solving system of linear equations, matrix inversion by
Gauss-Jordan method .
Reference Books :
1. Numerical Mathematical Analysis James B Scarborough
2. Numerical Analysis
3. Finite Differences
B.S. Grewal
H.C. Sexena
Oxford & IBH Publishing
Khanna Publishers
S. Chand & Co.
& Numerical Analysis
4. Probability & Statistics
M.R. Spiegel
Mc Graw Hill
5. Engineering Mathematics
Bali & Iyengar
Laxmi Publications Ltd.
MA 205
Mathematics-IV
Fourth Semester ( CE & ME Branch )
L
T
P
C
2
1
0
6
Statistics :
Measures of central tendency, dispersion, moments, skewness & kurtosis.
Introduction to probability. Additive & multiplicative Laws of probability, conditional
probability, independent events. Probability density function, distribution function,
Binomial, Poisson & Normal distributions.
Curve fitting- Method of Least squares, fitting of straight line & parabola.
Correlation & Regression- determination of correlation & regression coefficients &
determination of lines of regression.
Numerical Analysis:
Finite differences, Interpolation & extrapolation. Newton’s forward & backward formulae,
Lagrange’s
formula
&
Newton’s
divided
difference
formula
for
unequal
intervals.(statements & applications of the formulae only)
Numerical differentiation & integration, Trapezoidal rule, Simpson’s 1/3rd & 3/8th rules.
Numerical solution of transcendental & algebraic equations- Method of Iteration &
Newton-Raphson method.
Solution of system of linear equations :
Gaussian elimination method with pivoting strategies , Gauss Seidal method, LU
decomposition & Cholesky
decomposition. , Band matrices & Tri-diagonal matrices. &
their application in solving system of linear equations, matrix inversion by Gauss-Jordan
method .
Reference Books :
1. Numerical Analysis
B.S. Grewal
Khanna Publishers
2. Finite Differences
H.C. Sexena
S. Chand & Co.
M.R. Spiegel
Mc Graw Hill
& Numerical Analysis
3. Probability & Statistics
MA 101
Mathematics-I
First Semester ( All Branch )
L
3
1
0
T
P
C
8
Differential Calculus :
Successive differentiation, Leibnitz’s theorem & its
application. Indeterminate forms,
L. Hospital’s Rules. Rolle’s Theorem, Lagrange’s Mean value theorem, Taylor’s &
Maclaurin’s theorems with Lagrange’s form of remainder for a function of one variable.
Curvature, radius & centre of curvature for Cartesian and polar curves.. Partial
differentiation, change of variables, Euler’s theorem & Jacobian.
Integral Calculus :
Reduction Formulae. Asymptotes for Cartesian and polar curves. Curve tracing. Area & length of
plane curves. Volume & surface area of solids of revolution (for Cartesian and polar curves).
Differential Equation :
Solution of ordinary differential equations of first order & of first degree: Homogeneous
equation, Exact differential equation, Integrating factors, Leibnitz’s linear equation,
Bernoulli’s equation.
Differential equation of first order but of higher degree, Clairaut’s equation. Differential
equations of second & higher order with constant coefficients. Homogeneous Linear
equations.
Reference Books:
1. Differential Calculus
Das & Mukherjee
U.N. Dhur & Sons Pvt. Ltd.
2. Integral Calculus
Das & Mukherjee
3. Elementary Engineering Mathematics
4. Engineering Mathematics-II
U.N. Dhur & Sons Pvt. Ltd.
B.S. Grewal
Santi Narayan
Khanna Publisher
S. Chand & Co.
MA 102
Mathematics-II
Second Semester ( All Branch )
L
T
P
C
3
1
0
8
Matrices :
Rank of a matrix , Elementary transformations, Consistency and solutions of a system of
linear equations by matrix methods .Eigen values & eigen vectors. Caley-Hamilton’s
theorem & its applications.
Solid geometry :
Straight lines. Shortest distance between skew lines . Sphere , cone, cylinder and conicoid .
Infinite & Fourier Series:
Convergence of infinite series & simple tests of convergence . Fourier series in any interval .Half
range sine & cosine series .
