Syllabus Of Noida International University

Hi I am a new student in the Noida International University so can you please provide me the syllabus for the Master degree static’s course for the university so I can have an idea???

[shikha]

Well the University of Jammu was established in 1969 by an Act of the State Legislature which effectively split the Jammu and Kashmir University into the separate Universities of Jammu and Kashmir.


Masters Degree static’s Programme(Consisting of 4 Semesters)


FIRST SEMESTER

1. Course No. ST-406 Title : Real Analysis

Credits: 4 Maximum Marks : 100

Duration of examination : 3 hours. a)

b) Semester examination : 80 Semester assessment : 20

OBJECTIVES : This course introduces the students to concepts of Real Analysis.

Unit I: Introduction to Real number system, introduction to n-dimensional Euclidean space: Limit Points of a set-open sets, closed sets etc. (will be developed through general metric space and Rn will be considered as a special case Compact sets, Bolzano-Weirstrass theorem, Heine-Borel Theorem.

Unit II Sequences and Series of real numbers, limit superior, limit inferior and limit of a sequence their convergence, Cauchy sequence, Cauchy products.

Unit III Uniform convergence of sequences and series, Stone-Weirstrass theorem, power series, Fourier Series, Mean Value Theorem, Inverse function theorem, Implicit function theorem.

Unit IV Improper integrals of first and second kind for one variable. Uniform convergence of improper integrals, differentiation under the sign of integral-Leibnitz rule, multiple integrals and their evaluation by repeated integration.



2. Course No. ST-407 Title : Linear Algebra

Credits: 4 Maximum Marks : 100

a) Semester examination : 80

b) Semester assessment : 20

Duration of examination : 3 hours.

OBJECTIVES : This course introduces the students to concepts of Linear Algebra.

Unit I

Algebra of matrices, elementary matrices, linear transformations, row and column spaces of a matrix, rank
and inverse of a matrix, null space and nullity, partitioned matrices, Kronecker product, fields, vector
spaces, sub spaces, linear dependence and independence, basis and dimension of a vector space, finite,
dimensional vector spaces, completion theorem, examples of vector spaces over real and complex fields.

Unit II

Vector spaces with an inner product, Gram-Schmidt Orthognalization process, Hermite canonical form,
generalized inverse, Moore Penrose generalized inverse, left weak and right weak g-inverses, Idempotent
matrices, solution of matrix equations. Gauss elimination method, triangulation method, Jacobin method
and Gauss-Siedul iterative method.

Unit III

Real quadratic forms, reduction and classification of quadratic forms, index and signature, triangular
reduction of a positive definite matrix, characteristic roots and vectors, Cayley-Hamilton theorem, similar
matrices, Hermitian quadratic forms.

Unit IV

Algebraic and geometric multiplicity of a characteristic root, spectral decomposition of a real symmetric
matrices, reduction of a pair of real symmetric matrices, singular values and singular value decomposition,
vector and matrix differentiation.