Course Archives    Theoretical Statistics and Mathematics Unit

Course: Analysis IV Time: Currently not offered Level: Undergraduate

Syllabus Past Exams Syllabus (Introduction to Function Spaces): Review of compact metric spaces. C([a; b]) as a complete metric space, the contraction mapping principle. Banachs contraction principle and its use in the proofs of Picars theorem, inverse and implicit function theorems. The Stone-Weierstrass theorem and Arzela-Ascoli theorem for C(X). Periodic functions, Elements of Fourier series - uniform convergence of Fourier series for well behaved functions and mean square convergence for square integrable functions. Reference Texts: 1. T.M. Apostol: Mathematical Analysis. 2. T.M.Apostol: Calculus 3. S. Dineen: Multivariate Calculus and Geometry. Top of the page Past Exams

Midterm 04.pdf 05.pdf 07.pdf 07a.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf 20.pdf 22.pdf 23.pdf Solutions 13.pdf 15.pdf 16.pdf 17.pdf Semestral 03.pdf 03a.pdf 04.pdf 07.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf 21.pdf 22.pdf 23.pdf Solutions 13.pdf 15.pdf 16.pdf 17.pdf Supplementary and Back Paper 09.pdf 10.pdf 11.pdf 12.pdf 15.pdf 17.pdf 18.pdf 19.pdf 22.pdf Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]