Complex Analysis:
Function of a complex variable, Analytic functions , Cauchy-Reimann equations, Complex line
integral , Cauchy’s theorem , Cauchy’s Integral formula. Singularities and residues, Cauchy’s
Residue theorem and its application to evaluate real integrals.
Differential calculus :
Taylor’s & Maclaurin’s theorems with Lagrange’s form of remainder for a function of
two
variables, Expansions of functions of two variables . Errors & approximations. Extreme values of
functions of two & more variables
.
.
Reference Books:
1. Matrices
2. Solid Geometry
3. Laplace Transforms
4. Higher Engineering Mathematics
Frank Ayres
Santi Narayan
M.R.Spiegel
B.S. Grewal
5. Engineering Mathematics
Bali & Iyengar
6..Advanced Mathematical Analysis
Malik & Arrora
Mc Graw Hills
S. Chand & Co.
Mc Graw Hills
Khanna Publisher
Laxmi Publications Ltd.
S. Chand & Co.
MA 201
Mathematics-III
Third Semester ( All Branch )
L
3
1
0
T
P
C
8
Integral & Vector Calculus :
Double & triple integrals, Beta & Gamma functions . Differentiation of vector functions of
scalar variables. Gradient of a scalar field , Divergence & Curl of a vector field and their
properties, directional derivatives. Line & surface integrals. Green’s theorem , Stokes’
theorem & Gauss’ theorem both in vector & Cartesian forms ( statement only) with
simple applications.
Integral transforms :
Laplace transform : Transform of elementary functions , Inverse Laplace transforms. Solution of
ordinary differential equation using Laplace transform.
Fourier transforms: Definition, Fourier sine and cosine transforms, properties, relation between
Fourier and Laplace transforms.
Z-transform: Definition, standard z-transforms, properties, initial and final value theorems,
convolution theorem. Inverse z-transform, application to difference equation.
Partial Differential Equation:
Formation of partial differential equations (PDE), Solution of PDE by direct integration.
Lagrange’s linear equation . Non-linear PDE of first order. Method of separation of
variables. Heat, Wave & Laplace’s equations (Two dimensional Polar & Cartesian Coordinates).
Reference Books:
1.Vector Analysis
Frank Ayres
2.Advanced Mathematical Analysis
Malik & Arrora
Mc Graw Hills
S. Chand & Co.
3. Advanced Differential Equations
M.D.Rai Singhaniya
4. Complex Analysis.
M.R.Spiegel.
5. Higher Engineering Mathematics
B.S. Grewal
6. Engineering Mathematics
MA 202
Bali & Iyengar
S. Chand & Co.
Schuam’s out line Series
Khanna Publisher
Laxmi Publications Ltd.
Probability Theory & Stochastic Processes
Third Semester ( ET & CS Branch )
3
1
L
T
0
8
P
C
Probability :
Introduction, joint probability, conditional probability , total probability, Baye’s theorem , multiple events,
independent events.
Random Variable:
Introduction, discrete and continuous random variables, distribution function , mass / density function ,
Binomial, Poisson , Uniform, Exponential, Gaussian and Gamma random variables, conditional
distribution and density function, function of a random variable .
Bivariate distributions, joint distribution and density, marginal distribution and density functions,
conditional distribution and density, statistical independence, distribution and density of a sum of random
variables.
Operation on one Random variable:
Expected value of a random variable , conditional expected value , moments about the origin , central
moments , moment generating function, variance , skewness and Kurtosis,covariance, correlation and
regression, monotonic and non-monotonic transformation of a random variable (both discrete and
continuous).
Stochastic Processes:
Definition of a stochastic process , classification of states, Random walk, Markov chains, poisson
process, Wiener process ,stationary and independence, distribution and density functions, statistical
independence, Kolmogorov equations, first order stationary processes, second order and wide sense
stationary, time averages and ergodicity , correlation functions, covariance function.
Spectral characteristics of random processes:
Power density spectrum and its properties, bandwidth of the power density spectrum, relationship
between power spectrum and autocorrelation function, cross power spectral density and its properties.
