MSC Maths in NIT Warangal

I am a student of NIT Warangal please give here Scheme for M. Sc. (Applied Mathematics) course of the institute ?

[Kiran Chandar]

As you want I am here giving you Scheme for M. Sc. (Applied Mathematics) course of NIT Warangal .

Scheme for M. Sc. (Applied Mathematics) course:

I – Semester:
C & Data Structures
Discrete Mathematics
Linear Algebra
Numerical Analysis
Ordinary Differential Equations
Programming Laboratory
Real Analysis

II Semester:
Complex Analysis
Computing Laboratory
Integral & Discrete Transforms
Mechanics
Probability & Statistics
rPatial Differential Equations
Seminar
Topology

III Semester
Fluid Dynamics
Functional Analysis
Mathematical Programming
Mathematical Programming Lab.
Numerical Solution of Diff. Eqns.

Electives:
Methods of Applied Maths (or)
Mathematical Modelling (or)
Dynamical Systems

Seminar

MSC (Applied Math): Scheme of course


MA 501 – Real Analysis (Common to both the streams)

Basic Topology, finite, contable and uncountable sets - metric spaces - compact sets - perfect sets - connected sets.

Riemann Stieltje’s integral : Definition and existence of the integral - Properties of the integral - integration and differentiation of integral with variable limits.

Improper integrals : Definitions and their convergence - Tests of convergence, b and G functions.

Uniform convergence : Tests for uniform convergence - theorems on limit and continuity of sum functions - term by term differentiation and integration of series of functions.

Power series, convergence and their properties.

Fourier series : Dirichlets’ conditions - existence - problems - half range sine and cosine series.

Scope as in : Walter Rudin, Principles of Mathematical Analysis, McGraw Hill Book Co.



MA 502 – Discrete Mathematics (Common to both the streams)

Sets and propositions : Combinations of sets, Finite and Infinite sets, uncountably infinite sets, principle of inclusion and exclusion, mathematical induction. Propositions, fundamentals of logic, first order logic, ordered sets.

Permutations, combinations, numeric functions, generating functions.

Recurrence relations and recursive algorithms : recurrence relations, linear recurrence relations with constant coefficients, homogeneous solutions, particular solutions, total solutions, solution by the method of generating functions, sorting algorithm.

Relations and functions : properties of binary relations, equivalence relations and partitions, partial and total ordering relations, Transitive closure and Warshal’s algorithm.

Boolean algebra : Chains, Lattices and algebraic systems, principle of duality, basic properties of algebraic systems, distributive and complemented lattices, boolean lattices and algebras, uniqueness of finite boolean algebras, boolean expressions and functions.

Graphs and planar graphs : Basic terminology, multigraphs and weighted graphs, paths and circuits, shortest paths in weighted graphs, Eulerian paths and circuits, Hamiltonian paths and circuits. Colourable graphs, Chromatic numbers, Five colour theorem and Four colour problem.

Trees and cut-sets : trees, rooted trees, path lengths in rooted trees, spanning trees and BFS & DFS algorithms, minimum spanning trees and Prims & Kruskal’s algorithms.

Scope as in : C.L.LIU : Elements of Discrete Mathematics, McGraw Hill.

Reference Books : Tremblay and Manohar : Discrete Mathematical Structures with applications to Computer Science, McGraw Hill Book Co., New Delhi

Mott, Kandel and Baker : Discrete Mathematics for Computer
Scientists.


MA 503 – Linear Algebra (Common to both the streams)

Systems of linear equations - matrices and elementary row operations - uniqueness of echelon forms - Moore-Penrose Generalised inverse.

Vector spaces - subspaces - bases and dimension - coordinates - linear transformations and its algebra and representation by matrices - algebra of polynomials - determinant functions - permutation and uniqueness of determinants - additional properties - elementary canonical forms-characteristic values and vectors - Cayley Hamilton’s theorem - annihilating polynomial - invariant subspaces. Simultaneous triangularisation - simultaneous diagonalisation - Jordan form - inner product spaces - unitary and normal operators - bilinear forms.

