#1
7th May 2015, 10:01 AM
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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?
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#2
17th July 2018, 08:24 AM
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Re: M Sc Maths Syllabus Shivaji University
Hii sir, I Wants to get the Syllabus of the Advanced Calculus Subject of MSc Mathematics of the Shivaji University ?
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#3
17th July 2018, 08:24 AM
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Re: M Sc Maths Syllabus Shivaji University
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 |
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