Noise:
White Noise , shot noise, thermal noise, noise equivalent bandwidth.
Reference Books:
1. An Introduction to Probability Theory and its Applications (Vol. 1 & II)-W Feller (John Wiley & Sons).
2. Probability , Random
Variables & Stochastic processes
3. Probability & Stochastic processes
Papoulis
McGraw Hill
C.W.Helstrom
McMillan, New York
A.Leon-Garcia
Addison Wisley
for engineers
4. Probability & Random processes
for electrical engineers
5. The Theory of Stochastic Processes – D R Cox and H D Miller ( Chapman & Hall Ltd.)
6. An Introduction to Probability Theory and its Applications (Vol. 1 & II)-W Feller (John Wiley & Sons).
MA 203
Discrete Mathematics
Fourth Semester ( CS Branch )
L T
3
1
P C
0
8
Boolean algebra:- Binary relation , equivalence relation , Partial order relations, PO-set, Totally
ordered set, Maximal and Minimal elements. Well ordered set. Lattice, bounded lattices,
sublattice, distributive lattice, modular lattice, irreducible elements, complemented lattice.
Boolean Algebra, Boolean functions & expression ,
minimization of
Boolean functions &
expressions.(Algebraic method and Karnaugh map method)
Logic gates :- Introduction, Design of digital circuits
and application of Boolean algebra in
switching circuits.
Graph theory:-. Introduction, Basic definition, incidence and degree, adjacency, paths and
cycles, matrix representation of graphs( directed and non-directed). Digraphs. Trees.
Mathematical Logic:
Statement Calculus- sentential connectives, Truth tables, Logical equivalence, Deduction
theorem.
Predicate Calculus- Symbolizing everyday language., validity and consequence.
Modern Algebra:
Algebraic structures, Semi group, Monoid, Group, Cyclic group, Subgroup, Normal subgroup,
Quotient group, Homomorphism of groups.
Ring, Integral domain, Field. Vector space , Linear dependence & independence . Basis &
Dimension.
Recurrence relations & Generating functions.
Reference Books:
1. Set Theory and Logic
R.R Stoll.
2. Discrete Mathematical Structures
G. S. Rao
3.Discrete Mathematics and Structures
S. Balgupta
4. Modern Algebra
5. Graph theory
S. Chand.& Co.
New age International
Laxmi Publications
Herstein
New age International
Harary
Narosa Publishing House
MA 204
Mathematics-IV
Fourth Semester ( CE & ME Branch )
L
2
1
T
0
P
C
6
Statistics :
Measures of central tendency, dispersion, moments, skewness & kurtosis.
Probability density function, distribution function, Binomial, Poisson & Normal distributions.
Curve fitting- Method of Least squares, fitting of straight line & parabola.
Correlation & Regression- determination of correlation & regression coefficients &
determination of lines of regression.
Numerical Analysis:
Finite differences, Interpolation & extrapolation. Newton’s forward & backward formulae,
Lagrange’s formula & Newton’s divided difference formula for unequal intervals.(statements &
applications of the formulae only)
Numerical differentiation & integration, Trapezoidal rule, Simpson’s 1/3rd & 3/8th rules.
Numerical solution of transcendental & algebraic equations- Method of Iteration &
Newton-Raphson method.
Solution of system of linear equations :
Gaussian elimination method, Gauss Seidal method, LU decomposition & Cholesky
decomposition.& their application in solving system of linear equations, matrix inversion by
Gauss-Jordan method .
Reference Books :
1. Numerical Mathematical Analysis James B Scarborough
2. Numerical Analysis
3. Finite Differences
B.S. Grewal
H.C. Sexena
Oxford & IBH Publishing
Khanna Publishers
S. Chand & Co.
& Numerical Analysis
4. Probability & Statistics
M.R. Spiegel
Mc Graw Hill
5. Engineering Mathematics
Bali & Iyengar
Laxmi Publications Ltd.
MA 205
Mathematics-IV
Fourth Semester ( CE & ME Branch )
L
T
P
C
2
1
0
6
Statistics :
Measures of central tendency, dispersion, moments, skewness & kurtosis.
