Course Archives Theoretical Statistics and Mathematics Unit | |||||||||||||||||||||||||||||||||||||||||||||||||
Course: Analysis IV Instructor: Soumyashant Nayak Room: G23 Time: Currently offered Level: Undergraduate |
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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. Evaluation:
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[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute] |