Course Archives Theoretical Statistics and Mathematics Unit
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Course: Analysis IV Instructor: C R E Raja 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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Midterm
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