Introduction to probability. Additive & multiplicative Laws of probability, conditional
probability, independent events. Probability density function, distribution function,
Binomial, Poisson & Normal distributions.
Curve fitting- Method of Least squares, fitting of straight line & parabola.
Correlation & Regression- determination of correlation & regression coefficients &
determination of lines of regression.
Numerical Analysis:
Finite differences, Interpolation & extrapolation. Newton’s forward & backward formulae,
Lagrange’s
formula
&
Newton’s
divided
difference
formula
for
unequal
intervals.(statements & applications of the formulae only)
Numerical differentiation & integration, Trapezoidal rule, Simpson’s 1/3rd & 3/8th rules.
Numerical solution of transcendental & algebraic equations- Method of Iteration &
Newton-Raphson method.
Solution of system of linear equations :
Gaussian elimination method with pivoting strategies , Gauss Seidal method, LU
decomposition & Cholesky
decomposition. , Band matrices & Tri-diagonal matrices. &
their application in solving system of linear equations, matrix inversion by Gauss-Jordan
method .
Reference Books :
1. Numerical Analysis
B.S. Grewal
Khanna Publishers
2. Finite Differences
H.C. Sexena
S. Chand & Co.
M.R. Spiegel
Mc Graw Hill
& Numerical Analysis
3. Probability & Statistics
MA 301
Numerical Methods &
L
T
P
C
Computations
Fifth Semester ( ET & CS Branch )
2
1
0
6
Numerical Analysis:
Finite differences, Interpolation & extrapolation. Newton’s forward & backward formulae,
Lagrange’s formula & Newton’s divided difference formula for unequal intervals.(statements &
applications of the formulae only), evaluation of functions , minimization & maximization of
functions .
Numerical differentiation & integration, Newton’s general quadrature formula, Trapezoidal rule,
Simpson’s 1/3rd & 3/8th rules.
Numerical solution of transcendental & algebraic equations:- Method of Iteration & NewtonRaphson method.
Numerical Solution of a system of linear equations :
Gaussian elimination method with pivoting strategies , Gauss-Jordan method & Gauss-Seidel
method. LU decomposition & Cholesky
decomposition.& their application in solving system of
linear equations. Matrix inversion by Gauss-Jordan method .
Numerical solution of ordinary differential equations with initial value:
Taylor’s series method , Eulers & modified Eulers method , Runge-Kutta method of 4th order.
Reference Books :
1. Numerical Mathematical Analysis James B Scarborough
2. Numerical Analysis
Oxford & IBH Publishing
B.S. Grewal
3. Finite Differences
H.C. Sexena
Khanna Publishers
S. Chand & Co.
& Numerical Analysis.
4. Engineering Mathematics
MA 441
Bali & Iyengar
Modern Algebra
Laxmi Publications Ltd.
L
T
Eighth Semester (Elective –III, Open ) 3
P
C
0
0
6
Posets & Lattices :
Partial order relations, Po-set, Lattices & Boolean algebra.
Groups :
Groups , Subgroups , Normal subgroups , Permutation group . Lagrange’s Theorem . Cyclic
groups Quotient group , Homomorphism of groups , First three isomorphism theorems . Inner
Automorphism . Normalizer / Centralizer of an element , Centre of a group . Conjugacy relation
, Class equation , Sylow’s Theorems. Subnormal & Normal series , Solvable group ,
Commutators . Nilpotent groups .Free groups.
Rings :
Ring , Integral domain , Field . Ideals & Quotient rings , Homomorphism of Rings , Maximal
Ideal , Minimal Ideal , Prime Ideal , Principal Ideal , Principal Ideal Ring / Domain (PIR / PID) ,
Euclidean Domain , Polynomial Rings. Field of quotient of an integral domain. Field extensions.