Scope as in : Hoffman and Kunze : Linear Algebra, Prentice Hall of India, New Delhi

Reference Books : V. Krishnamoorthy et al : An introduction to linear algebra, Affiliated East West Press, New Delhi

P.G. Bhattacharya, S.K. Jain and S.R. Nagpaul : First course in Linear Algebra, Wiley Eastern Ltd., New Delhi, K.B.Datta : Matrix and Linear Algebra, Prentice Hall of India, New Delhi



MA 504 – Ordinary Differential Equations (Common to both the streams)

First order differential equations - linear differential equations of higher order - linear dependence and Wronskian - Basic theory for linear equations - method of variation of parameters - linear equations with variable coefficients.

Solution in power series - Legendre and Bessel equations - systems of differential equations - existence and uniqueness theorems - fundamental matrix - non-homogeneous linear systems - linear systems with constant coefficients and periodic coefficients - existence and uniqueness of solutions - Gronwall inequality - successive approximation - Picard’s theorem - nonuniqueness of solutions - continuous dependence on initial conditions - existence of solutions in the large.

Scope as in : S.G.Deo and V. Raghavendra: Ordinary differential equations, Tata McGraw Hill Pub. Co., New Delhi

Reference Books : M. Rama Mohana Rao : Ordinary differential equations - Theory and applications. Affiliated East West Press, New Delhi

E.A.Coddington : Introduction to Ordinary differential equations, Prentice Hall.


MA 505 – C & Data Structures (Common to both the streams)

C-language : Introduction, types, operators and expressions, control structures, functions, header files, scope rules, pointers and arrays, address arithmetic, command line arguments, structures - struct, union and typedef, input and output.

Stacks and Queues : Introduction, information hiding, specification and implementing of stacks and queues, Linked stacks and queues

Recursion: The principle of recursion and recursion algorithms, Examples of recursion

Lists : Specification and implementation of lists, singly linked and doubly linked lists, circular lists.

Searching and Sorting : Sequentail search, Binary search, Hashing, Selection sort, interchange sort, Shell sort, Insertion sort, quick sort, merge sort, radix sort, Address calculation sort.

Scope as in : Lipschitz (Scaum’s Series) : Programming in C

Horowitz and Sahni : Fundamentals of Data Structures., Tennenbam : Data Structures using C



MA 506 – Numerical Analysis (Common to both the streams)

Interpolation : Existence, Uniqueness of interpolating polynomial, error of interpolation - unequally spaced data; Lagrange’s, Newton’s divided difference formulae. Equally spaced data : finite difference operators and their properties, Gauss’s forward and backward formulae - Inverse interpolation - Hermite interpolation.

Differentiation : Finite difference approximations for first and second order derivatives.

Integration : Newton-cotes closed type methods; particular cases, error terms - Newton cotes open type methods - Romberg integration, Gaussian quadrature; Legendre, Chebyshev formulae.

Solution of nonlinear and transcendental equations : Regula-Falsi, Newton-Raphson method, Chebyshev’s, method, Muller’s method, Birge-Vita method, solution of system of nonlinear equations.

Approximation :Norms, Least square (using monomials and orthogonal polynomials), uniform and Chebyshev approximations

Solution of linear algebraic system of equations: LU Decomposition, Gauss-Seidal methods; solution of tridiagonal system. Ill conditioned equations.

Eigen values and eigen vectors : Power and Jacobi methods.

Solution of Ordinary differential equations: Initial value problems: Single step methods; Taylor’s, Euler’s, Runge-Kutta methods, error analysis; Multi-step methods: Adam-Bashforth, Nystorm’s, Adams- Moulton methods, Milne’s predictor-corrector methods. System of IVP’s and higher order IVP’s.

Scope as in : Jain, Iyengar and Jain : Numerical Methods for Engineers and Scientists, Wiley Eastern

Reference Books : Gerald and Wheatley : Applied Numerical Analysis, Addison-Wesley.

Aitkinson : Numerical Analysis, John Wiley and Sons.



MA 507 – Programming Laboratory (Common to both the streams)

Simple programs in C languages using pointers, pointers to arrays functions., String manipulation, File processing, [Creation, addition, deletion display and counting the No. of nodes of linear, Doubly and circular linked lists], Program to implement Stacks and Queues, application of stacks to evaluation of postfix expression, conversion of infix to post fix expression, Programs on Recursion, Programs for Searching [sequential and Binary search]

Programs for sorting [selection sort, bubble sort, Insertion sort, merge sort, shell sort, Radix sort].

Here is the attachment.


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NIT Warangal Stadium
Off Warangal-Hyderabad Highway
National Institute of Technology Campus
Warangal, Telangana 506004