Give me the Old Question Paper of msc Maths1 year in Nagpur University or the syllabus…

As you want to download syllabus and question papers of M.SC Maths 2nd Year Course of Nagpur University, so here I am providing syllabus:

Nagpur University M.SC Maths 2nd Year Syllabus

M. Sc. Semester-III
Compulsory Papers
Paper I :- Complex Analysis
Paper II :- Functional Analysis

Optional :- Papers (Any Three)
Paper III :- Fluid Dynamics-I
Paper IV :- General Relativity
Paper V :- Operations Research-I
Paper VI :- Algebraic Topology-I
Paper VII :- Operator Theory
Paper VIII :- Nonlinear programming
Paper IX :- MATLAB Programming

M. Sc. Semester-IV
Compulsory Papers
Paper-I :- Dynamical Systems
Paper-II :- Partial Differential Equations

Optional Papers (Any Three)
Paper III :- Fluid Mechanics-II
Paper-IV :- Cosmology
Paper V :- Operations Research-II
Paper VI :- Advanced Algebra
Paper VII :- Algebraic Topology
Paper VIII :- Banach Algebras
Paper – IX :- Computational Fluid Dynamics

Paper XI (Complex Analysis)
Unit 1:
Impossibility of ordering Complex numbers. Extended complex plane and
stereographic projection. Elementary properties and examples of analytic Functions:
Power series, analytic functions.
Unit 2:
Analytic functions as mappings, Mobius transformations. Power series
representation of analytic functions, zeros of an analytic function, index of a closed
curve.
Unit 3:
Cauchy’s theorem and integral formula, the homotopic version of cauchy’s theorem
and simple connectivity, counting zeros; the open mapping theorem, Goursat’s
theorem, Classification of singularities, residues, the argument principle.
Unit 4:
The maximum principle. Schwarz’s lemma. convex functions and Hadamards three
circles theorem. Phragmen-Lindelof theorem.

Paper XII (Functional Analysis)
Unit 1:
Normed spaces, Banach spaces, Further properties of normed spaces. Finite
dimensional normed spaces and subspaces. Compactness and finite dimension.
Bounded and continuous linear operators.
Unit 2:
Linear functionals. Normed spaces of operators. Dual spaces. Inner product space.
Hilbert space. Further properties of inner product spaces. Orthogonal complements
and direct sums. Orthonormal sets and sequences. Total orthonormal sets and
sequences.
Unit 3:
Representation of functionals on Hilbert spaces. Hilbert adjoint operators, self
adjoint, unitary and normal operators. Hahn-Banach Theorem, Hahn-Banach
Theorem for complex vector spaces and normed spaces. Reflexive spaces.
Unit 4:
Category theorem, Uniform boundedness theorem, strong and weak convergence,
Convergence of sequences of operators and functionals. Open mapping theorem,
Closed linear operators and closed graph theorem.

Paper XIII (Mathematical Methods)
Unit 1:
Fourier integral theorem. Fourier transform. Fourier cosine and sine transform. The
convolution integral. Multiple Fourier transform. Solution of partial differential
equation by means of Fourier transform.
Unit 2:
Calculations of the Laplace transform of some elementary functions. Laplace
transform of derivatives. The convolution of two functions. Inverse formula for the
Laplace transform. Solutions of ordinary differential equations by Laplace transform.
Unit 3:
Finite Fourier transform. Finite Sturm-Liouville transforms. Generalized finite Fourier
transform.
Unit 4:
Finite Hankel transform. Finite Legendre transform. Finite Mellin transform.

Nagpur University M.SC Maths 2nd Year Syllabus

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