1. Modern Algebra
Surjit singh & Zameeruddin
2. Modern Algebra
I.N. Herstein
3. Modern Algebra
Khanna & Bhamri
Vikas Publishing House
New age International
Vikas Publishing House
****************************************
MA 442
Functional Analysis
Eighth Semester (Elective –III, Open)
L T
3 0
P
0
C
6
Matric Space :
Definition and Examples of metric space . Open Sphere, Open Set & Closed Set. Convergence
of sequences, Cauchy sequence, Complete Metric Spaces, Sequentially Compact Metric
Space, Continuous mappings.
Topological Space :
Definition and examples, Trivial and non-trivial topology, Cofinite topology, Usual Topology with
special reference to R. Continuity and homeomorphism.
Functional Analysis :
Linear space, subspace, basis, dimension, normed linear space, Banach space, continuous
linear transformation, Conjugate space, Inner product spaces, Hillbest space, Orthogenality,
orthonormal sets, Cauchy’s Schwartz’s inequality, Bessel’s in equality.
Linear operators, Self adjoint operator, normal and unitary operators, Projections, Spectrum of
an operator. The spectral theorem.
******************************
Reference Books:
1. Introduction to Topology and
Simmon G.F.
Tata McGraw Hill
2. Functional Analysis
B.K. Lahiri
World Press Pvt. Ltd.
3. General Topology
Lipschutz
Schaum Outline Series, McGraw
Modern Analysis
Hill Book Company.
MA 443
Mathematical Modeling
L
Eighth Semester (Elective –III, Open )
T
P
3
C
0
0
Mathematical modelling techniques, classification with simple illustration.
Mathematical modelling through ordinary differential equations.
Modelling through difference equations.
Modelling through partial differential equations.
Modelling through integral and differential - difference equations.
Modelling through calculus of variations and dynamic programming.
Modelling through mathematical programming, maximum principle and maximum entropy
principle.
***********************************************
Reference Books:
1. Mathematical Modelling
J.N. Kapur
New age International
2. Advanced Engineering
Mathematics
E. Kreyszig
New age International
3. Higher Engineering Mathematics
B.S. Grewal
Khanna Publishers
4. Operations Research, Methods
C.K. Mustafi
Wiley Eastern
and Practice
5. Numerical Methods for
Engineering Problems
N.K. Raju & K.U.
Muthu
Macmillan India
Limited
6
MA 444
Operation Research
Eighth Semester (Elective –III, Open )
L
T
P
C
3
0
0
6
Introduction to Operation Research (O.R):
Meaning of O.R. Principles of Modelling. Features and Phases of O.R.
Linear Programming:
Introduction, Formulation of Linear Programming Problems (L.P.P), Graphical solution
procedure. Idea of Convex set & convex combination of two points, Fundamental Theorem of
L.P.P. (proof not required ). Solutions of L.P.P. Simplex Method . Big-M methods.
Transportation Problems(T.P):
Introduction. Mathematical formulation. Definitions of Balanced, Unbalanced T. P. Rules to find
initial Basic feasible Solution (B.F.S) of a T.P.- North West Corner Rule, Vogel’s approximation
Method. Solution algorithm of T.P. Solution technique for unbalanced
T. P. Resolution of degeneracy. Examples.
Assignment Problems(A.P):
Introduction , Mathematical Formulation. Reduction theorem ( proof not required). Definitions of
Balanced and Unbalanced A.P. Hungarian Algorithm for solving A.P. Solution technique for
unbalanced A.P. Examples.
Sequencing Problems:
Introduction. Definition. Solution of Sequencing problems. Processing n jobs through 2
machines, 2 jobs through m machines ( Graphical method), Processing n jobs through m
machines.
Integer Programming Problems(I.P.P):
Introduction. Pure and mixed integer programming problems. Gomory’s Cutting Plane technique
for solving I.P.P. Examples.
Reference Book:
1.Operations Research
Kanti Swarup
Sultan Chand & Sons
2.Operations Research
S.D. Sharma
Khanna Publishers
3.Operations Research
J.K. Sharma
MacMillan India Ltd
4.Operations Research
Hira and Gupta
Sultan Chand & Sons
5.Operations Research
Hamady A Taha
Prentice Hall of India
6. Linear Programming
P.M.Karak
New Central Book Agency