M Sc Maths Syllabus Shivaji University

I am doing M.Sc. Mathematics Course from Department of Mathematics - Shivaji University and looking for M.Sc. Mathematics Part - I (Sem. I) Syllabus so please inform me if it is available on official website of Shivaji University?

Hii sir, I Wants to get the Syllabus of the Advanced Calculus Subject of MSc Mathematics of the Shivaji University ?

[pooja]

Shivaji University, established in 1962, is in Kolhapur, Maharashtra, India. The university's campus is 853 acres, and is named after Chhatrapati Shivaji Maharaj, founder of the Maratha Empire

The Syllabus of the Advanced Calculus Subject of MSc Mathematics of the Shivaji University is given below

Advanced Calculus


Unit 1 : Sequences of functions: Pointwise convergence of sequaences of functions,
Examples of sequences of real valued functions, Definition of uniform
convergence, Uniform convergence and continuity, Cauchy condition for
uniform convergence, Uniform convergence and Riemann integration, Uniform
convergence and differentiation, double sequence uniform convergence and
double sequences, mean convergence.

Unit 2 Series of functions: Rearrangement of series, subseries, double series,
Rearrangement theorem for double series, Multiplication of series, Power series,
multiplication of power series, substitution theorem, reciprocal of power series,
Real power series, The Taylor series generated by function, Bernstein's theorem,
Binomial series, Abel's limit theorem, Taubers theorem.

Unit 3 Multivariable differential Calculus: The Directional derivatives, directional
derivatives and continuity, total derivative, total derivatives expressed in terms of
partial derivatives, The matrix of linear function, Jacobin matrix, Chain rule,
mean value theorem for differentiable functions, A sufficient condition for
differentiability, sufficient condition for equality of mixed partial derivatives,
Taylors formula for functions from Rn to R1

. The inverse function theorem
(Statement only) The implicit function theorem (Statement only) and their
applications. Extrema of real valued functions of one variable, Extrema of real
valued functions of several variables.

Unit 4 Path and line integrals, Multiple integrals Double integral (Theorems without
proof) Application to area and volume.( Theorems without proof )Greens theorem
in the plane. Application of Green's Theorem.Change of variables, special cases
of transformation formula.Surface integral, change of parametric representation.
Other notations for surface integrals, stokes Theorem Curl and divergence of a
Vector field. Gauss divergence Theorem.


Contact Details :
Shivaji University
Address: Vidyanagar, Kolhapur, Maharashtra 416004